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This is a hand-edited transcription produced from Scans by Bayerische Staatsbibliothek using OCRmyPDF and translated with GPT4 via ChatGPT

Nobility of the sword, its splendor is expressed in three books, according to science, art, and experience.

Second Book

PROLOGUE TO THE READER.

IF sciences acquire nobility by their antiquity, none should be preferred over that of Arms, given that even before the creation of the World there was war in Heaven between good and evil Angels: if by utility, none has been found so far from which more fruit can be derived than from Arms, considering that with them Cities, Kingdoms, Provinces, and Monarchies are won: if by deeds, none will find more heroic actions than among the Military factions: if by objective, they will take the palm, because being peace the end of war, there is nothing more to desire on earth, according to the Angel’s Canticle: Gloria in excelsis Deo, & on earth peace to men of good will. If by necessity, God Himself will deliver the verdict in favor of Arms, His Divine Wisdom wanting no other more effective means than war to conserve and maintain the Universe in its being. The Elements, battling among themselves, make and unmake everything found in the visible and most hidden aspects of nature. The most accepted opinion among Philosophers is that there are four, but the fight is recognized only between two, which are Fire and Water, with the other two (Air and Earth) serving as either battlefields or intermediaries between these two combatants. The Arms with which they fight are the first four qualities, which are heat, dryness, coldness, and humidity: the first two belong to Fire, and the other two to Water.

The governance of this militia was committed to the two Luminaries Sun and Moon: the Sun corresponds to the Element of Fire, and the Moon to that of Water. The Sun has Mars himself as its General Captain, and the Moon has the Planet Venus as a companion or associate. Jupiter, whose name is derived from the verb Iuvare, which means to help, presides over the Element of Air, has heat and humidity as Arms: with heat it assists Fire, and with humidity it favors Water. Saturn, who rules over the Earth, has orders not to take the side of any of these two combatants; its Arms are coldness and dryness: with coldness it opposes the heat of Fire, and with dryness the humidity of the Waters. Mercury has no designated Arms, and thus on any occasion takes them in favor of the Planet with whom it is found.

Some inequality seems to lie between these two battlefields; because the Sun and Mars, which predominate over Fire, are much greater and more powerful than the Moon and Venus, which are in charge of the Waters: but the supreme Artisan and Military Architect, knowing that in this inferior world there were to be many wars, battles, and conflicts, wanted from the beginning to give us documents of this science, showing us how the weaker ones must deal with the strongest.

The Divine Providence made in favor of Water, as inferior in strength, a grand fortification, with which surrounding the whole Earth, it defends the Waters from the Arms of the Sun, which are its rays. This fortification is situated in the middle Region of the Air, its walls are crystalline, but so cold, that they not only resist the Arms of the Sun, but also prevent the hot exhalations, which rise from the Earth, from passing to the supreme Region of the Air, where they want to ascend to become Comets, and there like rebels reveal themselves, and in company of it or under the banners of the Sun, wage war on their natural lord, which is the Earth from where they ascended, and also on the waters. At certain times some manage to breach the walls; but as they are rare, they don’t take long to die, like traitors, at the hand of the very fire, from whom they thought they were sheltered. Those that remain prisoners, and cannot ascend, are also punished for their disobedience; because just as on Earth offenders are condemned to the Galleys, to row the Armadas to where the Prince needs to wage war; so also up there these exhalations (which are called winds) are condemned to carry through the Airs the Squadrons of clouds to different parts of the World, where, turned into water, they can fight until they destroy or defeat their enemy. It also happens sometimes that these exhalations (either because the opposites press them too hard, or because they feel very strong) tend to resist, which results in great tumults, until they discharge their artillery, firing rays against Heaven, and against Earth; but in the end they are forced to calm down, and return again to the Earth, turned into water, stone, or ash.

All of this is permitted by the Air in its jurisdiction, because as it is neutral, and positioned between two powerful princes, it requires great diplomacy for its preservation; and so, while it gives transit and lodging to the rays of the Sun, it also recognizes, for its own interests and for its own preservation, the necessity to admit that fortification in the middle of its region, in favor of the waters.

Saturn doesn’t seem any less attentive to politics than its neighboring or adjacent Jupiter, because while it hosts the waters in its caves and trenches, as seen in the Seas, Lakes, Rivers, Ponds, etc. that are found in all parts of the Earth; also, in order not to appear suspicious, and not to seem wholly united with the waters, it allows Fire to have its Castles, or guard bodies, in different volcanoes that are scattered around the World, which for the most part are near the waters, or in the midst of them, like for example, Mount Etna in Sicily, Hecla in Iceland, Vesuvius near Naples, another in Java, in the Bandas, Moluccas, Philippines, Sumatra, Mauritius, and in Japan, etc. And if it sometimes allows the Fire to mine the waters, as happened in 1638 when a volcano erupted two leagues away from the Sea in the Island of St. Michael in the Azores; it also allows the Water to counter-mine through subterranean conduits, to thwart the designs of its enemy, which are to seize everything, and convert it under its empire and dominion.

Everything of greater importance in the warfare that is practiced today, and has been practiced among men for over six thousand years, is found worked out and executed between these two valiant combatants. The two main things that this science looks to are, above all things, self-defense, and then offense against the adversary or enemy: to defense belong the fortifications of the Cities and Castles, etc. To the offense pertains Artillery, and other types of Arms.

The main of these Weapons, to which the others are subordinate, are fortification and Artillery. The fortification (which is the first) we know through Philosophical discourses and a posteriori, exists (even though it is invisible) in the middle of the Air region, by whose means not only are the things referred to regarding the rays of the Sun and the exhalations that rise from the earth achieved; but also the vapors that rise from the Water are kept captive, which not finding a clear passage, are forced to return to the earth made into water, snow, hail, fog, frost, or dew.

The other, pertaining to the Artillery and all the fire weapons, we see is nothing more than an imitation of what the Elements do, when with thunder, lightning, or flashes they get to fight or combat that fortress that is in the middle region of the Air.

The three military actions to which all the others of an Army refer, are marching, encamping, and fighting. Marching can be through friendly or enemy territory; and whatever the type, order is always necessary above all. Encamping can be in open or flat terrain; and this can be far from or within sight of the enemy; but however it may be, the general maxim is that it should be done in such a way that the camp is secure on all sides, and all occasions for advantages that the enemy can take advantage of are taken away. The third, which is Fighting, is the action of greatest weight and consideration, and to which the others of an Army are directed; and in order for it to be done correctly, it is necessary to have great knowledge, not only of the number and forces of the Squadrons and Battalions that it comprises; but also of those of the enemy, along with all the advantages, which can be used, regarding the number and quality, both of the people and the Weapons, and the terrain: and as these are difficult things to achieve, much prudence and experience are necessary for their success.

What concerns us now (for the confirmation of what we have said about those celestial and valiant champions) will be to examine whether in their form, or military policy, they observe these maxims, so necessary in the lower wars and battles; and looking at all of them carefully, we will not only find these three rules practiced; but also many others that we cannot reach: because just as the Weapons on Earth are called: Vltima ratio Regum (the last resort of kings), so are those of the King of Kings; and the supreme providence does not wish to reveal such high and mysterious secrets, such as those enclosed in the noble science of Arms, so as not to give occasion to men to be adored as Gods of the Earth, through too much power, as Alexander did, etc.

The first action, which is to march, is found among the Sun and the Moon, along with the rest of the Army of Stars (which is why in the phrase of Scripture it is called Militia). This is observed with such order and harmony that, so far, none of them has changed or altered a point in the form with which they began their first movements, both natural and violent or accidental, observing within themselves a certain contrariety and opposition, because at the time that they are all carried with the movement of the First Mobile from East to West, each one of them fights and strives to move to the opposite side, which is from West to East, and from South to North, or from North to South.

The second action, which is to lodge or quarter, is observed among the planets with such precision, that in no way their positions could be improved: thus it is said that when the stars fought against Sisera, they held their positions. For a better judgement, the curious reader may consider the four hypotheses that have been most accepted among the most illustrious philosophers and mathematicians of these times and those of the past. The first is from Ptolemy, the second was originally from Aristarchus, and now newly revived by Nicolaus Copernicus. The third is from Tycho Brahe, and the fourth is from Martianus Capella.

In the first one (which has been well received for many centuries among the most learned), we see the Earth, which along with the water, make a globe, which being in the middle, comes to be surrounded by all those famous combatants: everything around is surrounded by the element of the Air, in whose middle region is that fortification (of which we speak) represented by the sign of the clouds: and after the supreme region of the Air, the region of Fire follows; and whether this element is found next to the concavity of the Moon, or that according to the opinion of some, there is no more Element of Fire than the Sun itself: whatever the case may be, we see that the Moon (whose charge is to defend the waters) occupies its due place, which is to be immediately next to the Elemental Region, and the closest to the waters, so that none of the others can hinder the aid that it needs to send at all times to its camp. It has Venus very close, from whom it can receive help, for being both of the same nature, although Mercury is in between in the second Heaven, it has no strength to obstruct the communication of these two planets. In the fourth Heaven the Sun has its Royal Tent, and immediately next to it, is the Field of Mars, which occupies this position, to make it understood to the kings, that in order to preserve the Majesty, the observance of the laws, and the reputation, both among their subjects and vassals, and among strangers, it is necessary to have the Arms very ready and very handy, to use them on any occasion that may arise: with the caveat, that if they fail, it will certainly lack any of these three things, and with them the Monarchy. Jupiter is placed very wisely in the sixth place, between Saturn and Mars, to prevent the communication of these two enemies of human nature: because if they came together, although the coldness of Saturn could temper the heat of Mars, on the other hand, combining the dryness of both with that of the Sun, they would quickly dry up the radical moisture of all things, making the construction of the Universe vain or imperfect. It can also be noted that, just as the Air in the elemental Region occupies the place that is between Fire and Earth, and separates these two Elements, so that united they do not consume that of Water, Jupiter’s position in the ethereal or celestial Region is very appropriate, to achieve the same effect.

The second one, which is from Copernicus (although arranged with grand harmony), for contradicting the sacred Scripture, is not accepted among Catholics. The other two, which assume the Earth to be immobile, are considered more adjusted. Here it should be noted that Venus is between the Sun and Mars, to temper the heat and dryness of both, with its coldness and moisture; and Jupiter, as in Ptolemy’s, is lodged between Saturn and Mars, to temper the dryness of both. There is much to say about this beautiful circumvolution, in which the Moon always keeps its place next to the Elemental Region; but as our intention is only to point out these mysteries, we will leave the discourse of this matter to astronomers and philosophers, and move on to the third action, which has no less to understand than the first and second.

The third and final action, which is to Fight, is so high and so arduous, that for it one could say: This is the work, this is the task. It is such a hidden and recondite matter that we can hardly discourse on it. We know well that there is a war between the Elements and Planets; but the way they have to wage it is not easy to know or perceive: it is a very accepted opinion among philosophers that the Sun, with its rays, which God has given him for weapons, hence poets call them arrows, fighting generates gold in the bowels of the earth; but no one will dare to describe the form of his work. The same is done by the Moon, and the other Planets, not only with metals, but also with everything that is enclosed under the animal, vegetable, and mineral, each one striving to create people of their faction, favor those of their partiality, and offend the opposite. We have examples of this truth in many things that have sympathy or antipathy with others, such as the magnet stone with the poles of the world, and with steel; the quicksilver with gold, rhubarb with bile, etc.

Some particularities, about this work or fight, have been observed and traced by the Judicial astrologers, having found by experience, that due to different positions that they acquire in relation to each Horizon, they act with more force, in regard to their own movements, as to being slow, fast, direct, retrograde, or stationary, for being or aspecting in their houses, exaltations, triplicities, and terms, and they are found weak in their detriments, and falls: the Sun is found exalted in the sign of Aries, which is the house of Mars, its General Captain; and the Moon in Taurus, which is the house of Venus, its assistant. The Planets also have strength when they are in conjunction, or benevolent aspects with those of their faction, and the good ones receive detriment when they are surrounded by the unfortunate, and thus acquire strength, or weakness, with respect to being in the Apogees or Perigees, both of their Eccentrics and their Epicycles.

The planets have many other passions and ways of acting, the effects of which are better known to those who study this science professionally; but the effects caused by the two Luminaries with their encounters or aspects are known to everyone in general, especially the effects that the Moon causes in all the sick, forcing the humors to also fight each other, which is what they call a crisis; and this occurs when the Moon reaches the square aspect or opposition to the place where it was at the beginning of the bedrest. This truth is also clearly seen in the conjunctions that the Sun makes with the Moon, and the other square aspects and oppositions, which is what we call the New Moon, the first quarter, or the last quarter, and the Full Moon: and above all in the tides, having such jurisdiction, and sympathy with the waters, that it forces them to leave their center to pass muster, or to render vassalage; and this twice each day, once in the presence of the same Moon, and the other in the presence of its lieutenant, which is its opposite point: on the other hand, it seems that they would want to go to favor the Moon, because when they see it in conjunction with the Sun, then they make their greatest effort, which is what we call spring tides, because they rise more than other times, because they judge it in that occasion in greater trouble. There is an opinion among astrologers that the great conjunctions of Jupiter and Saturn (which is when passing from the triplicity of Fire to the triplicity of Water) cause very great alterations in the World, transporting Monarchies or Empires from one region or house to another: they always occur in a space of 794 years, and eight of them have passed since the creation of the World until now, according to the most received count. From here we have to ponder that these changes, and great alterations, are only made when these Planets pass from the field of Fire to that of Water; because although they make their minor conjunctions in a space of twenty years, a little less, and the media in 198.5: in this known change of triplicity, as it is not of the opposite party, they are not felt in the World as many novelties as in those that are made in the Signs of opposite nature, and subjects to these two combatants, or someone of their jurisdiction. Not only do the effects of this war or strife feel the winds, Seas, minerals, vegetables, humors, and Monarchies; but also in the things of greater taste has its domain the contradiction; because in music we see, that fighting the low with the high, never is felt greater sweetness, than how much the voices proceed with contrary movement; and in what is heard of greater harmony, which are the clauses, it has been found by experience, that for the ear to reach to taste of the consonance, which they call False among the Musicians. From here the opinion of the great Homer is proved, that removed the contention, the beauty of the Universe is removed.

All of this discourse was not necessary to persuade the greatness and excellence of this science; because as the Divine Majesty has created man in His image and likeness, and is all-powerful, everyone is inclined to command and power; and as there is no sovereign command without Arms, the argument is evident; hence it follows that everyone universally shows signs of this impulse and inclination towards Arms.

And I confess that I have been greatly affected by this inclination or generous effect, even before I had the use of reason, which has continued in me in such a way that in the midst of my greatest occupations, I have never ceased to seek all possible means to attain some knowledge of this science; and so I have judged that before aspiring to know how to have a large or small number of fighters, with another equal, greater, or smaller; it was necessary to know how each one, or in particular, is to have with another of his equal, greater, or smaller.

Having established this, I tried to arrange the means to achieve it, which are good teachers, seeking the best, and the most reputable of my time, and after them, all those I judged advanced in the knowledge of this subject. I made my understanding participate in the exercise of the body, with the reading of the best Authors, which has been the Commander Don Geronimo Sanchez de Carranza, and Don Luis Pacheco de Narvaez, very notable in this profession, through which I wanted to put the idea of a fortification, to help somewhat the enthusiasts of this science, judging that it will not be of little fruit, and utility for those who want to avail themselves of it: although it seems that these Authors have put the seal, and that plus ultra cannot be found; however considering that there is still room for opinions, both in Spain and abroad, works to perfection that is required. The cause of this, as I have observed and carefully considered, arises from not having treated them with the method that is required to cause evidence, because instead of treating it like a mathematical science, to which this science is subaltern, it has been treated with philosophical terms, which without mathematical demonstrations, rather serve confusion than clarity; this is evident, because just as in all of Europe, Asia, Africa, and America, the method of the rules of military science is observed, observing in all parts of Spain, France, Italy, Germany, Flanders, and England, the same form of fortifying, and besieging places, as well as fighting in the field with the Armies; it follows that if in the Skill of Arms (which is a part of military science) they had recognized some universal propositions, or maxims superior to the others, they would also have admitted them all, as they have done the ones of the militia, because it is natural to all, to seek what is known to be good: and since this has not been done, it is an indication that it has not been known until now, in what consists the Science, and Skill of the Sword, to which by excellence the use has given, that passes the plaza of law, the name of Arms in general, either because it is the foundation of all the militia, or because it virtually encloses the contemplation of the highest mysteries of a science, by means of which Kingdoms are preserved, and Monarchies are expanded.

What we must seek now is the remedy for this inconvenience, and do so, that assuming that the skill of Arms belongs to the name of science (like that of which it is subaltern, which like it is received by all parts where its news arrives) is the course we must follow, that to put into practice the science of Arms, it must be having consideration to its two main parts, which are defense, and offense.

The offense in our Skill must be with the Sword; but the defense that could accompany it, seems it should be the buckler or round shield; but as our intention is to deal first with the Sword alone, and not accompanied, it seems that what is intended cannot be achieved, given that one of the main parts on which this science is based, which is the defense, will be missing. Although it has a hilt that represents a small shield or buckler, it is not enough to cover the entire body: so this science may have some imperfection.

But as the Creator, who has made all things with such harmony, forming all animals, and given some offensive weapons, others defensive, and others both offensive and defensive, made man superior to all; it was evident that he was not going to deny him what he had granted to his subjects. His Divine providence gave man, along with the rational soul, not only the invention of offensive and defensive weapons; but also the faculty to form defensive ones from the very offensive: this will be evident in our doctrine, because we will show in its place, that the skilled fencer with his Sword, can form a shield for his defense, as large as the Romans used in their military; and because this defense must be invisible, this makes it even more mysterious.

The commitment is great, but this is the subject of the work, in which I hope to perform; and I confess that if this could not be achieved, then neither would a science as necessary as that upon which the preservation of life, honor, and property of men depends, and upon which the practice of a thing, from which all the utilities and greatness that can be known, are followed, and we express with individuality in these writings.

The method we follow seems appropriate to the subject, because just as mathematicians and cosmographers, when they have wanted to deal with the structure of the Universe, in order to do so with more utility and ease, have imagined and formed bodies that have resemblance and connection to the matter they have wanted to deal with (like spheres, and celestial and terrestrial globes) and in gnomonics or perspective, they have formed pyramids, or cones, to represent to the sight the ideas of those which being invisible, are caused by the air of objects, and visual rays; we too, having to deal with offense and defense, have judged it convenient, and even necessary, to use something material, such as a shield and fortification, so that through these two things the idea of what we really need to do for our defense can be formed, adhering in this to the opinion and sentence of Aristotle, who says: Nothing is in the intellect that was not first in the senses.

Assuming that in everything we must observe the order that mathematicians follow in their demonstrations, which is to use lines when they cannot use bodies, we will represent with them the form of our Castle, always adhering to the universal maxims that are observed in the fortification of the Places, which is to proportion them, not only to the people who are to be in them; but also to the number of enemies, and to the effect of the Weapons with which they could be attacked. Since our intention is that this Castle is only for the defense of the Skilled, and that his adversary with a Sword alone is the one who must attack him, we will try to proportion it in its place.

INTRODUCTION

TO THE ART OF THE SWORD.

The first book of this work dealt with the speculative part, which is Science, as a proper action of the understanding, and discourse, through which the rational soul exercises its powers; for this reason, the ancient Greeks touched upon and taught the three radical principles, from whom Celio Rhodignio sagaciously compiled the three means, which perfect perfect knowledge, and he called them cognitive powers. The first defined the Science of the mind. The second, Art of the cogitative power. The third, Experience, or consummate opinion; for just as reason discovers and manifests what opinion holds within itself, so the experience of the things that are subject to it, requires less reason and discourse. From this it follows that there is a certain mode of knowledge, which is an active portion of natural science, and to this the Ancients called it Magic, which taken the meaning of the term in a good part, is wisdom, and perfect knowledge of natural things, through the application of agents and patients: from which naturally produced admirable effects, investigated and achieved by the operation of the mind, which is intellectual, and what is known by it is science, the first cognitive power. From this the first Book was formed, to instruct the true Right-handed in the science of the Sword Instrument, with such knowledge and perfect understanding, that by the mutual application of agents and patients, admirable effects naturally result in defense and offense; as seen in what in common language is named Skill, if this is achieved by its true causes, and application of Agents and Patients, according to the cognitive powers compiled by Celio.

In this second Book includes the second Power, which is Art; and this is proper to the cogitative power, where human discourse and thought pass from speculation to practice, by means of the cogitative power, reduced to Art by precepts and rules, deriving from one Being to another, until it finds that which is capable of evident demonstration. As Pedro Gregorio taught, using the doctrine of Marcus Julius Cicero: Nothing is as sweet as knowledge in everything. And as this is not opposed to the condition of human nature (as the Philosopher limited) so that we do not transcend the limits of human science in inquiry, seek the particular precepts, which in a certain way are mutually distinct from each other: concluding, that there can be a unique general Art that communicates them. And I persuade myself (he says) that it is possible, if due attention is given, in all things; for there is always a genre, in which all species participate, and agree, although they differ in some properties. And consequently, it will sufficiently be clear, that once the genre is fully known, the notion of species easily offers itself in the specific, not unlike in a River the section of rapids, and divisions are known, if the radical Source, which is mother of its currents, is followed. From which it is not inconvenient, nor impossible, that a unique instrument is found, that perfects the diverse works, in the diverse Arts, whose use causes diverse conveniences. These are the words of Pedro Gregorio, which the curious can see expanded in its original.

The specific doctrine of this Art of the Sword, in which, without exceeding the limits of inquiry, particular precepts have been sought, which, while in a certain way mutual among themselves, are also diverse, perfecting this Art in such a way that its rules and precepts are communicated, always finding a primary genre, where the species participate and agree, even if they differ in some properties; as in the genre Wound, or Trick, from where, as from a radical source, just like in a River, the other rapids and specific divisions pour out and emerge, if by the mother it is traced back to its principle, it is easily led to the most general genre Wound, or Trick, which is the radical source. By this method and doctrine for defense and offense in man, such an instrument has been found, with which the diverse works of this Art are perfected: with such operation, that by the mutual application of Agents and Patients, admirable effects naturally result, because all Art imitates nature.

Therefore Celio explained that in the nature of things, the regime is in two modes: one universal, the other particular: and exemplifies them in God, to demonstrate them in man, the Lesser world. For just as in the universal corporeal creature (which is the Greater world) the Spiritual Virtues are all subject to the Supreme Governance; in the same way the bodily members and the animal virtues are ruled by reason, which is the Master, which is in man in proportion, like God in the world; and by the true resemblance of this regime, reason can level and discourse with thought, from where human knowledge through the cogitative Power, is considered natural, or rational, as Pedro Gregorio noted.

Natural knowledge is that which all sensitive Animals partake of; and this is called Instinct, perceived, either by innate native force, or by the sensual organs. If it is by innate native force, it leads every Animal to a kind of notion of what is contrary to it, or useful to it: and this notion, as sensual, is also perceived by the senses, and the objects that participate with them, such as hearing, sight, taste, smell, and touch. In this way is defense and offense, in one who is totally ignorant of the precepts and rules of this Art, acting purely by natural knowledge of contraries or useful things, rudely perceived by the notion shared by the bodily senses.

Rational knowledge is that which is proper to man, perceived by different means; because it is either native, or adjunct, or proper intellectual force, perceived in the animal essence, as by discourse, and action of reason, by observation, or experience of the entities of causes, and of acts, constituted in rules, and precepts in such a way, that it results in Art.

Pedro Gregorio noted ten rational degrees, which are generally beneficial in all Arts, and especially in this one of the Sword. The first, is constituted in what is to be known, which, when inquired, is exterior Matter, in which the form is recognized by the subject, and the object, in relation to the cognizant. The second, is through the Organs of the senses, according to their application, and not the contrary; just as light is perceived by sight, which in darkness is ignored, etc. The third, by the Organic Perfection of the same senses, well or badly disposed; since the short, or imperfect in sight, or in hearing, etc., does not perceive the true knowledge of external things as they are, but according to the more or less perfect capacity of the senses, which are the instrumental means of perceiving. Fourth, by the inner Sense, to whom the exterior senses join, if there is no impediment, or passion that prevents the exterior senses from communicating to the inner sense, as to a common recipient, from where that faculty to transfer to the rational, the knowledge acquired by the senses, are called common faculty, and in it begins to work the animal force. Fifth, for that Power, which the Greek Philosophers named Phantasy, where the imaginations of things comprehended by inner sense are conceived; for this reason, those perfections of Phantasy are called intellectual, for the intellectual mode of its formation in the inner sense, because the incorporeal concepts do not have the real dimensions of the bodies; of which, what is perceived in the Phantasy are simulacra. Sixth, by the Estimative called inferior Judgment, where the previous comprehensions are judged, and what they are simpliciter, before the discourse, or reasoning make the distinctions: and in this degree of knowledge, only the prestige of Animals ascends, without going any further. Seventh, by the Cogitative, in that species that the Greeks call Dianoia, the Latins superior Judgment; in which the comprehended images (for the examination) in judgment, are transferred to discourse: and in this way, due to the variety of simulacra, and the very summary communication, or comparison of things, various opinions arise. Eighth, by Reason, or ordered consultation, that from many different things, those that make up a concept are chosen and joined. Ninth, by the Understanding, where the true determination is made, after reasoning; finding quietude the cogitation of the mind, and undoubted science: and this is named acquired intellection, distinct from the infused. Tenth degree results, from all the nine previous, and common ones, by which the notion passes to the understanding, and is instituted in the Memory, which is the receptacle of images, and of knowledge, and of reasons acquired in the understanding, which also finds quietude there, without agitation, or conflict of the Weapon: because from the concurrences it perceives the legitimate organization through Art. And of these ten degrees of knowledge is Ancephaleosis 1. the Object, 2. Sensible organization, 3. Prepared organization, 4. Common sense, 5. Phantasy, 6. Estimation, 7. Cogitation, 8. Reason, or Consultation, 9. Understanding, and 10. Memory, as Pedro Gregorio noted.

Through all these degrees, perfect knowledge is achieved in this Art, producing four beings.

1 This is what philosophers consider a Natural Being, because it is innate to nature itself: and through the understanding and knowledge of humans, a natural apprehensive concept is perceived, which is qualified as a first notion, or first rational concept, as in this Art, where by natural being, without passing to the last degrees of reasoning, a natural being is perceived, enough to form a concept, or knowledge, that by artfully wielding the Sword, one can achieve self-defense, and offense to the opponent.

2 But as this crude simple knowledge, acquired by the formation of a natural being, is not enough, one moves to another Being that they call of reason, which is the second notion in the fifth, sixth, seventh, and eighth degrees, until the mind is suspended, reasoning in some verisimilar concept, which is pure being of reason.

3 As this is still imperfect to demonstrate with undoubted certainty, the understanding does not rest, because it remains in Phantasy, Estimation, Cogitation, and Consultation: so for a more perfect form, it moves to the Real Being, in which the understanding finds rest, without fluctuating the other Powers of the Soul in the concept, according to science.

4 Even this is not sufficient for indisputable demonstration, because it is only acquired in memory, as a receptacle for the preceding degrees; resulting in what they call a Mathematical Being, demonstrable, and infallible, intra & extra, necessary, and mandatory for this Art: recognizing among others the same Pedro Gregorio, that the Royal Mathematical speculative, is about that Being, which is How Much continuous, or How Much discrete, as has been explained in the Logic of this Science, from where this Art is produced, in which one proceeds to the formation of its precepts, and rules for Mathematical Being: whose consideration is different from the one admitted by philosophers, that Aristotle dealt with in his Metaphysics, passing in this Art to other considerations, that work in that part that looks at lines, angles, surfaces, and bodies, by continuous and discrete quantity, in which numbers are essential.

Aulus Gellius and Celio Rhodiginus argue that mathematical disciplines are to a certain extent like elements and degrees, through which one ascends to high considerations. Through Cicero’s doctrine, Celio himself conceded that mathematicians, in the great obscurity of things and in the hidden depths of the Art, find the firmness of demonstrations, seeing themselves as in a mirror of clear, shining, and bright truth, just as in this Art is sought, for being properly military, as is deduced from Pedro Gregorio: for this reason the good Soldier (who corresponds to the Latin Milite) must be wise in mathematical disciplines, Geometry, and number (which is why its term is derived from the Greek word Mathesis, which means Discipline) in which the Being that is formed is Mathematical, perceiving in the understanding an infallible concept such, that digested by the degrees of knowledge, and by the natural Beings of reason, and real, admits visible demonstration by the Arguments Problem, and Theorem, which are the most powerful in this Art of the regime of the Sword, not omitting in science those that are produced from Logic, and Dialectic.

From all the above it is recognized that the second cognitive Power, is like the object of this second Book; with which one enters with the due notices to its intelligence, rules, and precepts, in which it is Art, and this in genre is that which, consisting of precepts, and rules, is included in the others in such a way, that it configures within its limits all its perfection, by means of the Thinking, and Operating Power, acquired by the ten degrees of knowledge repeated, and by the four Beings Natural, of Reason, Real, and Mathematical.

In force of this Definition, Art derives from Arcto Arctas, which means to tighten, or constrain oneself within narrow limits; just as every Art is tightened, and girded by the precepts, and rules of which it consists, and includes it.

Art is also the correct action of forming things: for this reason the Greeks (according to Ambrosius Calepinus) call the Arts Sciences, although Logicians, and Dialecticians distinguish Art and Science, in which the latter produces Art: but Art does not produce Science. Because Science is achieved with pure reasoning, like Logic; and Art with the observation of the rules, and precepts, of which it is composed and consists, like Dialectics in the formation of syllogisms, etc.

For these reasons, Art is understood to be in two modes, considering it in speculation and in effect: from where the speculation is named Theoretical, to Theorice, which as Quintilian ended, is that which does not admit an external act of the same thing that it studies, being content with the understanding in speculation. In the second mode, Art is practical, or effective, to Praxos, a Greek word, which means action such as work. Thus the Arts, are either in the part of inspection, estimation, or knowledge of things by the degrees, and Beings repeated, or they are of the effective action, whose purpose, and perfection is the act; in such a way, that after it, no other effect remains. In one, and the other mode, speculative, and practical, is the Art of the regime of the Sword, which in common language is called Skill, for consisting of intelligence, and exercise.

In a broader understanding, Art is named Astuteness, as much in virtue as in vice: such term is admitted in the Art of the Sword, as far as it aims to be cautious, or to prevent oneself against the caution, or cunning of the contrary: from which results to call Trick to that specification, which cunningly is worked to achieve the own defense, and the offense against the opposite combatant, by means of the disposition, and operation; as said the Poet.

Instructed in Pelaſga’s deceit and art

Let the curious see Quintilian for the distinction of the Arts, with which here is excused what could form a volume.

With more specificity it is recognized that the Arts, whose purpose is the correct use and regime of Arms, accept the name of Military from Militia, which is Art, as it qualifies, and approves Pedro Gregorio. Thus the Milites (whom the common Spanish call Soldiers) properly are the professors of the intelligence, and exercise of Arms; especially the main Queen of all, which is the Sword, whose regime consists of acquired Art: and in this part, although they are numbered among Artisans, they are the most noble: as using the maxim of Vegetius, Simon Astaro Velscio concluded: That in all combat, not so much the multitude, and untaught virtue, as much as the Art, and exercise, usually cause the victory, optimum (he says) any soldier, who in defense of the Homeland moves to the noble study of Arms, seeks the glory impatient of leisure, to achieve fame from the wars.

From reason, and actions Pedro Gregorio infers that the militia consists of a fight, or combat, which is challenge, aggression, and defense. Because in various ways you fight resisting, and resisting, which is the same as defense, and offense in the Milites; and for this the real instrument is the Sword, and its Art, and regime the most noble: for which reason there are diverse species of militia, understood, and explained with terms, or proper names, distinguishing themselves by the reason of the Arms, and the combat. To avoid the equivocal is understood by the term Militia that which includes Milites, and Arms, as noted the same Pedro Gregorio.

All this generic makes, and suits the specific of this Art of the regime of the Sword, and Arms to her together, that all includes what in common is understood by Dexterity, and Dexter: whose rules, and precepts are useful, important, forced, and necessary in every man who girds Sword. Astaro Velscio recognized the reason in the sentence of Vegetius, which he explained in these words: Those who are not well excited in Arms, either perish unhappily fighting, or negligent become cowardly, turning to flee from the victorious, without presuming themselves equal to the others.

For this reason, in all times the understanding and exercise of Arms, and especially of the Sword, superior to all, usual and companion to all those who decently gird it; and so preeminent, and noble this Art that is treated in this book, teaching it in imitation of Antiquity, as in drawing in shadows, with the Swords that are called Black, although more lustrous, and sharpened they show: for which reason the Greeks to this Art signified it with the term Scimachia; just as in Painting in those lines, or shadows, that form the drawing, its Art is understood by the compound name Sciagraphia. Demonstrations are proceeded in both Arts by means and mathematical arguments; with which the perfect knowledge of one and the other in the speculative, and in the practical, coming through the Mathematical disciplines in the understanding, and exercise of the most recondite of these Arts; and mainly of this regime of the Sword, and its adjuncts, Dagger, Rodela, &c.

For greater clarity, since the term Sciamachia is not common, Celio Rhodignio (Learned investigator of the lessons, words, and ancient names) noted that the Greeks called Experts (that is, Wise) of the Sciamachia, those who shadowily exercised, combating with the black Swords, to teach, and train themselves to use the white ones in the militias. Concordant Plutarch who affirms, that the Milites hurting themselves aerially with the Swords, were trained for the Armies. The same Celio, explaining to Galen in the term Sciamachia, understands it as that exercise that deals with the meditations of Arms, and especially of the Sword, which by such means are learned: and not as the Semidocto Vulgo deceived, to what is noble Art of the meditation of the Arms, calls Fencing; being so distinct from the Sciamachia, as Juan Ravisio Textor noted, making different the Arts, as the curious can see. It is not to be wondered, that the Semidocto Vulgo deceived, abuses the terms of such exercises, as Celio noted, since Angelo Vigiano, held in estimation, called Schermo, which corresponds to Fencing, to the meditation, and exercise of the Sword, as also without noticing the strength of the diction Grima, some common deceived, have fallen into the same error, that Angelo Vigiano, for not being versed in the purity of the lessons, and proper terms, that with so much attention used the ancient Greeks, and Latinos, to whom of necessity has been discussed to speak of this Art of intelligence, meditation, and exercise of the Sword, for its nobility, signifying it in its own terms.

So also the antiquity, for Schools and exercises of Arms Sword, and Lance, built, and dedicated Gymnasiums, which the Greek named Xysticos: whose premises, according to Epicharmus, and Diphilus, constructed the Gymnasium in such a way, that in its interior there was the last one reduced to a triangle; and among the famous was the one that was in Phlye, named Xystus, dedicated in favor of the exercises of Arms of Hercules, and Amphitrion, to whom were directed the contests of Lance, and Sword, as recognized by Cielo Rhodignio, calling Anchemachos to those who fought with such Arms, in such places; of which was such estimation, that Pausanias noted as a considerable circumstance, that every day the Gymnasium was cleaned, so that in it there were no thorns, which in such grounds are born. So much care was put into the meditation, and exercise of the Sword and Lance, Queens of Arms, this in the Campaign, and the other more in all combats.

Celio understood those of Sciamachia as the exercise and course in which the Roman soldiers habitually trained with sticks, and the Army Doctors instructed them, as Vegetius explains. As such, it is considered very important in all political nations to take special care to ensure that the nobility are trained in arms through meditation, intelligence, and exercise. Pedro Gregorio, among the noble arts necessary for the Republic, admits in the first place those that are beneficial either to the body or the soul: and of these, the most preeminent ones, he qualifies as Letters and Arms. And from the Arms, the Gymnastic exercise, which as has been repeated is the meditation and exercise of the Sword and Spear: and he notes, that it belongs to the strength of the spirit, but with such a medium, that it does not exceed, because they would be Athletes. And in noble youth, Gymnastic exercise is decent to achieve strength in the body and spirit, with such knowledge, that they overcome honest dangers.

Among the Chaldeans and Egyptians, fathers taught their children the trades they practiced, so that in tender age they would become fond and skilled in paternal ministries, in which they would preserve themselves. Therefore, as noted by Herodotus and Diodorus Siculus in the Soldiers, to whom they called Calasyries, and Heromotivies, they were not allowed another Art than that of Arms, the noble fathers teaching it, not at their will, but at the will of the constitutions, educating the children in childhood, pointing out Masters who perfected them by classes in Arms, and among the Yrenas, who were very wise, and skilled in fights: and so, those who imitated them well were called. Yrenas, which was a noble title.

Xenophon relates of the Persians that they had a place called Free, distinct from the sales forum, and in it was the Royal House, and the noble youth were raised, divided into four classes with Masters, and Preceptors, with twelve Princes assisting, who were Prefects. Until the ages of sixteen and seventeen, they studied Letters and Moral virtues; and after reaching an older age, for twenty years they devoted themselves to the exercises of Arms, being fit for the militias; and after passing fifty years, they were counted among the Elders, and they were admitted to the Councils and Governments. Cornelius Tacitus speaks of the Germans and the care they took in teaching physical agility and the exercise of Arms. The histories of Greeks and Romans are abundant in how much they strived in the teaching of Arms, especially the Sword; and the same examples are seen in other nations. It was demonstrated that for the Spanish, the Sword is native and ancient, speaking of its preeminence and estimation, which here excuses the repetition and prolixity: it suffices to corroborate the above, and that Quintus Curtius, praised Alexander the Great, who had Leonidas as a Pedagogue in Arms, from whom he imitated pride.

As essential and fitting for nobility, this art of meditation and the handling of the sword is for the defense and offense of the man who wields it. The fight with such a weapon is found both in one-on-one duels, and group against group, expressed in different terms such as Duel, Single Combat, Contest, Challenge. Cicero, in expressing defensive and offensive weapons, said: Weapons of a duel are bronze and iron. Duelo in antiquity was said to be the same as Bello (War), and from there to Bellona, the deity they made of war or combat. Paulo Boecio, a modern author who wrote expressly about lawful and unlawful duels, holds that Duelo is derived from a coin that is worth two. Among others, the curious can see Andrés Alciato, and others compiled in the volumes of Doctors.

Monomachia is the same as Duel in a singular contest, with the intention of what they called common Purge, which was two individuals fighting over a grievance or action that lacked ordinary proof: of whose formalities are extensively found in the laws of the Lombards, whom most nations in Europe have emulated in this respect. Celio Rhodiginus attributes the invention of the Monomachia to the Mantineans, discussing it at length, and with curiosity. The Spaniards use the terms Challenge and Defiance in place of Duel, Monomachia, which was also admitted in the laws and codes of Spain, with the same purpose as Monomachia, as can be deduced from the laws of the Partida, and compiled. And of the formality, and the term Challenge, and defiance there is enough in the Regnicolas Expositors of the collected Laws, and of the Partidas: and well Otalora, and Juan Garcia, &c. and of the common, curious, and elegant Belisarius exprofesso, and Juan de Lignano and Largo Guido. Pedro Gregorio Tolosano learnedly formulates all this.

Contest is a more generic term; it thus comprehends all the species of Combat, Fight, Contention, Argument, Battle, or Battle, for victory, for interest, or for the prize, of many against many, said Cornelius Tacitus: Embio against them Cavalry, and Infantry, and certò ambiguo. The four most famous classic Contests of the Greeks are Olympic, Pythian, Isthmian, and Nemean: whose prizes the Greek Epigram included, which the Latin translated:

Four sacred contests are reported to the Argives Two for humans, and two for heavenly beings. To Phoebus and Jupiter, Archemorus, and little Melicertes, The prizes were apples, wild olives, celery, and pine.

The rites of Antiquity ceased, and the Sword remained for all honorable or necessary contests: it is carried as a commitment to know its Art, more than for its ornamentation, as it will not be appropriate to say that it is worn to look good, nor will it fulfill the obligation in which it constitutes if its understanding and exercise are not meditated upon, especially in nobles, in whom the Sword is a symbol of legitimate defense and offense, for the person, for the Prince, and for the Fatherland. For all this, the Art of Arms is needed to be governed: for this reason (considered Pedro Gregorio) that Arms is an acquired Art, by precepts and rules, and with them the Romans, and other nations, obtained for their Kingdoms, Provinces, and Cities, wealth, fame, and glory, from where rightly said Vegetius: That the Art of Arms, is the Art of Arts.

Cicero recognized that there are two ways of contest, one by reason, the other by force; and although the first is the most proper in man, because the other is common to brutes; nonetheless, when the first is not enough, it is lawful to resort to the second: and for this, which is done with the Sword, its Art is needed, bringing meditation to strength, through what is called Skill.

Overall, the consideration that Celio Rhodigino makes is worthy, that in Philosophy the main thing is to seek the truth: and discussing some Arts, according to Plato, and Aristotle concludes, that Philosophy is the head of discipline, and learning, and with respect to the body, it finds that two Sciences are comparable, which are Medicine, and Gymnastics, that of them, one reconciles health, and habitual goodness, and the other considers, the diseases of the soul, and its affections, that Philosophy seeks to remove them: and this instructs us in what is beautiful, what is clumsy, what is just, and what is unjust, what should be desired, and what should be avoided. Therefore (he says) a certain Author informed that the Philosopher must be born of a legitimate marriage (this is from noble parents) for according to the Latin proverb, not every wood makes a Mercury. And from example he argues, saying: If in the contest of the Olympic games, which were warlike exercises, none was admitted, if not the generous by lineage, without stain, or defect; why in the studious that are Letters, does not the same rule apply? It then follows that Arms require more nobility, as they are nobler than Letters. This consequence, and how it should be understood, requires the common dispute of the precedence of Arms, and Letters; in which they are preferred, and how they are qualified?

Legal scholars accept the text of the Prologue of the Institutes as the core of the issue, where Emperor Justinian, rehashing the concepts, made a quasi parallel, in the explanation of which the Expositors who have glossed the period have committed themselves; and omitting the multitude of the ancients, modern Doctors Juan de Redin and Antonio Picardo, and those who concur in their opinion, are content to give equality to Letters and Arms. Nunez dealt with it at length, forming a not insignificant book on the controversy in Dialogues. From the rest, some flowers are selected, which will be the crown of this introductory discourse to this second Book of the Art of the Sword, Queen of Arms, whose meditation and rule is not foreign to letters, being the Art of Arms.

Those who precede Letters to Arms, make use of the action of Alexander the Great, who, finding among the rich spoils of Darius, King of Persia, a box of gold and precious stones of inestimable value, asked Leonidas, what jewel could be found of higher esteem, to make it worthy of such superior custody? Alexander replied that of greater value and nobility was the Iliad of Homer; making it clear how far Letters are ahead of all other exercises and Arts in the minds of the Wise. They add Philip, father of the Great Alexander, who pondered as supreme happiness in the birth of such a son, to be in the time of Aristotle, so that he could be his teacher. If estimation is made by antiquity; created the Universe, the Precept was first, the Law and Sciences in Adam; and afterwards by his offense the flaming Sword, which versatilely exercised the Cherubim.

The purpose of War is Peace, and in it Letters, not Arms, rule the Kingdoms, rule the Monarchies with the splendors of Laws, Justice, and Letters, which in Peace are ruled by Arms.

The rational soul is an image of its Creator, and in it, through the exercise of its powers, knowledge is acquired, and man is distinguished from the beast, aspiring to little less than an Angel crowned with glory and honor: and for such a feat, Letters are enough, without the clamor of Arms.

In Princes, Kings, and Emperors, the Council of the Wise places Letters before Arms, needing the former for the latter to subsist; to which are added the laws of the Wise King D. Alfonso, saying: Although in all ways it is convenient that there are good and wise men who advise and help, etc.

In comparison, the examples cited by Pichardo are celebrated. Emperor Hadrian, who relied on Julius Celsus, Salvius, Julian, Priscus and Neratius, literati, and not soldiers. Antoninus Pius and Valens, who admitted to superior estimation to Marcianus, Marulus, and Jabolenus, etc. Marcus Aurelius the Philosopher, who honored with supreme honors Scævola, and other Wise in Letters. And Alexander Severus, to Sabinus, to Paulus, and to Ulpianus. And they conclude that the building of the Temple was not granted to David, one of the nine of fame in Arms, but to Solomon the peaceful, famous in Letters.

In the strength of such foundations, in the face of Letters, they show the words of the Lawgiver. The Imperial Majesty, not only adorned with Arms, but also with Laws, should be armed, so that at all times of war and peace, it can govern in righteousness. And in the Roman Prince, not only in battles against the enemies does he exist victorious, but through legitimate procedures, he expels the crimes of slanderers, and is as religious of the law, as magnificent triumphant over the vanquished opponents. To the lights of the same text, there are no lack of reasons and authorities in favor of Arms. Plutarch notes that when Themistocles was asked whether he would like to be Achilles or Homer? he replied to the one who questioned him: And you, would you like to be the Victor, or the Trumpet of Victory? Hannibal, at the persuasion of Pyrrhus, entered to hear the Philosopher Phormion, who read precepts of War; and having paid attention to him, after the lesson, the Carthaginian burst out: I have seen madmen, but this is greater, that he dares without sight of War to judge it, with the error that he is always blind to light, and colors.

In terms of Letters, the soul perceives information either by reading or by listening to the sound of words: but Arms are perceived by more senses and are acquired by all the faculties, working, experimenting, and reasoning, not only with attention but with danger: hence, Arms precede Letters. As for antiquity, celestial spirits were first before the earthly man; and the first war was between Angels and Demons.

In human matters, Cato observed, and repeated: The Romans then assumed the Empire, when they began to attend to letters, and the studies of the Greeks. Cicero affirmed, that military virtue exceeds in excellence all other virtues. Valerius Maximus pondered the precedence and importance of Arms, saying: Now I come to the most principal, ornate, and establishment of the Empire of Military discipline, firmest bond, from whose bosom all triumphs flowed. Alexander Severus always repeated: The discipline of the elders has the Republic, which if we slip from it, the Roman name and the Empire we lose. Justus Lipsius, applying the sentiment to the words of Marcus Tullius, pronounced: The homeland, freedom, vassals, and even Kings, are under the protection, shelter, and presidency of martial virtue. Sallust repeated: Liberty, the homeland, and relatives, are defended with Arms. Cornelius Tacitus encapsulates the concept in this sentence: Vain studies of the forum, and in silence the acts of civil arts, if military glory decays: everything else will be easily feigned, but it cannot stop being a good Captain the Imperial virtue.

Thus Lipsius concluded in the resolution of Flavius Vegetius, exhorting to the estimation of the military Art, without which the other Arts cannot be. For this reason, the Sword is not authorized by the civic Toga, but the Toga by the Sword; as it is proven by both rights, granting the Imperial Majesty a Sword to the Political Magistrates. And it satisfies the slight doubt about the building of the Temple, that David with the Sword made the acquisition of wealth, if Solomon the peaceful built the fabric.

Drawing from all the understanding of the fundamental text to the argument, reconciling, that in Arms, and Letters, in Laws, and the Sword, there is no opposite emulation, but a certain reciprocal union, with which prudence, and valor are directed towards the consistency of the Empire; whose happiness is sustained on the two columns, Arms and Letters, in which it is necessary to follow the doctrines of Simon Astaro Volsio, and Pedro Gregorio, who more excellently than others elucidated the certain conclusion, of the disputed question of this endeavor.

Clement of Alexandria conceded that military skill is part of the Imperial Art; because the Art of War is part of the science of Reigning: since, as in every Art, and discipline there are specific precepts to perfect the work, which the Artisan must observe, and follow; it is no less important for the one who fights to follow the certain precepts of the military discipline, especially: That in the actions of Arms, it is not lawful to sin twice, as Plutarch said. And the reason was given by Vegetius, because the mistakes that are made in combat are irreparable. Politics is called the Soul of the Republic, or the Kingdom, because its virtue is like Prudence in the human body; so defined it Isocrates.

The universal reason for governing is divided into two parts, one of Peace, the other of War, as Theon the Sophist said: Two times contain all the affairs of men, War, and Peace. And the same Isocrates: War (he said) & Peace, have the greatest force in the lives of men. On this basis Pedro Gregorio founded, and what Prince who rules, must know, what belongs to War, and what belongs to Peace: that’s why in antiquity, the Popular Ministers, and the Captains of the Armies, were separated by the different Ministers, choosing the Experts of the Military Art in the offices, and military positions, and the Togati (men in togas) in the public urban offices: but in the Sovereign Prince, both faculties are united; Virgil confirmed this.

Remember, Roman, it is for you to rule the nations with your empire.
These will be your arts: to establish the pattern of peace,
To spare the subdued, and to subdue the proud.

And Valerio Flavio said to Augustus:

You protect the Italian affairs with arms, adorn them with customs
you correct them with laws

In this way, the Sword will defend the Laws, and the Laws will temper the fury of the Swords: in such a way that the Laws avoid Wars or preserve Peace; and with Arms Peace and Laws are established, confirmed, and defended, as elegantly explained by Emperor Justinian: The ancient Romans, from such modest beginnings, constituted such a large Republic, that it subjugated almost the world of lands, and they could not have ruled and defended such an Empire if they did not equally use the power of Arms and Laws; accommodating themselves to one and the other, with Pretors suitable for each exercise.

In the same substance, he repeated, concluding: That the Ancient Romans, to their Emperors they called Praetors; because they similarly showed strength in instructing Arms in the Armies, as much as in leading the Laws to order in what is right, and decent. The union of the powers of Letters and Arms, was taught by the Praetor of France; and the reason to unite in a supreme head, was expressed by Pompey Jurisconsult.

The Military Art is part of civil skill, said Plato: and in the City, Republic, or Kingdom, Arms and Laws have union; because one without the other, do not subsist. From where Cicero recognized that the Military virtue gives excellence to the other virtues, saying that the forensic praise, is presided, and secured in the warlike tutelage. Everything that is in the Republic, and the political Empire, is directed with Arms, so that we live in peace with the Laws, giving the hand of Letters to Arms, and Arms to Letters, as it results from both canonical and civil rights.

To escape such a plight, politicians have equally favored the Sword and the Pen, fearing any criticism in determining primacy. And rightly so, as a monarch needs the brave and wise; it would be a sure downfall to lean towards the Pen or the Sword. When danger is suspected in one, choosing the other is met with greater risk: Incidens in Scytlam, cupiens vitare Carydim. Spain mourned one in Wise Don Alfonso; France, the other in Charles the Eighth. To avoid these problems, a modern man represented Pallas armed in a symbol, with this motto: Armis & Literis. And so was the coat of arms of Julius Caesar when a statue was erected for him, with the globe at his feet, a sword in his right hand, a book in the other, and this epitaph: ‘Ex utroque Caesar’; as with both blades he won so many diadems. The relationship between Letters and Arms is close, and they live so intertwined, hand in hand for their endeavors. That’s why Edward, King of Portugal, took a spear surrounded by a serpent as his emblem: with the serpent being a symbol of wisdom and the spear symbolizing war (thus, the Romans to the province where they moved the war, opening the Temple of Janus, threw a spear), he wanted to secure the throne with Letters and Arms, and could not achieve it better than with the connection. For their union, Solorzano cried out in emblem 26. Minerva and Vulcan, occupied a Shrine, which together earn adoration. The decorum is not in the Arms, nor do they shine with the brilliance with which they are adorned when the Letters seek to separate: ‘Non solum Armis’, put by the greatest Politician, drawing a shot of bronze and a squadron: either because this one does not achieve accuracy without the rule, or because in the government without the rule of science, men would be bronze; as he who found himself a Prince, put only in value the north, linking success in just the shot.A Cherubin was placed at the entrance of Paradise with a blade; but no, as he is the fullness of knowledge, God wanted to teach Adam to govern, tying valor in a wise subject. The Sun is the beginning, and on one side it has Mars, and on the other Mercury; for the Prince who comes to rule, Arms and Letters are the clearest coat of arms: Marco Brutus recognized it well when, after Caesar’s death, he ordered a cap and a dagger to be carved on the coins with this letter: ‘Libertas’: because flattering Letters or Arms in government would have been a tyrannical regime. The Egyptians, in every mystery, in the Academy of Memphis learned to paint Mercury with two faces, one aspect of an old man, another of a young man, on a brave standard, because in the one who comes to rule, knowledge must be combined with valor; the spirit and courage of a young man, with the maturity of an old man. Of these two extremes the Empire is made up, says Quintilian: We choose a soldier when he’s young, we make him a commander when he’s old.: because as a Jurisconsult said, speaking of both:

Yet one does not lack the help of the other.

And Ajax from Ulysses:

I am as strong in battle as he himself is in speaking.

The Sword and the Pen are the two poles upon which certainty rests; and indeed, knowledge does not dull the blade, but rather leaves it more luminous: the sword does not weaken in the hands of a wise man, but if it seeks more luster, it commits with even greater determination. Both Letters and Arms vanquish chimeras, as happened to Bellerophon: With counsel and bravery. Without their bond, what was accomplished with ease through their union would have been impossible. Their value was revealed in that emblem where Arms and Letters were united in the figures of Ulysses and Diomedes, with this soulful inscription: Alone nothing, together very much can be achieved. What could have been conquered separately, together there was no impossibility they could not subdue. They were born as sisters and queens. Solomon declared it when, in the fountains mentioned, he engraved cherubs, palm trees, and lions at the base: He also carved Cherubim, Lions, and Palms: because the Palm belongs to both the Sword and Knowledge. The Laurel is the crown of both Mars and Apollo; hence the same nobility must be found in Arms and Letters, in the brave and the wise, since their patrons share the same crown. No king should fear loss in ventures where Arms and Letters are crowned, nor when both are observed united in his kingdom. Mathathias considered his sons to be glorious, you will be glorious, and believed they would restore the Kingdom of Israel: it’s no wonder, when Judas’s Arms were combined with Simon’s Letters. Alexander the Great always kept beneath his pillow a dagger and Homer’s Iliad, not wanting the steel to ever be without the guidance of a wise man; nor a wise man without the defense of steel. The ancient Germans entered councils armed so that in the sight of Letters, Arms would be inspired; and Arms would defend the Letters. Emperor Frederick III expressed the same idea, having as his emblem a book with an arm resting on it, and this epigraph: This rules, that protects. Cultivate the minds with knowledge, and handle the Arms; for as King Alfonso of Aragon said, in books, one learns to fight, and with arms, the laws of reason are defended. This beautiful combination has always been praised in a prince, as was Theodosius: A leader by counsel, a soldier by hand. And Mithridates: A leader by counsel, a soldier by example. The two captains of Greece, one wise and the other brave, were united so that victory against Troy could be achieved under their auspices: Counsel and assistance, mind and hand, spirit and sword. In this lay the glory of the city of Athens, having a supreme court of power located on a rock dedicated to Mars; but given to the wisest, whom they called Areopagites. The Egyptians did not crown a king who was not wise and a priest, hence by the three crowns they were called Triumphant. And finally, uniting the helmet with the sweetness of Wisdom (which is why Alciatus put it as a shelter for bees, where their swarm had made honeycombs from the nectar of flowers) showed the same correspondence between Arms and Letters; for knowledge illuminated the Arms, and the Arms honored knowledge.

This style is that of the politicians. In preserving them, they put forth effort, as these are the bases upon which the pillars of an empire rest; always doubting, like another poet observing two beauties.

Both are beautiful, both require careful cultivation.
It’s a tough decision, whether this one or that one comes first.
This one is more beautiful than that, but that one is also more beautiful than this.
And while we greatly appreciate this one, we appreciate that one even more.

This is why, for military judgments and sentences, the robe-wearing Magistrates should have expertise, as so many classical authors instruct, who have written learned volumes, explaining and commenting on the titles of Re militari, de Captivis, & postliminium, &c. And in royal law, as much and as wisely as the Titles and Laws of the Second Partida, charters, and ancient rights of Spain teach, in which the kingdom’s subjects have noted and debated the most essential aspects of war.

In those who profess the military arts, Astaro Velscio noted: That to govern them and achieve victories, the first gift of the supreme Captain is military science: that this, and the other Arts are perceived, not so much in practice, as in doctrine, thus requiring the reading of books to validate experiences. With such a mindset, Julius Caesar, to prepare for the difficulties of war conflicts, wrote observations on his own events. And the same Astaro Velscio praises Lazaro Suendio, Maximiliano Segundo, Rodolpho, and George Baſtha, that in the armies, besides being studious and learned, their most treasured possession was their books.

If we pay close attention, all the greatest Captains from all nations and times were knowledgeable in the most Political and Liberal Arts. Among the Hebrews, wise men were Moses, Joshua, David, Judas Maccabeus, and others, as manifested in the Sacred Scriptures.

Among the Greeks, we find learned individuals like King Philip of Macedonia, his son Alexander the Great, Themistocles, Alcibiades, etc. Among the Romans, there were many who were both wise and brave, with both qualities found in a single individual. The number of such people mentioned in histories is so vast that it would take a large book just to list their names. The curious can read Plutarch, Titus Livius, Dion Cassius, the Theatre of Human Life, and other compilers of illustrious men and will find so many that it’s astonishing. One should also read the histories of Kingdoms, Provinces, and Cities and will realize how brilliant the Princes and Captains were when combining Letters and Arms, surpassing those who were only brave or only devoted to Letters. And among them, modern examples worthy of note from Italy and Spain include the excellent Antonio de Leyva. Under his guidance, the Grand Duke of Alva, Don Fernando Alvarez de Toledo, secretly trained, choosing such a Master because he was exceptional in his time in both sciences and the sword, in wisdom and courage, in mathematical disciplines and in war tactics. The student perfected himself so much that he could rival the master in glorious competition, making his knowledge and bravery known through his example, including his two right-hand men in his work, Colonel Mondragon and Sancho Davila, as skilled with the sword as they were cultured in Letters. Worth noting is the time Davila defeated a Giant in Moncalvo in single combat, even with uneven weapons, as the Giant fought with an excessively large broadsword, and Sancho Davila, like David against Goliath.

In naval class, Andrea Doria was notable, finding a worthy counterpart in the Marquis of Santa Cruz, always victorious in all challenges. And many others, distinguished in valor and knowledge (as is necessary in a field that demands such consistency) as the histories recount.

He was the crown of general captains for his knowledge and the sword, the one who deserved the name of the Great Captain, Gonzalo Fernandez de Cordova. This title was extended, as if by inheritance, to the also great D. Gonzalo Fernandez de Cordova, whose studies and knowledge are attested by his words, writings, and actions. Superior to many in Mathematics, he chose as his teacher and companion the Reverend Father Claudio Ricardo. His prowess with the sword is attested by the many pitched battles in which his victorious reputation echoed throughout much of Europe. The same could be said of those of his bloodline and house, with pen and trumpet, deserving to be immortalized in honor of Spain and to the admiration of the world.

Worthily in Letters and Arms, the two Marquises of Aytona, father and son, were famous. They were General Captains with superior governance in Flanders and Catalonia, illuminating both sciences with the sword and the sword with the sciences. They wrote and acted, acted and wrote with such perfection that to see one, it would seem there was no life or subject for the other. This won’t be an exaggeration when considering their writings and military actions found in theories and practices in the vast volumes about all aspects of war. The compilation of which the Marquis D. Guillen de Moncada formed with demonstrations of fortifications, marches, encampments of armies and baggage, orders of battles, and their practice, both in infantry and cavalry. Responding to the wonder of how one can act and write with such accuracy on a subject is the verse of the Spanish Poet, who said:

Alternately taking the sword and then the pen.

No less deserving in his merit was the great Ligurian, Marquis Spinola, who in Ostend displayed his knowledge in new machines and methods of expulsion, and in wielding the sword, with which he rightfully acquired the supreme command of the Armies of Flanders, yielding the triumph of Breda to the Most Serene Infanta Doña Isabel Clara Eugenia of Austria. In appreciation of such a great General, she accepted the applause and entered on her palfrey amid the thunderous roar of salutes, the sky being torn by the warlike harmony of drums, fifes, and trumpets, with flags and standards waving; this triumph rivaled that of the Romans, even exceeding it in circumstances. Later, Marquis Spinola passed on his gifts of letters and arms to his son and heir, and Spanified his blood with that of the brave Marquis of Leganés, who as a supreme emblem, atop so many political and military titles, by positions and victories, received the nickname of Phelipez, from our lord King Philip IV the Great, greater in letters and the sword than the Great Alexander. While the Macedonian had as a teacher in gentile letters the celebrated Aristotle; in the divine and human letters, he was not inferior to Don Garceran Albanell, of Catalan nationality, Archbishop of Granada, who in the sciences was the teacher of the great Philip, monarch of vast worlds. If in the Mathematical Disciplines, understanding, and practice of the sword, the Great Alexander had Leonidas as a teacher; for the Great Philip, it was Don Luis Pacheco de Narvaez, the admiration of nations, master of Dexterity, and General Teacher with his writings, for all those in his time who professed and esteemed, as they should, the regime of the sword, the most noble and estimable gift for those who wear it with dignity.

For its realization, I intend to explain in this second book the Art of the Weapon Instrument Sword to the enthusiast, so they can grasp the maxims with Mathematical principles, in which the conclusions become evident, in such a way that they explain in what they do and do in what they say; for in the Art if the warnings are not explained, or (speaking strictly) the precepts, they are dead works, they are signals without meaning, a perspective without soul, and doctrine without doctrine: and to achieve everything, it is necessary to have exerted all effort for its realization.

It is difficult, however, here to use oars and wind.

It has cost difficulties to address the matter, but the effort will serve as a reward, satisfying myself with knowledge, since it is the prize that cannot be lacking, and of the highest esteem, as Horace sang.

From where nothing more is generated by itself,
Nor does anything thrive similar or secondary,
However, Pallas took the honors closest to him.

I will consider myself fortunate if I manage to achieve the endeavor that I conceived many years ago, without stopping until I demonstrate it, so that arms may attain the glories that have been hidden; not because they didn’t possess them, but because the difficulty of achieving them deterred even the most spirited souls from trying. However, I decided to overcome everything, saying with the poet Propertius:

I undertake a great journey, if glory gives me strength:
A crown easily obtained does not please a man.

And Cicero in his Academica:

To us, these wonders the very Creator of the gods has given
Slow and too late, but with everlasting fame and praise.

CHAPTER ONE.

SPECIFIC KNOWLEDGE OF THIS ART, and what arguments it uses

The Philosopher defines that Art is the habit of acting with reason on the truth. And conversely, art is also to act on the false with reason (though apparent) concerning that in which a diverse thing is possible. An example in this Art of wielding the Sword, which is the habit of acting on the truth with certain reason; and it is also a habit of acting on the false with apparent reason, as demonstrated in this Book.

From this, it follows that the habit and determination in any Art is due to the collection of its precepts, as defined by Pedro Gregorio. Although the precepts and rules are often considered universal rather than individual, as in Medicine, where the subject named Juan or Pedro is not debated, but the human body, because science does not apply to all particulars individually, as individuality cannot be the principle, according to the Philosopher. Therefore, Art is knowledge based on universals, and experience is of particulars, as taught by the same Philosopher. Adding that all Arts and Sciences, not only in terms of parts but also in terms of genres, exist in something perfect, where what pertains to the genre is sufficient; because in individual Arts and Sciences there are certain principles and general precepts that, according to the subject matter, are precisely distributed (like a calculation) into parts. And subjects are limits in which one transcends from one Art or Science into another Science or Art, like from Arithmetic, whose subject is number, one transcends to the Heavens due to Astrological considerations, and from the passions of Geometry to bodily magnitudes. For this Art, Geometry and Arithmetic are accepted as subordinate, which are the basis for understanding continuous and discrete quantity, deriving precepts to understand and demonstrate the regime of the Sword, in defense and offense, using this Art to transcend into others, and others into it. Because, as the Philosopher said: All Arts in common have among them a certain bond and correspondence, in which they participate from one another.

Cicero noted to the same end that this is a unique cause, turned by nature in all men: for the most rustic, if any difficulty is proposed, even if it is of an Art they do not know, the mind immediately seeks reason through the principles of common knowledge, necessary for reasoning, even if confused; and more so in the rough, lacking knowledge and principles of Art and Science. And yet, through the exercise of the spirit in experience (though without order), it prepares the understanding in its own way to learn a concept in which it finds peace, and until it achieves it, it does not rest; and from such origins, Arts have been produced, not so much by mere reasoning, but by the ordering into rules and precepts.

Pedro Gregorio used the example of gold, which is purified and extracted from mineral impurities, acquiring its purity and splendor through the techniques that refine it to its finest form; even if these techniques do not add to its essence, at least through artistic purification, it becomes smooth and radiant. The human understanding, clouded by ignorance, if it is cleansed and purified through acquired Sciences and Arts, returns to the lights granted to it by its Creator, being reduced to the intellectual purity that, cultivated by precepts and rules (which constitute Art), is perfected for the management of that instrument dedicated to one’s own defense and, when necessary, lawfully to the offense of the opponent.

The reasoning derives from what the Philosopher considered, noting that all Sciences and Arts have a specific kind of Being, principles, and causes of the subject: for example, Medicine is concerned with health, Geometry with the principles of magnitude, Point, Line, and Surface, and Arithmetic with the principles and causes of number, etc. From this, the same Philosopher concluded that all Beings can be reduced to a common one. Thus, Galen reasoned, proving that there are Sciences and Arts that presuppose one another.

The above is confirmed in this Art of governing the Sword, which, as has been said, is a habit of acting the true by certain reason, and the false by apparent reason. This is characterized and achieved by a collection of rules and precepts. Even if for this purpose it leans on the universals of other Arts, they are not applied as if foreign but as intrinsic to this one: acknowledging the stated maxim, that Arts and Sciences have a certain bond and correspondence among them, participating in each other, especially in ways of proving and demonstrating. Through these means, obstacles and errors of the spirit are eliminated, leaving the understanding free in its purity, refined like gold by the precepts and rules that constitute Art: reducing in this Sword Art the Natural, Reasoned, and Real Beings to the Mathematical Being; achieving in propositions the demonstration by mathematical arguments, whose disciplines in the speculative regard consider things abstracted from all sensible matter, treating the Mathematical Being metaphysically. As for the practical aspect, it moves to the Physical, where the entity and the reason for the sensible matter are conjoined, as Proclus taught. For this reason, the Arts that proceed by the precepts and proofs of mathematical disciplines are ennobled above other Arts and Sciences, due to the clarity of the demonstrations, which, excluding all that is dubious, calm the understanding with the infallibility of the conclusion, as achieved in this Art through mathematical arguments, used in it, which are Problem, Theorem, Lemma, and Corollary. These are necessarily (as essential) explained here, because from them arises the certainty of the proposition, both in mathematical disciplines and in this Art, where it is argued, concluded, and demonstrated by such terms, understanding that the main ones are Problem and Theorem, and from them arise the less prominent ones, which are Lemma and Corollary.

A Problem, according to Clavius and others, in terms of a mathematical argument, is that demonstration by which the establishment of the proposition one wishes to demonstrate is achieved, with a certain quality, such that based on a chosen principle, different figures can be established, like constructing an equilateral triangle on a given straight line, as Euclid showed, or another of a different kind. Due to the ambiguity it allows in constructing figures, triangles, or quadrilaterals, or others that differ, it is named Problem, analogous to questions, which Dialecticians, for the same reason of ambiguity, call Problematic, because they admit probability from one side or the other of the question. Thus, in Mathematics, the Problem is the one that, based on a given principle, achieves the proof of various demonstrations, not ambiguous, as is allowed in Dialectics, but with the clarity that the mathematical argument requires. Therefore, the Dialectical Problem and the Mathematical Problem are of distinct species, as seen in the Philosopher, and in Euclid in the 14 Problems he demonstrated in his first Book. The same observation can be made in others and in their expositions, recognizing that the Mathematical Problem differs from the Dialectical in the evident certainty with which, without ambiguity, it infallibly proves the demonstration of the proposed question, which the Mathematician calls Proposition.

Mathematicians call a Theorem that argument which considers in its demonstration some quality, or property, qualities, or properties of its own constitution in its expressed formality. For this reason, the term Theorem means contemplation or speculation, as deduced by Cicero (Tulio) when discussing Fate, and in mathematical terms, as noted by Clavius, and as seen in Euclid in the 34 Theorems of the first book, which consist of as many theorematic propositions. The most famous of these is the one he placed in proposition 47, which in order of theorems is number 33. The arguments Problem and Theorem differ in that the Problem proves the proposition, according to how it is constituted, showing clearly how it is made; and the Theorem does not teach to form any constitution, but to investigate, through mathematical contemplation, the qualities of the figure in its form, demonstrating in what is evident or deceptive the proposition, according to its formal qualities. As Clavius noted, if it were proposed in the form of a Problem that straight lines were to be drawn from the ends of a semicircle to its circumference meeting at a point on the periphery, forming a right angle or right angles, such a proposition would be ridiculous, because it is not problematic, but theorematic: as all angles that are created in the semicircle, with lines drawn from their ends to the circumference, are necessarily right, as proven and demonstrated by Euclid. The same is recognized in the distinction between Problem and Theorem; otherwise, it would suggest ignorance of Geometry and Arithmetic and the types of their main arguments, Problem and Theorem. Although both, as the highest genus, are included in the term Proposition, just as the term animal includes both man and beast. Therefore, mathematicians form distinct the terms of the conclusion of the Problem and Theorem because in the Problem it concludes by saying: Quod faciendum erat, which corresponds in Spanish to, this is what was proposed to demonstrate. Although signified by different terms, the purpose of the arguments Problem and Theorem is the same, which, by different means, are reduced to achieve infallible and evident demonstration, which is the difference by which Mathematical Syllogisms are distinguished from Dialectical ones.

From these two primary arguments, Problem and Theorem, (as not always, nor in all propositions is there necessarily such formality), arise two other mathematical arguments, less prominent, but also demonstrative and evident. They are chosen so that what has been demonstrated can be more easily grasped and understood, deriving in a mathematical way another infallible final syllogism in more concise terms. Of this kind is the argument called Lemma, which, as a derivative, is used for other demonstrations, not so much as primary, but for some specificity derived from the foundational arguments Problem and Theorem. Because of the Lemma, it is said to be a construction for the demonstration of some Theorem or Problem that was foundational in the demonstration, facilitating its understanding through the mathematical syllogistic argument named Lemma, so that it is clearer, more concise, and easier to grasp. Hence, Cicero, by the word Lemma, interpreted it as Assumption, which is the same as something taken from another.

The fourth mathematical argument, widely used, is what they call Corollary, whose term is more translative than proper. Going back to its etymology, Marcus Varro, Suetonius Tranquillus, and Caelius Rhodiginus provided various interpretations, most of which are unrelated to the role of the Corollary as a mathematical argument. In this context, it is understood as a complement that tightens and completes the main argument and demonstration, whether it be a Problem or a Theorem, drawing infallible consequences from the primary argument with which the proposition is adorned and completed. Thus, Caelius, citing Pliny, said that a Corollary is the same as a supernumerary, alluding to Varro’s notion that a Corollary is what is added as a complement or capstone. Mathematicians use the argument Corollary with various phrases, saying: Ex hac propositione constat, Sequitur etiam, Ex hac propositione pari ratione, Manifestum est, Constat enim, Ex his perspicuum quoque est, Ex hac propositione colligitur, &c. and in other ways, all of which mean that the Corollary is a mathematical consequence that is added, encircles, or caps, or is supernumerary to the foundational proposition Problem or Theorem, following the nature of the main argument and demonstration, depending on the proposition to complete it and surround it with evidence. In any manner, if Corollary derives from Corolis, the curious can refer to the cited authors and the expositors of Euclid and to Apollonius of Perga. It’s worth noting that even though the learned Father Christoval Clavius of Bamberg, in the prolegomena he wrote for the exposition of the Elements of Euclid, frequently used the Corollary, he omitted its explanation, having delved into the arguments Problem, Theorem, and Lemma (a noteworthy omission). Here, it has been necessarily touched upon because in this Art of wielding the Sword, commonly called Destreza, the method of proof by mathematical arguments is pursued, wherein demonstrative evidence is found, making use of mathematical disciplines as arts that are subordinate to this one.

To further facilitate understanding, I will place in the second chapter of this book the definitions of the Method given by ancient authors. Following this, I will continue with the other materials that make up the Destreza, aligning myself with little variation in the names and terms with those that are accepted as good. This is because my intention is not to complicate, but to assist as much as possible, in order to simplify the fundamentals and true understanding of this science, so that its operations are so well-regulated and adjusted that practitioners can enjoy in them the fullness of perfections that are possible within the potential of man.

CHAPTER TWO.

ART AND METHOD OF THIS Book

Should we consider the reason why, among so many writers that antiquity has had in all sciences and faculties, only some have stood out, gaining the general approval of all and leading those who came after them to follow in their footsteps and acknowledge them as masters in their fields (like Aristotle in Philosophy, Cicero in Rhetoric, Euclid, Apollonius, and Archimedes in Geometry, Ptolemy in Astronomy and Cosmography, Vitruvius in Architecture, and Hippocrates and Galen in Medicine) we will find that it has been simply because they followed the method that their subject matter demanded.

In the Art of Arms, several authors, both Spanish and foreign, have written. Especially among our own are the Comendador Jerónimo de Carranza and Don Luis Pacheco de Narváez, with the approval that is widely recognized. And although both of these two authors have received and continue to receive great acclaim, we still see opinions regarding their teaching methods, given that Don Luis wrote against Carranza, and there have been those who wrote against Don Luis. Even now, many promise they can write against all their works. Up until now, there hasn’t been a way to form a true judgment about who is more correct; approval and criticism of these matters are often reduced to the contingency of a battle, which can be subject to countless accidents. Sometimes, those who understand the theory best can fail in practice, either due to a lack of practice or through negligence.

My intention in this work (as seen in the first book of the Science and as will be recognized in this one about the Art, and in the one that will follow on Experience) is not to contradict anyone. I simply aim to find the best order or method and to pave the way for everyone to judge, not only who wrote best on this subject but also how well practitioners of this science perform. There is a significant number of them throughout all parts of Europe. The subject may seem challenging, but nevertheless, using the means that these great men have employed in their works, I hope to achieve my aim, as can be seen from this discourse. And I dare say that anyone who follows this method will be able to judge accurately the validity or falsehood of any maneuver, whatever it may be. If this is the case, it seems to me that from now on the inconvenience of introducing any doctrine that is not true and well-founded will cease. However, to understand what a method is, it would be wise to define it according to the perspectives of serious authors, both ancient and modern.

DEFINITIONS OF METHOD

Juan Gramatico and Eustachio say that it is a habit that reasons and establishes with a foundation. Tarabella says that it is an acquisition of knowledge about things. Simplicio states that it is a progression to the knowledge of something through a well-ordered path. Jerome Borrie defines it as a short, straight, certain, defined, easy, and unique path by which we come to know sciences. Another modern author says that it is a path that leads to knowledge without error. Plato refers to method as the form of the sciences and the arts. Anaxagoras says that it is a gift of the mind. Aristotle calls it the nature of things. And others say that it is a certain reason or way of investigating the truth, either through definitions, divisions, or discourses.

Authors give us many types of methods, such as Demonstrative, Resolutive, and Compositive; however, all are encompassed under these last two. The Resolutive, which they call Analysis, serves to search and inquire about the sciences, and the Compositive to teach them.

The Resolutive starts from the object of the thing that is intended to be inquired, as more universal, and goes backward through its categorical and predicamental degrees until it stops at the most specific and particular subjects and predicates. The Compositive, on the other hand, starts from the particulars and concludes with the universals.

The most universal object of the Art of Arms, when two combatants with equal, double, or single weapons face each other, is to teach the skilled one to strike and defend against the opponent’s attack. Although this proposition is universal for all weapons, my topic in this second book is to discuss the single sword, as the queen of weapons, and the discourse that will be made on it can easily be applied to all weapons.

Considering what immediately precedes striking a blow and defending against the opponent’s, after considering the Agent, the Patient, and the Instrument, I find nothing more immediate than movements. These movements are either made by the body or by the arm and sword. The movements made by the body are of two kinds: they either move from place to place, called Compasses; these can be along straight lines or circles which are named Curved. Those that can be made along straight lines, although they might seem infinite, as there are infinite straight lines that can be drawn from a center to its circumference, I have reduced them to eight distinctions: just as cosmographers, to navigate a ship at sea and direct it to any part of the world, were content to divide the horizon into 32 equal parts to avoid confusion, I am satisfied with a division into eight parts to regulate the movements of the Fencer, within the small space of a hall, where he must practice for his instruction.

The circular movements from place to place will be of two kinds: either by the common circle or by a particular circle of the opponent, whom we call Greatest Orbit. The circular movements around the center will be of six distinctions. The first, with the heel of the right foot as the center of a small circle formed by the tip of the same foot, and the other foot will move by a concentric circle. The second, with the heel of the left foot as the center, the right foot forms a circle. The third, where the tip of the right foot can be the center. The fourth, the tip of the left foot. The fifth, both heels can be centers simultaneously. The sixth, the tips of both feet can be centers of their respective circles. This is what, through Analysis and Division, I have found concerning the matter of movements, which is essential for Skill in Arms: because the sword, by itself, can do nothing unless it is moved, and according to the manner of its movement, will dictate the technique. But as there are so many distinctions in how it can be moved, which at first glance seem incomprehensible, it is necessary for me to emulate the model of the ancient philosophers who, to regulate the movements of the heavens, relied on mathematical sciences, imagining Points, Lines, Angles, Surfaces, and Bodies where none appear. It will not seem unreasonable that if, through these considerations, they have been able to regulate the distinct movements of all the heavens at such great distances, predicting the timing, duration, and magnitude of solar and lunar eclipses and their distances from Earth; I, through the same considerations of imaginary Points, Lines, Angles, Surfaces, and Bodies, intend to regulate the movements of the sword within the brief span of its sphere with a six-foot radius. And if, through these same considerations, there has been a way to regulate the movements of a ship on the unpredictable seas, ensuring it can voyage to any part of the world it wishes, I will also be able to govern the movements that the Fencer must make within the small space of a maximum circle with an eight-foot radius, which is the distance I consider between two combatants when they are in their proportionate center.

In order for mathematicians to better facilitate the understanding of their ideas and what they discovered in their sciences to others, they did not merely content themselves with imagining the aforementioned things; they also crafted physical models suited to their intentions. Just as astronomers, to better explain the structure of the heavens and their movements, constructed the celestial globe and spheres. In these, they not only represented circles that needed consideration, such as the Zodiac and Equatorial, but they also depicted the stars, organized in their constellations, with their correct distances from one another: they created different works to understand the movement of each of the planets.

Geographers created a globe on which they represented the Earth and the seas, along with the most notable features found on it. Through this globe, we can see in an instant what otherwise couldn’t be easily understood.

Those who dealt with perspective crafted their pyramids and conic figures; and from their various sections, they derived rules, not only to portray things in perspective as they appear to the eye but also so that the end of a Gnomon in painted clocks can depict, on any surface, the diurnal and annual movement of the Sun.

Architects, when they have to create a masterpiece, first draft its design and then create a model. This allows them not only to better explain their idea but also to perfect it if it happens to have any defects. They follow the belief of Aristotle that nothing is in the mind that hasn’t first been in one of the senses. It is well known that anyone can make a better judgment about a work by seeing its model rather than just looking at its floor plan and elevation, unless they are very experienced in forming such ideas.

Thus, in imitation of such great men, in order to clarify the idea I have developed on the Skill of Arms and simplify its method, I envision a circle, a model suitable for the subject at hand. As this concerns a kind of military discipline, it seems appropriate to liken it to a movable castle. I envision each of the two combatants to be in their own specific castle. Each one has its imaginary bastions of great use, and I am convinced that this is the only means to easily grasp the fundamental principle of the entire Skill.

I will demonstrate how it is possible for the swordsman to defend this bastion with great ease and with many advantages. Such advantages are akin to those considered between one who fights shielded from a castle or fortress and the one who must assault it. This situation is often seen in the military as being a six against one advantage. Even if it’s just two against one, it suffices for the defender to be assured that, if he guards well, he cannot be defeated by his opponent. I will give the rules for guarding it, after first explaining each of the movements that come together in the formation of the maneuver and the use of each, both for defense and for offense. I will show how to attack the opponent’s stronghold, in case he neglects to guard it. I will attempt to examine the strengths and weaknesses of this castle, focusing on the offensive and defensive weapons that protect it. Ultimately, I will endeavor to apply, wherever possible, military maxims and precepts (as the subject permits). This is because there isn’t much difference between the Skill of Arms and military art, other than battles being either between two individuals or many. The general principles and rules are almost the same, as I will try to demonstrate throughout this work.

A castle or fortress, as practiced in these times, in order to resist an enemy, needs both defensive and offensive weapons. The defensive ones are its walls, parapets, or ramparts and similar structures that offer protection. The offensive ones come in two types: those to keep the enemy at a distance, so that they cannot approach the stronghold without being exposed or facing evident danger, and those like the musket, for close combat, as well as the arquebus, grenades, and other similar weapons.

The castle in which I envision the swordsman, or his adversary, has its imaginary wall, not only with a protective layer, forming with it a shield large enough to cover the entire body; but it also forms with the strong part of his Sword another larger shield, offering greater defense, as will be demonstrated in its respective section. The tip of the Sword keeps the enemy at bay and serves the same purpose as artillery in a fortress; if the opponent approaches too closely without cover, they are at risk of being attacked. The blade of the Sword is also there to strike, either with a cutting or reverse blow, especially if the adversary recklessly comes too close. Moreover, one can strike with the proximal end using the tip, as will be shown later. One can also make a circular motion and wound because if the opponent isn’t defensive in correspondence to the approach, the defender can strike while retreating, or even without retreating, depending on the approach and distance, be it near or far.

In besieged strongholds, their fortifications like bastions, embankments, moats, and external works aren’t the only defense; when the enemy tries to breach the wall or dig a tunnel underneath it, the defenders inside create additional fortifications within the same stronghold. The same privilege is granted to the swordsman; if through negligence, the opponent achieves a favorable position, the swordsman is allowed to reinforce his defenses by retreating within the jurisdiction of his castle, to whichever part he deems most advantageous.

Strongholds can be conquered by assaulting them forcefully, tearing down walls and embankments with artillery, using the power of gunpowder through mines; or by scaling them when there are few defenders inside, or by diversionary tactics attacking from different sides, or due to the negligence of the guards, or due to internal discord among the defenders.

The same can happen in this castle, for victory can be achieved using force, subduing the opponent’s sword, which serves as a wall, or striking with an initial intent when it’s poorly defended due to negligence or ignorance of where to place the defense. You can strike with a secondary intent, trying to divert the sword by attacking different parts, forcing the opponent to defend one part, leaving another defenseless. Through negligence, when the opponent himself provides opportunities. And the last is when movements, both of the body and feet, arm, and sword — the soldiers that defend this stronghold — are not united and in agreement.

Given that there is so much similarity between this imaginary castle and the real fortifications built for the defense of kingdoms and provinces; it is fitting that I describe the shape and magnitude I want to attribute to it. Three main principles or guidelines are adhered to, or should be adhered to, in fortifications. The first is that it’s built so sturdy that it can withstand the weapons with which it is expected to be assaulted: this will be demonstrated in our fortress, for if this proof were lacking, all skill would be in vain. Its primary foundation is defense, and it would matter little to our swordsman if he was taught to wound or kill his opponent if, at the same time, due to lack of defense, he was wounded or killed himself. The second principle is that it should provide adequate space for defense, allowing also for retreats if necessary. This rule will be adhered to in this castle, making it large enough so the swordsman can defend within it and make his retreats if required. The third guideline is that it can be defended with the weapons present in the stronghold, and in this regard, the defense lines are adjusted according to the range of a musket or arquebus: in our stronghold, I’ll follow the same rule, drawing from our defense line, which is the length of the sword, to determine its size.

The shape that was traditionally given to fortifications was round because it was stronger, more spacious, and more regular; but modern designers have changed it, introducing bastions with angles, which is more suited for defense. In this stronghold, I will apply the round shape, as almost all the movements made with the sword are in a circumference; I will also use angles in the manner of bastions, because it is deemed suitable for the purpose I aim for. To easily grasp the understanding and precision of the concept of this stronghold, I will first lay out the specific and appropriate terms of this science, the principles, guidelines, and common sayings, along with the definitions of Geometry applied to the use of the sword. With this knowledge, we can construct our stronghold; and once built, we can proceed by adhering to its precepts, focusing on the most essential and necessary materials found in the art of swordsmanship, demonstrating them mathematically, to satisfy our swordsman’s understanding. With this, his imagination or apprehensions will be assured, and his discourse (which might arise from this concept) will be at ease, for the more perfect the act of understanding is, the more perfect is the union of the understanding with the thing understood.

CHAPTER THREE.

WHERE TERMS specific to this Science, and those adapted from it ARE INCLUDED.

The Definition is what explains and declares the essence of a thing, which must consist of both genus and difference; and the perfect definition should correspond with what is defined.

Requests are like practical principles that ask if something can be done: such as drawing a straight line from any given point to another.

Axioms are speculative principles that don’t pertain to the practice or method of doing something, but only propose a truth: like things equal to each other are also equal to a third thing.

Hypotheses or assumptions are not principles per se, nor are they clear to everyone, but only to those who make them, and they can also be false, as demonstrated by the rule in Arithmetic known as False Position. In Astronomy, the hypotheses that have been crafted about the heavens, the one by Ptolemy is accepted as true; but many others are not true, like the one by Copernicus, which assumes that the Earth moves and that the Sun is fixed at the center of the Universe: however, the conclusions drawn from it are true. In our work, and specifically in this one on the management of the weaponized instrument known as the Sword, we will adhere mostly to the Definitions, Requests, Axioms, and Hypotheses as accepted by the venerable authority of the ancients, whose understanding we will begin to explain in alphabetical order.

ABSOLUTE
Absolute is that which does not relate to another, nor has any reference in any order.

ABSTRACT
Abstract, this term is clarified with the above; in such a way that it is something common to many particulars, special or general. Pedro is good, the Sword is good, the movement is good; goodness is attributed to these subjects. And because they all agree in having goodness, this term, Goodness, is abstracted from the more particular subjects in which it is found.

ACCIDENT
Accident is what can occur to a subject and can also leave it without corrupting it.

ACTION
Action is an emanation through which the effect derives from its cause while it is being produced; this is considered even in the instantaneous. The fencer refers to it as instantaneous (because it truly isn’t) as it happens over time; however, due to its brief duration, it is termed so (in contrast to other actions termed permanent), or because the pose or posture needs to be quickly dissolved or removed. In this scenario, the action is considered not in the principal act but in what follows it. This term is transcendent and encompasses all.

Action of the active potency is an accident dependent on the substantial form, by which the doer moves towards the receiver. It’s a movement directed to produce some form: if substantial, it’s called generation; if accidental, it’s alteration. It divides into intensification or remission, or it’s termed augmentation if related to quantity, or local movement if it’s the acquisition of a new place alone. This movement, as it emerges from the operator, is termed Passion; thus, action and passion are the same movement. In fencing, it is regarded as a genre, with species being the accidental action, emanating, and immanent, intrinsic and extrinsic, voluntary, and necessary.

Accidental action is any movement outside of natural. Emanating action is that which passes onto another, like pressing, forcing, subjecting, diverting, and perfect attacks. Immanent action is that which remains within the doer, such as the movements of inviting, providing an opportunity, feints, and steps. Extrinsic action is that which is visible to us, like raising the arm, moving the sword, or moving the body from one place to another. Intrinsic action is that of the animal virtue in the mobile, in all internal operations: in humans, it divides into two - the first being spiritual, which is understanding, loving, and remembering; the second, which is common, is that of the muscles, tendons, and cords, which compose and organize the human body. Voluntary action is what the man does for some end, purely by his will. Necessary action is the natural movement, following the violent one.

ASSAULT
In general, an assault is a limited act, without final resolution from itself. It’s a feigned idea, cloaked in deception. It’s a cunning stratagem, a threat without execution, and the wound that results from it most of the time isn’t of its same kind. It has two distinctions, perfect and imperfect; and by types, circular, semicircular, and straight. A perfect assault is one that has parts proportioned to wound, forcing the opponent to change posture; it’s when the fencer draws a diagonal line squared to the opponent’s face, and the stance corresponds; and by the union it then has with the opponent’s sword, passes below it to form a reverse cut, with a concluding movement. An imperfect assault is made directly to the face when the stance is given by the line of the common diameter, and the same effects will follow. It’s also termed impertinent when, regardless of the type executed from the outside, it’s attempted without breaking the distance of proportion.

Circular assault is when a slashing wound is formed, and without executing it, a reverse cut is formed and executed; and an assault of a reverse cut, but a slash is executed. Semicircular assault is that which is made with half a circle, or a portion of the larger or smaller one, from top to bottom, or vice versa; it can be imperfect if executed with a lack of distance or disposition, and perfect if it has distance and disposition. Straight assault is when, with accidental movement, a thrust is made directly from the line of contingency to the face and no further below; it can be either perfect or imperfect, depending on the beginning and end of such movement.

ACT
An Act is a connection between power and object, and arises from both. It is distinguished as intrinsic and extrinsic (as mentioned in the action) and as active and passive. In Fencing, it’s categorized as a genre, and its species are: active, common, corruptive, dispositional, generative, passive, privative, permanent, instantaneous, particular, mixed, of union, proximate, and remote. Active Act is the manner in which the fencer prepares to strike, based on a proportional medium, and deprives the opponent of the ability to strike by controlling their sword; and everything else where he does not suffer from another or resists their actions. Common Act is that which, when performed by one of the combatants, gives the opponent the same disposition they took for themselves. This is found in the middle of proportion of equal weapons, and likewise, in the common distance. It is both active and passive. Corruptive Act is the one that approaches another entirely in non-being, and in both considerations is active. Passive Act is what one does being propelled by the force of another. Privative Act is a form in which the fencer deprives their opponent of the general power to act or the particular one, or reduces them from general to particular, and from particular to none. Permanent Act is when one strikes the opponent prematurely or after the time; either by the posture of the sword, arm jurisdiction, or by gaining degrees to the profile, through the shortcut, the right angle, or the concluding movement. With these, one can continue to strike. It’s called this way because one can remain in any of these positions, as the opposing sword remains where, without new movements, it can’t strike. It’s both active and passive. Instantaneous Act is when one strikes the opponent at the beginning of the slow movement, or the primary natural movement, when the sword is removed from the one controlling it, swiftly moving to the proportional medium. Particular Act is dispositional, and what any of the combatants do, without transferring it to the opponent. Mixed Act, both active and passive, is what the dominated sword does, resisting the action or impulse of the one dominating it. Act of Union, both active and passive, is when a movement that the opponent begins is matched with another of its kind, causing it to finish earlier than it would have, if it were just by its mover’s action. Proximate Act is when there’s nothing mediated between it and the power, like between sight and light, or between the end of a violent movement and the start of a natural unimpeded one. In Fencing, it’s when the proportional medium of a trick has been chosen, and there’s no impediment to execution.

Remote Act is one that follows from a distant power, and something mediates between the two, without which it wouldn’t exist. Like the ability to reach Spain, where between the power and the act of arriving is the mediated aspect, which is navigation. In Fencing, it’s when there’s neither distance nor a proportional medium for a certain strike.

AGENT
An Agent is the one who produces the action, according to how it produces it, and the one who actively operates in another. In this way, the active production is the action that comes from the agent. In another sense, an agent is an impulse that drives the actor to the point where he acts and through which potential is converted into action, and the act comes out of the potential. The agent is also the one that acts on another either actively or passively, such that in a subject there can be active action and passive reception. For the use and understanding of Fencing, it is distinguished as strong, weak, greater, lesser, minimum, active, and passive.

Strong Agent refers to the back edges of the sword, in relation to the other parts in which its quantity or length is divided. Weak Agent is the tip of the sword, in relation to the back edges or any other part, from them to the tip. Greater Agent is the body, which we call the Whole, in relation to the arm and the hand. Lesser Agent is the arm, in relation to the body and the arm of each, of which it is a part. Active Agent in Fencing is when one controls with greater degrees of force of their sword, that of the opponent, and the latter is not powerful enough to resist. Passive Agent is the sword that, with fewer degrees of force, wants to act on the greater force of the opponent’s by controlling or diverting it, which then suffers more than it acts. Both Active and Passive Agent is the inferior sword, which due to reinforced touch, can withstand the impulse of the one controlling it. At that moment, it both acts and suffers, by virtue of the aggregation, which is the act of the aggregative power.

AGGREGATION
Aggregation is the combination of some things while they remain distinct from each other, as when two swords are aggregated. This concept can be applicable or is evident in desires, increases, and other ends. From the material aspect of the aggregation of instruments, there arise aggregations of virtue contained within them, which a fencer can utilize if they recognize it. This is because often, aggregation is about power added to power; from such action, one’s desire can receive an increase, guiding them to act more, or to perform the same action with greater security or firmness. If a fencer does not recognize this, they will fail in their technique, for we would say that in the aggregation they found no power to act.

REACH
In Fencing, Reach refers to when there’s such a distance between the center of the arm (with which one intends to strike with any weapon) and the opponent’s body that there’s a point of contact on the opponent’s body.

ANGLE
An Angle is formed from the touch or inclination of two lines that meet at a point and are not straight. These lines can both be straight, both curved, or one straight and the other curved. Based on these differences, specific names are given to the angle, calling it rectilinear, curvilinear, or mixed.

A Right Angle in a person occurs when one aligns the arm straightly, without involving any of the extremes from top to bottom. This encompasses its domain from the direct vertical to the chest’s diameter. A fencer will be positioned in a right angle in any part of its jurisdiction, in relation to themselves and their opponent, whenever they imagine a straight line passing from the direction line through the arm’s center, the sword’s hilt center, to its tip, or by the line imagined to pass through the hilt’s center (moved as far as possible from the body) occupies the common intersection of the primary vertical plane with the upper plane parallel to the horizon.

An Upper Right Angle in a person is formed when the body and right arm are positioned at the point where the shoulder meets the neck, also referred to as the arm’s jurisdiction. A Lower Right Angle in a person is formed by the arm’s straight line with the body’s vertical side. An Obtuse Angle is larger than a right angle, and in this position, the arm and body form a straight line. An Acute Angle is smaller than a right angle and is formed in low stances, where the arm is not entirely close to the body, nor the hand to the thigh. A Mixed Angle is formed from the touch of a straight and a curved line; in a person, when the arm is bent, and with the straight line considered in the chest (which we call contingent), it forms an angle in the right collateral line. An Upper Angle in swords refers to the sword that dominates above the one being dominated. Conversely, a Lower Angle refers to the sword that is dominated by the one dominating. An internal angle refers to the angle formed by the swords touching, corresponding to the body of each of the fighters. An external angle is formed when one sword is placed over another, corresponding to the outside part of each fighter. A corresponding angle faces the right arm and sword of the attacker. To open the angle means that when a sword is in touch with another, either dominating or being dominated, without disengaging from it, with only the movement of the arm or hand, it moves its lesser degrees of force away from the greater degrees of the opponent. As a result, the angles formed by the touch either have larger sides or change in kind.
See Closing.

APPROPRIATE
Appropriate is a choice that the fencer makes from the means used by their opponent, in aggregation, increase, accident quality, time, place, and ways of acting.

DESIRE
Desire is an inclination towards one’s own good, according to the nature of each thing, and in any case, it is necessary to find it non-contingent. It is an abstract term from all particular, special, and general desires, and when narrowed down, it is considered in terms like increase, action, aggregation, accident, the appropriate, and other things, viewed as more specific than the mentioned name or as subordinates, even if they aren’t individuals.

ARC
An Arc is any portion of a circle, whether larger or smaller.

ASPECT
Aspect in Fencing refers to the correspondence of faces, bodies, and lines of the combatants after having executed a blow or while in position. Equality is a form in which one thing is equal to another, in power, in discrete or continuous quantity, and its dimensions, in its own, appropriate, or accidental qualities; in the arrangement of places, or in the aspects, etc. Its manifestations are proportion, measurement, dimension, and weight. In Fencing, where we use it with particular principles and diverse ends, it is with four differences: one of opposition, juxtaposition, equality of equal aspects, equality of opposite aspects.

Opposition of aspects in Fencing occurs when both fighters are at a right angle, and their right feet touch the line that forms the circle’s diameter. This means they face each other directly, even if their bodies don’t precisely align this way. Juxtaposition is when one fighter looks straight at the other’s sword. Equality of equal aspects is when the fencer reaches the infinite line of his opponent, and occupying it, without cutting it off, their left side corresponds with the right or the right with the left, and both faces look in the same direction.

Equality of opposite aspects is when the fencer is with his opponent, occupying the infinite line, and both right shoulders correspond equally, and the faces look in opposite directions from each other.

ATAJO
In Fencing, a Atajo is an impediment caused in the opponent’s sword, with or without touch. A higher-powered Atajo is the one that more greatly restricts the opponent’s sword. A lower-powered Atajo is the one that less restricts the opponent’s sword.

INCREASE
Increase is any majority that comes to the entity, either from the Art, nature, or exercise. This can either come to the body and its physical actions or the soul and its powers. This term, as a potential contingent, is also an abstract term that encompasses the desire mentioned above (since it is possible to increase) and other internal terms if it contracts with them.

GOODNESS
Goodness is the perfection that is considered in any thing. This is found in all things, because some perfections compose any subject, as integral parts in its physical being, while others adorn and illuminate it, like external qualities or accidents, making it more powerful for various acts.

QUANTITY
Quantity is a form whose subject is ‘how much’, and it is the reason things are said to be large or small, many or few. It is distinguished as continuous, discrete, and proportional: the continuous has two types, one of time and the other of space. Continuous quantity is the sword and all other things that have length, and the movement or movements of the technique, and the compass that is given by it. Discrete quantity is the number with which swords, compasses, movements, and angles are graded. Proportional quantity is one that, with another of its kind, has the same proportion. Continuous quantity in perpetual succession is also Time by which movement is measured, according to which in one and the other there are primary parts and postures that precede and follow. In another way, it is a Being in which created Beings are started and moved and have their beginning and end. It’s the novelty of things made up of many nows (called Now) according to before and after: it doesn’t have species, only parts, like centuries, years, etc. In Fencing, it is taken in two ways: the first by the very time in which all work has to be done, the other by the cut or reverse, resembling the year, which they signify by a circle that joins its end with the beginning.

CAPACITY
Capacity is a clear term and is properly considered in the agent and the passive; and often, the agent has more capacity to act than the passive has to receive, and vice versa. On occasions, they may have equality. Being more or less capable happens due to the accidents of place, instrument, time, quantity, and others. This capacity is also considered in angles, lines, movements, and compasses, taking them as subjects, although they are partial elements of the tactic.

CAUSE
Cause is where the effect depends on, so the cause is always before the effect, and always distinct and essential in its own right, because nothing created exists without a cause. However, there is a cause of causes, as Aristotle exclaimed. Natural causes in Philosophy are four: Material, Formal, Efficient, and Final; these are applied in Fencing, and the Instrumental cause is added.

In Fencing, the Material Cause is the movement, or movements, of both the sword and the body. The Formal Cause is the tactics and wounds that the fencer forms. The Efficient Cause of all movements in Fencing is the man. The Final Cause is the ultimate end (which is first in intention) of the movements of the tactics and wounds, encompassing and ending the other causes. The Instrumental Cause is the sword or any other weapon.

CENTER
Center is a term, or place, from which various effects originate and arise. In the physical and material sense, they arise from lines, movements, compasses, and angles. But in common terms that are explained, species are considered centers for the same reason. This name, or term, Appetite, is considered to be the center of all the others, because each one, according to its nature, has an appetite: in increase, there’s an appetite or inclination, which will be an appetite for increase: in the abstract, an appetite for the abstract: in action, an appetite for action: in aggregation, an appetite for aggregation: in the absolute, an absolute appetite, and in the accident, and all the others. And because appetite is predicated of these, they are said to have a center, which is the common Appetite, where they converge, like many lines to an end. If we talk about action, it’s the same, because appetite is action; and in increase, and the others, as long as they are acting or producing. Because of this affinity they have with the name Action, when considered as actions, their center is the action, since they converge and gather there. The same applies to increase, and the others, and in mathematical terms, the center of the circle; and for Fencing there are other considerations, and it is regarded as a genus, with its species being the common accidental, specific accidental, own accidental, of interval, of the arm, of the body, common of the combatants, common of the specific angles, and of gravity.

In mathematical terms, the center is a point that is in the middle of the circle, from which lines drawn to the circumference are equal among themselves. The accidental center of the Sword is any part of the opponent’s body where it stops to strike, also known as the place of choice or intention. The common accidental center of the Sword is the base of the arm, at any angle it might be; and it forms various movements, sometimes in kind, other times in number, distinct angles of the same quality, and lines.

The specific accidental center of the Sword is the elbow or wrist joint, in any position it may be found. The proper center is the heel of the right foot of each of the combatants when they are affirmed on a right angle. The common interval center is the midpoint of the distance between the combatants when they position themselves equally and directly on a diameter line. The specific interval center is the midpoint of the distance chosen by the fencer between himself and his opponent, gaining the degrees of the profile. The center of the body, considered in itself, corresponds to the groin because from there the two legs or material lines originate, and at their junction is the center, and on the floor where it corresponds: and this point on the floor is the center of the compasses that can be given to one side, another, backward, and forward, and their compounds and mixtures; the same is considered in the opponent. The common center is the one considered between the two combatants, in the middle of a circle imagined in the reality of the floor. The common center of the angles is the touch of the Swords, from where the lines they will form originate; and the specific centers are the fencers, with their arms and swords, causing them in their bodies: in many parts of it, various centers can be considered, which are easily omitted. The center of gravity is the earth, where everything heavy rests.

CLOSING THE ANGLE
Closing the angle is when the sword that is being subjected, or subjecting, passes (through the compasses) from the lesser degrees of force of the opposing sword to the greater ones; with this, all angles change their type at that moment, or become with smaller sides, always leading to a concluding movement.

CIRCLE
In Geometry, a Circle is a surface contained by a single line, called the Circumference, drawn from a point in its center. Any straight lines that emanate from this point and touch the circumference are equal and are called Radii. In Fencing, we refer to them as the Inner Circle, Outer Circle, Common Circle, Particular Circle, Own Circle, etc.

Inner Circle is considered between the two combatants when they stand at a right angle in the middle of proportion, its circumference touching the heels of their right feet. The Outer Circle is the one in which, when standing as previously described, its circumference touches the heels of their left feet. Common Circle is the one considered between the two combatants when they stand equally and directly on the Diameter line, and this is the same as the Inner Circle. The Particular Circle of the fencer is the one considered between him and his opponent after having gained profile degrees, even if it’s by another lesser degree. Own Circle is the one considered in the distance the fencer has from one heel to another when he stands.

COLUMN
In Fencing, Columna refers to the human body.

COMMUNICATION
Communication is an action through which the fencer often makes his opponent aware of his sword, the lines corresponding to him, the angles, and other resulting aspects. However, he should avoid sharing his power equally so that both can act; it should be more like a step, in which this specific case will be perfection.

COMPASS
Compass is the means by which we approach or move away from something. A compass in general is when the body moves from place to place with both feet, starting with one and followed by the other. They are measured like the step from the center of one heel to the center of the other, those taken with the right foot from the center of the left, and those taken with the left foot from the center of the right. In Fencing, its variations and types are Straight, Strange, Trembling, Transversal, Mixed of Trembling and Strange, Curved, and Mixed of Transversal and Curved.

Straight Compass is when any of the combatants move along the common or particular Diameter line of the fencer, which is always the shortest considered between him and his opponent, in order to approach him; it starts with the right foot followed by the left. Strange Compass is when either combatant moves backward in a straight line along the common Diameter, to distance themselves; it starts with the left foot followed by the right.

Trepidation Compass is taken between the inner tangent and the common Diameter, on either side of it. D. Luis de Narvaez defined it as Transversal. Even though this definition has been criticized as improper, there’s no reason to condemn it since the names given to things don’t alter their essence. And Don Luis focused on differentiating the terms and being concise without overlooking that this compass is a mix of trepidation and straight.

Mixed Compass of Trepidation and Strange is taken along any of the lines imagined between the tangent of the common Orb’s outer circle and its Diameter, extended on either side of it. Curved Compass is taken along the circumference of the circles of the common Orb and the largest Orbs of the means of proportion. Each combatant takes it on his opponent’s side. It’s also taken with the left foot for the concluding movement, as will be explained later. And there are cases when it’s taken starting with either foot, inside or outside the common Orb. Even though, strictly speaking, the compass taken along these circle circumferences is from point to point in a straight line, as nature always works in the shortest way, it is named Curved because the heel touches these circles.

Mixed Compass of Transversal and Curved, as defined by D. Luis, is taken for the concluding movement. Even though this definition has been seen as improper, it isn’t because it consists of genus and difference. This compass is taken along a straight and curved line with the right foot. For this reason, he called it a mix of both, emulating many mathematicians who, when a straight line joins a curved one, call it a mix of straight and curved.

COMPLEMENT
A Complement is something whose power lacks nothing in order to carry out the actions inherent to its being. This can be observed in all subjects mentioned in this treatise and in its parts when taken as subjects. Thus, it is the final form given to things or the one that ensues either in preparatory actions or in final or executive ones.

COMPOSITION
A composition or compound refers to any subject that isn’t simple and anything that has parts. In metaphysics, the species is composed of individuals, and the genus of species. Thus, desire, growth, abstraction, action, aggregation, and other terms previously mentioned, when considered universally, have a composition. Physical and material individuals also have it; since the initial, middle, and final parts constitute any line. Different movements in species, the strategy of movements, lines, compasses, and angles, and the art of fencing strategies.

COMMON
Common refers to what is applicable to many. This term significantly elucidates the essence of the art of fencing; because when choosing any strategy, movement, compass, angle, or line, the opponent tries to make it uniquely theirs. Meanwhile, the fencer, in the interim of this decision-making, recognizing what is common, chooses it for themselves and aims to make it uniquely theirs with a new operation and form. If the opponent is also a skilled fencer, they recognize that what their adversary is trying to make uniquely theirs, has common power for both defense and offense, and they utilize it. Among such skilled fencers, the battle continues for a long time without either being wounded unless there’s an oversight or a similar incident. All these choices are of transferred or appropriated means, as previously mentioned.

CONCORDANCE
Concordance is the similarity of two things in some aspect, or the agreement of two agents in a material action. However, among fencers (Diestros), the agreement should not be total, since this would result in equality, and the fencer (Diestro) should be superior. Thus, if the sword lowers and the opponent’s intention is to wound me, aiding it to descend aligns with his intention in this, which is to lower it. But it does so in a different manner and for a different purpose, whether to avoid being wounded or to wound him or to prepare for that. Therefore, there’s an agreement in lowering, a difference in the way of lowering, as it descends differently just as the two combatants are different. But in the terms they present, the Diestro’s action will be in complete proportion if there’s agreement; for perfection perfects it, fullness fills it, duration gives it existence according to its nature, power makes it powerful, order makes it ordered; and so on. All this with such proportion that, even though the operations performed by these terms are different, they are equal, as the power is as great as perfection, and duration is like both, and order is like all, and also fullness; because each one is considered as resulting from all, as there’s duration of perfection, fullness, power, and order. Thus, the universality of duration is a result of the other terms, and the same goes for any of the others.

CONSERVATION
Conservation in the art of fencing is a term that extends to many aspects. It can be the conservation of a means in an individual or the conservation of superiority when taken generally, even if the means initially chosen deteriorates. The fencer who manages to always maintain superiority over his opponent, despite changing specific strategies, will have reached the highest understanding and execution of Destreza. In this way, one can consider that it’s possible to conserve distance with different steps numerically and with different types of steps, and similarly in aggregation, regarding movements, and in other specific matters.

CONTINUATION
Continuation is the action carried out without interruption in time or intention. In any material action, even if it ends in a certain place without reaching its perfect end, as it had a beginning, middle, and end, it is said that there was a continuation between them. If it achieves a perfect end, the continuation is perfect. If various types of movements intervene in them, they are said to be done with a continuation from one to another. As they involve various means and dispositions, according to the paths where the sword goes, even if they are distinct from each other, if they are used with continuous actions and movements, it will be found that their means and dispositions are continuous, if there was no interruption from one to another, because they are strung on the same line, not materially broken. The same is considered for the lines formed with movements, where one will find that the oblique, and so on, are continuous; the same goes for angles, which also have a continuation from one to another since the lines and touchpoints that form them and the movements that cause them have continuity. They cannot exist without the interruption of time, which makes them continuous. In terms of purpose and the agent’s will, they can be continuous even if the movements are not. The same is considered for steps and other things. Thus, even in one species, if it is erased or ceases, it cannot be said that there is a continuation of that species, as it ceases to exist; there is in the genus, as when the six species of movements are made by one or two agents without interruption, the movement taken in genus, and as it is common to all, was continuous. The same goes for increase and decrease caused by an agent without interruption. The continuous is distinct from the contiguous, in that the contiguous is just one body being adjacent to another, each maintaining its distinctness without a connection that gives them unity: two men standing next to each other are only said to have contiguity, not continuity; the same goes for two swords, and this is called aggregation in Destreza, not continuation.

CONTRACTIVE
Contractive refers to the differences of contracted things in terms that differentiate them. Thus, it is something that joins the superior to the inferior, considering it as part of itself, whether from universal to genus, from genus to species, or from species to individual. For instance, if we say the term Action that we’ve discussed is very universal, it encompasses the action of the sword, the arm, and its movements, the angles caused by the contact of the swords, and the increases and decreases that can be newly made after being created. The consistency or lack thereof of lines that form the steps they make, all are actions, and all fall under this term Action, and all are products of the intellect. The word Action is universal, as the Logician says, and narrowing it down to the action of movement is discussing something that encompasses less than the term action by itself. The movement that approaches the term differentiates it from other actions that aren’t movements. Human understanding only operates by considering; however, it’s God who gave them the natures that man considers. Dive deeper, and one finds that movement can be done by the body, using the feet, or by the arm without moving the body. The first is movement of a part that changes places through the air but not the ground. In contrast, foot movement always changes both the ground and air. Given this significant difference, some are called steps, and others are called movements due to the diversity of partial agents since some are caused by the arm and others by the feet. But all are movements of more specific types or more specific genres; considering one as an arm movement and the other as a foot movement, what makes them contractive is the arm and the feet, which differentiates them. Following this, the understanding narrows it further. Speaking of arm movement, it says there are natural, violent, remissive, reduction, strange, and accidental movements. Speaking of each individually refers to movement narrowed down to species, with the genre common to all, as each one is a movement. They thus concur in genre, and the intellect contracts it, and what makes it contractive are the differences: violent, natural, remissive, reduction, strange, and accidental. For foot movements, the understanding recognizes that there is movement about the center and movement by steps; one is movement of part of the foot, and the other is movement of the feet and the whole, leaving the ground it occupied. This division is contracting the general concept of foot movement to a less general one. Here, what makes it contractive is the whole and part of the feet, which differentiate their modes of movement. From here, one descends to individuals. As these require material operations, though the intellect recognizes them, it is necessary for the body to enact them, subjecting them to many accidents. In these individual actions, if they are imperfect, one considers and observes if their beginning, middle, or end, whether in quantity, instrument, method, or if it comes from the step, line, angle, or movement, or in time and its duration, where its greater or lesser power arises. If they are perfect, it is necessary for all the parts owed to it to come together for the action to achieve fullness. In all these material actions, it is the man who contracts them, acting as the efficient cause from specific to numeric, and the difference, which is the contractive, is the form given to them. Even if these actions are transitory (thus erasing these contractive forms) this is in the material aspect, the memory of how they were is kept, and the intellect considers it and makes a judgment, either to imitate or to improve. This is contractive, which is a term opposed to the abstract, and has been explained with the above. It is no more than observing in which common reason specific individuals or genres agree and considering it with the understanding, which gives it being, although based on real things.

COUNTING THE LINE
Counting the line means placing one Sword over another by its length, and similarly when with the foot some of the imagined ones in the circle, or outside of it, are cut.

OPPOSITION
Opposition is everything that opposes the appetite of the opposite, or the appetite of its action; and there is a line that opposes a line, angle to angle, movement to movement, and compass to compass: and many times they come together, although preserving their distinct power and action; and in the aggregation there can be opposition, and it can cease to exist, because if one moves the Sword, and the other follows it with aggregation, there is no opposition of movements; although there can be of intentions, if I oppose its intention with aggregation, as powerful to impede its own, because in the material of movement, everything is a single movement; but if it remains when lowering, I oppose it by raising, and by moving away from reducing myself; and as this is recognized by touch, and perceived by sight, and remains almost in the same place, because the opposition is from movement to opposite movement perfectly between them, the actions are more perceptible, easier to recognize their powers, and what should be done: but following the Sword with aggregation, it seems to be subject to more accidents, because I oppose it to its intention, this, neither do I see it, nor touch it, although I conjecture it, and the Swordsman must recognize, whether it is orderly, or disorderly in its action; but the changing so many places in the air, makes the action of the opposition more difficult, to remain, and achieve its end. And finally, it is to recognize in the abstract the power of its will, when its intention takes it contracted in concrete, and for a single end: from which it follows that the wounds, tricks, or actions that are done with opposition of movements, or angles or the actual, are more perfect and safe, than in the future; in this way you can make considerations in the other terms with the opposition, which is a term very apt for great discourse. Example: I want to make a perfect movement, being the Agent, I understand that a diversion can oppose me, to vanish the line, which corresponds to its left eye; but this possible, I find that it is contingent, not necessary, because it depends on its will. If it does not oppose the diversion, this wound is thrown at the said eye, which is the touch that corresponds to it; but the intention of the Swordsman, or his desire is, or should be, that he opposes it, because then he opens an angle, which is occupiable, and entering, and subjecting the instrument with the left hand, he wounds where he wants: and in this he must recognize many things. First, that he only has to oppose a diversion. Second, that although this is contingent, in the same contingency he finds that it is more necessary to oppose it, than to stop opposing it, as it is more necessary to remedy the immediate and visible evil, than the future and more unknown. Third, that it is not contingent, but necessary for the opposite to do one of the two things. Fourth, that the contingency in the action of the opposite, or oppose the diversion, makes it contingent in the Swordsman, if he will wound through the line, or the angle. Fifth, that it is more contingent to miss the eye, than to miss the whole body; and thus has more security this second, than the first, particularly depriving him of the instrument. Sixth, that if the opposition of the diversion deprived him of one medium, it disposed another with more parts, and perfections for his defense, and offense of the opposite. Seventh, that if the diversion was opposition of a line, to the said diversion the Swordsman opposes a movement of conclusion, in which compasses concur, and the operation of both hands, for which it is more powerful and perfect, because it is common power, to more partial powers: and in this way other discourses can be made.

CONVENIENCE
Convenience is when two or more things share a similarity in something: it’s a participation in a single nature. In this sense, it’s more than resemblance. When convenience exists between two things, it can’t be numerical, and they can’t be considered two unless they are different, at least in number. The convenience will be in species; and species also have convenience in their genus. For instance, two straight, different lines don’t agree in number because one straight line isn’t the other. But in being straight lines, they have a convenience because each is described as rectilinear. A straight line and a curved or tortuous line don’t agree in species because a straight line isn’t described by the curve or tortuous attributes or vice versa. But they all agree in being a line, which is the genus, as all are described as lines. The same consideration applies to compasses, movements, angles, places, times, accidents, instruments, plans, actions, aggregations, accidents, abstracts, communications, conservations, and all the rest. Among all, some convenience is found, and it’s necessary to identify it.

CORRESPONDENCE
Correspondence is a relative term and must be in relation to another. It’s commonly said to have correspondence of places with respect to lines, either imagined or physical. Through these lines, one intellectually determines if there is a corresponding point of contact in their counterpart, based on their current disposition, and sight is the register of this. If the current disposition isn’t present, one considers and identifies the place from where it will come. This looks at whether it corresponds to their power to occupy it or if there is an obstacle in between. This is the means or mediated correspondence that one looks at to acquire the current state. The terms from where and to where have mutual correspondence, but they should not be equal in virtue. The expert should seek or choose it in a way that the contact point is prepared to receive and the expert’s point is ready to act, removing from the opponent all the terms and points that can signify correspondence, so that their opponent acts immediately. In the angles formed by the crossed swords, correspondence is considered, as in profiles and positions, such as if they were shoulder to shoulder, occupying the same line. Among compasses and movements, many correspondences will be found, and among all the other parts that make up a trick.

STRING
A string is the line that connects the ends of the arc with its own.

DEFENSE
Defense is what preserves one from being injured, thwarting the enemy’s tactics. Sometimes it’s at the beginning, sometimes in the middle, and sometimes at the end: without the beginning, it’s a defense of the disposition; in the middle, the same consideration applies; if at the end, it’s of execution. Defense can sometimes be caused by posture, other times by the movement of the arm and sword, sometimes by angles, and sometimes by compasses. All of these either erase the forms of the opponent or hinder their dispositional capabilities so they cannot come into effect. For this, knowledge of the power that immediately corresponds to the enemy in any position where body, arm, and sword are found, and the desires they may have to act, is necessary. Sometimes the advance defends, other times the knowledge of things in the abstract, and always the action, whether it’s relative aggregation, absolute action, or accidental action, such as using the appropriate means. Everything that causes defense contains goodness, and this can be complete or incomplete. Even though there can’t be defense without offense, often this offense is only from the power of the opponent communicated to the action, not a personal offense, and it’s not complete but partial. There’s also offense that isn’t defense, if both are injured at the same time or can injure. There’s also defense with offense that isn’t complete but incomplete; if being temporarily defended, a minor wound is given or such that doesn’t prevent further action, or if a concluding movement is made with a wound that doesn’t result in death, because even if it deprives the opponent of the instrument, it’s temporary defense, and the enemy remains standing. Thus, complete defense regarding that enemy consists in the deprivation of life; and so, one can elaborate with the other terms.

DEMONSTRATION
Demonstration is the proof made to verify if what has been proposed or conceived is true, to firmly establish the truth and recognize if the observed effect was necessary and what causes it had, even though here we talk about physical actions. The metaphysical also has its demonstrations and verifications; and some terms of this Treatise serve as means to demonstrate the truth of others through reason: and all, or most of them, to verify or demonstrate any tactic, its theoretical truth, and the practical truth of the theory; and when everything comes together to demonstrate anything, if it’s without dissonance, with such conformity, the understanding is firmly established in the truth that it contains, and with great assurance of correctness.

DEPENDENCY
Dependency is the perceived need that one thing has on another, either in its production, emanation, or after being produced and emanated. In this manner, it’s considered that effects depend on their causes. While being produced or while they are in the making (in fieri), they depend on the efficient cause and the end; for if either is missing, the production will cease. But after the act is done and perfected, even if the cause and the end cease, the effect will not. Yet in the effect, there are two other causes on which it depends; and whenever these cease, the effect will cease, which are the material and the formal. The absence of either causes the effect to cease, and this change can be made by the efficient cause or another.

TRUE SKILL
True skill is a habit acquired through practice based on demonstration, by certain, evident, and necessary principles derived from the reason of this science, in order to defend and attack in a battle of two opponents.

FALSE SKILL
False skill is the one that lacks the necessary foundations to achieve the end it aims for.

DIFFERENCE
Difference is such a well-known term that there’s no need to discuss it; however, it’s a significant term, and it’s essential to understand its universality and how it exists in all terms.

DIGNITY
Dignity is a quality that makes the subject superior to, or equal to, others. Some of these terms have greater dignity than others if they encompass more. Some tactics have more dignity than others if they have greater power or greater security. This must be considered in the means, lines, movements, compasses, and angles, as it exists in all of them; and between the beginning, middle, and end of operations, and the remedies corresponding to each one.

DIMENSION
Dimension is a measure and is a genus to length, width, and depth, or they are the subjects it measures, which we have discussed above.

DISPOSITION
Disposition is a means that the fencer recognizes as necessary or useful to achieve his defense or offense against his opponent. This can be chosen by him or given by his opponent. This disposition is found in actions while they are being carried out and in many already operated acts, at the beginning, middle, and end of operations. Disposition can be found in the freedom of the instrument and in its subjection, in width, length, and depth, and in all the components of the swordsmanship. A common disposition is when, between two battling, both can wound each other at the same time.

COMMON DISTANCE
Common distance is the one where both opponents can wound each other due to their reach, leaving their swords free.

DIVISION
Division is a breakdown that the fender makes from the common or the whole to its constituent parts that it encompasses or contains. For instance, movement is divided into six types, and steps into another six. This same division applies to angles and lines. The primary division of the lines states that there are physical and mathematical ones. Then, each of these parts is considered if it can be further divided, and it is done so. Since the swordsman performs the aforementioned tasks, it is considered to whom each of the mentioned things belongs: movements to the arm, steps to the feet, angles to the body, and the swords. Thus, the swordsman is divided into parts, making it easier to consider in each one its power, the order it says to act or receive, and the desire of each part. This is to divide the power, order, and desire collectively. Some swordsmen will be found in the movements of increase or decrease, some in abstraction, some in transferring means, others in the action of aggregation, others in the use and leveraging of appropriate means, others in preserving a means, others in understanding the centers, others in opposing, either by contradiction or difference, others in arranging, others in demonstrating, both dimensions, and the dignity and duration of maneuvers, and so on for the rest.

DUPLICATION
Duplication or repetition of a circle is when a cut or backhand is formed, and due to some impediment, it is not executed, and another of that kind or different one is formed.

DURATION
Duration is the persistence that a maneuver has or can have, either when it is being performed or once it is done. Duration is considered in all terms, according to the quantity of each one since all have being, and it’s impossible for it to exist without enduring.

EFFECT
Efect is what is produced by any Agente.

EFFICIENT
Efficient is the one who produces any effect. See what was said under Cause.

CHOICE
Choice is an act of will, in which one embraces one of the means presented to them. If this choice is based on what is perceived as better, the will follows the understanding, which recognizes it, as a faithful adviser. If one chooses the worse option, it is purely an act of will since the approval of the understanding concurs in the harm. The most disorderly action of the will in choosing is said to be more voluntary and free, as it deviates from the conveniences that reason and understanding propose in the most perfect way. In this disorder of choosing, the sinfulness of the action lies, and punishment follows sinfulness. These choices can be considered in all terms, or in each one of them.

EMANATION
Emanation is the one we have discussed under Action, and it is explained there.

THRUST
Thrust is purely simple and is executed only with the accidental movement. When it’s compound, it’s considered according to the figure it makes, and movements from which it’s formed, attributing to it, by species, the diagonal, the whole circle, half circle, a quarter of it, and others.

PRESS
To press, or to force the opponent, is to remove their sword from the good position in which it is, with a deviation or subjection.

EXTENSION
Extension: This term contrasts with intensity, and the opposites are qualities, knowing one, both are known. What is extensive is a power divided into many parts, with each part possessing little. Intensity occurs when a part corresponds with more degrees of power or is repeated many times. Nature provides some of these qualities, while Art provides others. The strength at the tip of the sword is given by the arm, and the longer the sword, the weaker it becomes because the power is distributed among more parts, and the size of the instrument weakens the arm’s ability to move it. United virtue is stronger than when it is divided, because in unity it is intense, and when separated it becomes extensive. The part, or arm, attached to the whole, or body, is more powerful with intense force than if it were separated and upright; because in this form, if it wishes to dominate, it applies little depth. But if the fist were placed in the groin with depth from the fist to the shoulder, it would have more intensity because extension is not considered in depth, but in width and length. Thus, profound knowledge in a skill, science, or Art is the one that delves deeper into its subjects, and it is aptly said that one has a deep understanding. However, someone knowledgeable in more subjects is said to have greater extensive knowledge. As this extension is considered in terms of length and width, which are on the surface of the entity, it is said that their knowledge is greater on the superficial or extensive level.

EXTERIOR
The Exterior is what is manifest to all; however, there are external signs that indicate the internal ones and reveal intention. For this, the exterior must indicate more than one thing. By recognizing this, the hidden aspect will be what the opponent’s will inclines to or chooses. There are external things that greatly hide intention, and the fencer should choose these so that their opponent doesn’t anticipate the remedy. Some are hidden in the action of desire, and others in the action of increase, etc.

EXTREME
Extreme is the last part of anything, or its end. For example, the ends of a sword (when viewed on its own, and without being held by a person) are the tip and the hilt. When considering its greatest length, and in width, you can consider the extremes from edge to edge. The same consideration applies to its depth. What is the end of a straight line can become the end of a curve or its extremity. Conversely, a body standing upright is a straight line, and its extremities are the head and feet. If this column or cylinder collapses, it takes the shape of a curved line, and the same head and feet, which were previously the ends of a physical straight line, become the ends of a physical curved line, drawing a mathematical straight line from the head to the foot. With this change, the human body creates new lines, but materially, the feet and head do not change because they remain as the head and feet. They are now extremities of a different thing, different in shape. Thus, it is said that a man reaches an extreme when he collapses, and further details will be discussed elsewhere. In compasses, angles, movements, and the rest, the extremities are considered. The perfection or imperfection of them will be based on the distances from one to another, their size, location, and others. Both extremities can collapse equally, or just one, but it will always produce a curve, even if not completely, as part of the line can remain straight and part curved. However, the imagined line will always touch both ends, and these are always straight in themselves, even if not in relation to their location because they can fall downwards. In the general terms that have been discussed, the extremities are the lowest and highest points, the beginning and end of the line. The first and last in terms of length, width, and depth of a composite are the beginning and end of distance, and one of the terms farthest from the center. The one that makes it evident is the most distant from the beginning, more than any other part of the composite. In fencing, it’s considered a category, and its distinctions or differences are the extremes of proportional distance, length, width, depth, near, and far.

Proportional distance extremes relate to two fencers, either on the plane considered above, between shoulder to shoulder or between foot to foot on the flat surface. It’s like the two points that are the ends of a straight line; it’s when the fencer, in terms of a right angle, reaches his opponent at only one point.

The length extreme in a person extends from the head to the feet, and in the distance between the two fighters, it touches each of the infinite lines on the common circumference, and on each of their right feet. The breadth extreme in a person is one shoulder to the other, or any of the collateral lines that form a quadrangle or parallelogram. The depth extreme is in two ways. The first is any of the two points or lines that in that dimension are equally distant from its center. The second (applied to Fencing) is the inclination that the body makes forward, moving the chest away without moving the feet from the right angle, and this inclination is only until the forehead aligns with the tip of the right foot, and the sword and arm are straight. The near extreme of proportionate distance is the position the fencer assumes when making a concluding movement, and when striking in opposition on the vertical line of the back. The far extreme of this same distance is from where the fencer strikes due to the length of the sword and right angle, touching only at one point.

EDGE
The sharp edge of the sword is the one facing the ground when the right arm doesn’t tilt either way; and the blunt edge is the one on top.

END
The End is where the beginning and middle rest. It’s a formality that caps the existence, power, and actions of something, either perfecting it, concluding it, or correcting it; all of which are executed in Fencing. Emanations of the end are perfection, effect, extremity, last, ultimate, tranquility, and the culmination of everything. We consider it as a category, and its variations or differences are of absolute deprivation, particular, detention, termination, perfect, imperfect, potential, and finalized.

ABSOLUTE END
The absolute end, or end of absolute deprivation, comes in two ways: by destroying the subject or subduing the instrumental cause, which is the sword, with a concluding movement. The end of particular deprivation occurs when we prevent an injury by moving aside, diverting, or subduing the opposing sword, remaining free for other actions. The end of detention is the concluding movement made to stop a descending sword strike at the beginning of its motion, when the fencer, being in a close distance, uses the left hand for the concluding movement without the need of his sword. The end of termination ensures the opponent can’t choose a proportionate method for any strike. The end of diversion is to divert the opponent’s sword when it comes to strike or, if stationary, to move it aside to strike him. The perfect end is when the fencer strikes his opponent and remains defended, or remains defended without striking if his decision was to use a common deprivation method. The imperfect end is when one strikes his opponent and is also struck by him. The potential and finalized end of movements is the extreme that each belongs to according to its kind: the high to the forceful movement, the low to the natural, the sides to the remiss, the back to the strange, and the front to the accidental.

FINITE
Finite is what has an end and is the opposite of infinite. The actions of the fencer, in the material aspect of Fencing, are always finite because the forces are finite. There’s an end of termination, and this is considered in relation to the Agent, or the recipient, or the end viewed as motive or intention. Regarding the Agent, for instance, if the fencer conveys a limited thing to another, marking an end where it was truly the beginning of Fencing and its contents, this is an end of termination. Concerning the power of the fencer, it is also an end, as he set a limit to his power, having the ability to go beyond. And in relation to the student, who is the recipient, if their capacity can accommodate more, what’s acquired or the boundary they don’t cross, is viewed as the end of termination. If the intention was to communicate more by the Agent or to receive more in the process, the interruption of not doing what can be done due to various reasons, is an end of termination concerning the end as an intention. And the end of perfection is when something is entirely and perfectly finished. This is even considered in the limited, because if the intention was not to give more, in relation to that intention it reached an end of perfection, even if not in relation to the recipient and the knowledge. The same is considered regarding the power of the Agent, if he communicated everything he knew but didn’t know everything. Here, there was an end of perfection concerning the Agent’s intention and power, though not in relation to the recipient if they had a greater capacity to receive more. However, if they didn’t have that capacity and were filled, it will have an end of perfection concerning what it is, but not concerning what it should be, because then the capacity itself is said to be limited by a poor temperament or disposition of the brain. These factors limit or end the capacity itself, and hence, it’s said to have a limited capacity. The end of deprivation is what makes something cease to exist, like death in a person, depriving them of what was due. This is considered in Fencing, in all actions that deprive the opponent of some desire, ceasing to exist, like an increase makes a decrease cease to exist, blocking, and the addition of free movements. And any difference that’s caused in the operation of the opponent makes the form they had cease to exist, and this is called the end of deprivation, considering them as ceasing to exist.

WEAKNESS
The Weakness of the Sword is its tip, in relation to the other parts of its length

FORM
Form is what gives being to a thing, whether it’s a form of substance or an accident.

FORCE
Force is in two ways: natural and accidental. The first is a virtue present in all things, both spiritual and physical, whether they are animate or inanimate. With this force, each acts out its own purpose, objectifying, animating, generating, producing, conserving, preserving, or corrupting, according to the activity of the active things, and the disposition, the course, and assigned limit of the passive ones. The accidental force, located in the limbs, is what we use to push or to overcome resistance, and with which we alter actions, shortening their duration, and placing the parts of the body that can be seized. In Fencing, we consider it in five ways: operative, resistant, intense, extensive, and reserved.

Operative Force is every action of natural movement, where one sword is placed over another, controlling it. Resistant Force is every action of violent movement, where the controlled sword resists the one controlling it. Extensive Force is when the person communicates the force they have to movements or tricks until it is exhausted, reaching the movement’s designated endpoint, and sometimes going beyond it and cannot be stopped. Intense Force is when the fencer distributes their own force in such a way that they can control any movement before reaching its ultimate straightness. Reserved Force is the same as the intense or moderated force.

GENERATION
Generation, when taken broadly, refers to any production where the Agent brings into the process, giving a new form to the matter upon which it acts. Hence, it is said that the generation of one thing is the corruption of another because, for the matter to receive the new form given by the efficient cause, it is necessary to lose the previous form it had. This loss is called corruption. These new forms, be they in the creation of lines, angles, compasses, movements, desires, increases, aggregations, or any intellectual or material operations, are all products, though from different causes.

GREATNESS
Greatness refers to the fullness that each thing possesses. This is a positive or absolute term when simply considered in any subject. However, if one considers whether its greatness is in relation to another subject, then it’s about viewing majority, equality, or minority. These are relative terms, and the greatness in which they are based will be so. But when considered without relation to another, it aligns with the aforementioned explanation. In this manner, one can consider the greatness of the desire of the Sword, of the arm, of the body, of movement, of increase, of decrease, of intention, of interval, of width, of length, of depth, and so on. This is viewing each thing as it is, without comparison to others. It’s like looking at the greatness of desire in each of these mentioned things, where the desire is limited to more specific things. One can also consider the greatness of desire in general, and the greatness will always be absolute. However, the majority of these great aspects, which is a relative term, will be possessed by the general desire.

DEGREES
Degrees refer to the initial and final parts that are considered in things, which are like steps, where some give way to others. These can be either of quantity or of perfection. Techniques have degrees of dignity, which is the same as degrees of perfection. Terms have degrees relative to each other, as some are more supreme, either because they encompass more or because they refer to the substance and essence, which represents their highest dignity. In each, there are these degrees in relation to the lowest and highest of each that has been considered, and in bodies, swords, movements, and the rest. Sometimes, attaining these degrees is perfection, while at other times it is about diminishing them, but it’s always about gaining degrees of power.

Degrees of Profile are the lines and divisible parts that are considered in the breadth of a man, from the right vertical to the left.

Graduation of the sword is divided into four equal parts, from the pommel to the tip.

Degrees of Strength in the Sword refers to each of the parts into which it is divided, and this applies to all weapons.

HABIT
A Habit is described as something acquired through many actions, and it facilitates operations. This is a very general term that can encompass others, such as the habit of thinking, the habit of desiring, the habit of acting, the habit of joining, the habit of moving, the habit of generating new forms, and so on.

WOUND
A Wound is the highest universal or category and doesn’t necessarily refer specifically to a slash, a reverse blow, their variants, a thrust, or its differences. It encompasses any rupture in the human body, made with any instrument like iron, stone, or wood, and their likes. Strictly speaking, a wound is not a technique, but rather the result of one. Although in common usage and for the sake of understanding, we make different considerations about it. We describe wounds as being inflicted before time, in time, and after time, which are of the first and second intention, of a full circle, half-circle, quarter circle, greater and smaller portion, of circle by the jurisdiction of the arm, the sword, and the profile. Within these categories are included the vertical, diagonal, decreasing, or tangent slash and reverse blows.

Wound before time is executed before the opponent starts any technique or voluntary movement. It’s said to be of the first intention. Wound in time is executed when the opponent begins some movement, before the end of the technique with which they intend to offend. It’s said to be of the second intention. Wound after time This is executed when the opponent has made all the movements of their technique, or is in the midst of the last of those movements. It’s said to be of the second intention.

Full circle wound refers to a slash or reverse blow of any kind that, in its execution, forms a perfect circle (as much as an arm can allow), connecting the end of the movement with the beginning. The same applies to the thrust, which, due to the sword being free, is executed from the inside or outside, making it a full circle.

Half circle wound refers to a half-slash or half-reverse blow, as well as the thrust, which in execution is made in a semicircle in any direction and from any side considered.

Quarter-circle wound is the thrust executed above the opponent’s sword on the right vertical line, with the sword tip traveling no more than a quarter of the circle considered across the chest. Even though other wounds might follow this composition and limit, only this one is given this particular name, much like a metonymy. A wound that covers more than a half-circle but does not complete a full circle is described as covering a greater portion of the circle. A wound that extends beyond a quarter-circle but does not reach a half-circle is described as covering a lesser portion of the circle. A Wound by the jurisdiction of the arm is executed from the infinite right line of the opponent, inflicted after time on their right side and upper right angle, which is above where the arm begins, without reaching their sword. A Wound by jurisdiction of the sword occurs when, through the sword, one enters and exits the technique, either from the inside or the outside, always controlling it.

Wound by the profile of the body is when, having gained advantage over the opponent’s position, one strikes on the diametral lines, or left collateral, or on the vertical of the same side, leaving the opposing sword free because it’s too distant and out of reach. Sagita thrust wound is the one that’s executed against the natural, remiss, or violent movements that the sword makes when it’s poised to slash, reverse, thrust, or to escape its confinement. Instantaneous wound is the same as the sagita thrust, it’s named this way because of the swiftness with which the wound must be executed and then return to a balanced position to avoid danger. It emphasizes the speed required, as nothing really happens instantly without any time passing. Permanent wound is a situation where the right-handed fighter can continue inflicting damage without the opponent being able to do anything, by any means, either to attack or defend, nor even to drop the sword to flee, as if they were tied up by their hands and feet. Diagonal thrust wound is the one that’s executed on the diagonal line of the square considered on the opponent’s chest, when the sword is pulled from the oppression placed by their adversary, and it is done with a concluding movement from the outside, and it’s also done with diagonal deviation. Vertical slash wound is the one executed on any of the vertical lines, descending straight down. Vertical reverse wound is the one executed on any of the vertical lines considered in the human figure. Diagonal slash wound is the one executed on the diagonal line that crosses the square considered on the face, or on the left side’s diagonal that touches on that side. Diagonal reverse wound is the one executed on the diagonal opposite to the slash, both on the face and on its right side. Tangential slash wound is executed on the tangential or cutting line that’s considered in the larger or smaller square of the human; and the reverse of the same kind, on the opposite line of the back or on the nape. Half-slash wound is executed on any of the diagonal lines of the squares considered on the face and its left side. Half-reverse wound is executed on any of the diagonal lines of the face, opposite to those of the half-slashes: they are also executed on the arm, inside and outside.

EQUALITY
Equality can be considered at the same time or at different times. If at the same time, it can either be at the beginning of the operation, in the middle, or at the end. If at the beginning, when taking a stance, there can be equality, though many things must converge for this equality to be complete: equal arms, equal instruments, equal strengths, equal speeds, equal bodies, and touching points, equal correspondence, equal foot positions, equal angles. From these equalities, equal effects can arise in actions, so no one would be deemed a skilled swordsman, because to be one, there must be an inequality with the opponent from the beginning, always being superior, not equal. If in the middle, when the swords are engaged, equality is even harder to achieve, because in addition to the aforementioned, the touching of the swords must involve equal parts of the instruments, and the engagement must be of the widths or depths. If width were joined to depth or edge (which are the same), equality would cease. It’s essential that one sword isn’t submissive, nor the other dominating because that too would end the equality. The tips and guards must also be on the same plane, and there must be equality in the angles they form. Since movements and changes of position make this impossible, it’s said that achieving such equality in the middle at the same time is unattainable. At the end, equality should also be avoided because if the results were equal and these results were wounds, they wouldn’t be skilled swordsmen. If there are no wounds and the focus is merely on neither party being injured, then there’s equality in not getting wounded. But in this equality, one can still be superior to the other, considering the intention. If one’s intention was to strike and the other’s to defend, the defender is superior, having achieved his intention and thwarting the opponent’s, so there isn’t true equality. If equality is considered over the different times that occur in the course of a duel, it takes on a different perspective, seen in repeated actions, either of opposing or varying types. For example, if one makes a diminishing movement and the other counters by increasing, then the first diminishes again, and the second increases; in this back and forth, there’s equality, but at different times. The same is seen in free and engaged states during engagement and separation. In other differing or diverse situations, equality can arise, seen as resulting from different times. For instance, if one opposes a spontaneous movement with a natural one, and to the natural movement, the other opposes a lax one. Similarly, if to the movement of repositioning, be it violent, spontaneous, or natural for wanting to strike, they oppose a step and the other things involved in the beginning, middle, and end of tactics, to counteract the means chosen by each swordsman. If this persists such that neither party strikes (even though both intended to), then there’s considerable equality in opposing, continuing, arranging, differentiating, preserving, choosing, recovering, corrupting, and defending, and in the intention to strike. Equality of positions is when one swordsman opposes the curve or transversal of the other on the opposite side. The equality of aspects was discussed in the letter A.

IMITATION
This is a relative term because it has to be in relation to another. Acting through imitation is not to act scientifically, nor to have a fundamental understanding of the matter. For this, one must seek the most perfect; and in choosing, there can be great deception, as one is prone to believe in something that isn’t born from a directive or advice, or advice from someone who can neither deceive themselves nor deceive us. This is exclusive to God. And even if one chooses the best, it’s a significant weakness to rely on someone who could deceive, not sharing the perfection they know, and assuming they are so perfect that they share without deceit. If one learns through imitation, they can only know specific things without understanding the reason behind their actions; otherwise, it wouldn’t be imitation. While universality can arise from specifics, one can’t attain it through imitation, because the specifics are infinite. Any minute difference can change a particular thing, denoting a new vision, which, even if not essential in substance, can be accidental in quality or circumstance. Since any of these things can make an individual different from what they were before, it can produce different effects. Therefore, there’s a lot to learn about a single particular through imitation. Hence, no swordsman, no matter how great, can have acted on every specific detail that needs action. Thus, they encounter new situations to address daily. But if they possess the universality of the Art, with general precepts encompassing infinite specifics, it gives them knowledge to act on every occasion, unhampered by what will undoubtedly hinder someone who acts through imitation. However, we don’t dismiss the method of learning by imitation. Even if one lacks comprehension to understand scientifically, the Art has found this method to elevate even the most unrefined, making them superior to what they once were, and more potent than those who neither know scientifically nor by imitation. We merely state that compared to a scientific swordsman, the imitator will always be far inferior. Those who are truly at fault are the ones who, having the capability, inclination, and time, avoid undertaking such a heroic task simply to avoid effort.

INSEPARABLE
Inseparable is a quality or accident attached to the subject, uninterrupted by time, for as long as the subject endures. This union is properly called inherence. The line is inseparable from the angle; the angle is inseparable from the arm and sword when in combat. From the body, shape and dimensions are inseparable. For a fencer, the skill is inseparable, or they cease to be a fencer. Intention is inseparable from the fencer; such that, if they act without intention, they cease to be one, and so it is for the rest.

INSTANTANEOUS
Instantaneous refers to something of very brief duration, in which the fencer cannot persist. Not because anything material can be done in an instant but due to its extreme brevity. In the same inseparable concept mentioned above, this is verified, because although acting with intention is an inseparable quality of the fencer; acting with this or that specific intention can be instantaneous, just as changes in forms that arise and corrupt in any battle are. The more instantaneous these changes of forms are, and the change in the corresponding particular intentions, the faster the understanding, and it demonstrates a more perfect skill.

INTENTION
Intention is the will directed towards a certain end, or it is the end for which the will moves. Thus, one might ask: what is the intention of the one who adds, of the one who increases, of the one who diminishes, of the one who opens, of the one who accompanies, of the one who abstracts, of the one who shortens, of the one who attacks, of the one who waits, of the one who alters, of the one who assists, of the one who cuts off, of the one who coincides, of the one who opposes, of the one who concludes, of the one who contrasts, of the one who corrupts, of the one who disturbs, of the one who breaks, of the one who repeats, of the one who unites, and so on for others.

INTERIOR
Interior is a hidden and concealed virtue. Here, we’re not discussing moral virtues, but natural things that possess this quality to produce their effects and imprint their forms. To uncover this virtue, one must be very skilled, because in this case, the exterior that is seen corresponds to various things. If the exterior only alluded to one thing, then the interior would be as exterior as the exterior itself. If the fencer recognizes all the actions that can be made from any stance, he observes all of them. Thus, none are hidden from him, and only the intention of the opponent regarding the chosen method remains concealed and interior to him. With a hidden virtue of the same nature, he prepares for the remedy. For this, it’s necessary to know the purposes that any stance might address. To make one’s intent more interior and concealed, one often assumes a stance such that it doesn’t immediately indicate its purpose but rather entices the opponent to strike at the exposed part. Knowing that approaching that part will be at a time when he can act on his hidden intention. However, this strategy is for those with little knowledge, upon whom such deceptions can work.

INTERMEDIATE
Intermediate is what is found to intervene or can intervene between the beginning and end of anything that has parts; and the same between the start and end of the beginning, the start and end of the middle, and the start and end of the end. If the action received a comfortable division, any of the aforementioned parts could be further subdivided: there are intermediate appetites, intermediate increases, intermediate actions, intermediate additions, intermediate accidents, intermediate intervals, there’s an intermediate in appetite, and there’s an intermediate in the increase, there’s an intermediate in the action, there’s an intermediate in the addition, there’s an intermediate in the accident, and there’s an intermediate in the interval; and so, it can be considered in other things.

INTERVAL
Interval is the duration of time that exists while one thing is done, or the time from one action to another; and this interval of time is the measure of all things that are done, whether they are material or imagined. These latter, although they cannot be thought without an interval of time, must be so swift and anticipated to the future act that, as much as possible, there is no interval from action to action but continuity, without giving the opponent time to think about what to do; because the time, or interval, that the fencer takes to consider what to do from any position, is common to his opponent, who can act before him and bring his intentions into confusion. From particular appetite to particular appetite, there’s an interval of time because the act of the will at the same time cannot work on two things, nor can imagination think of them unless successively; and the time from one to the other must have an interval unless two different types of increase are joined in one action, such as material increase and virtue; but even then, although they occur at the same time, considering them as they are cannot be without interval. The same applies to actions, additions, and the rest. The common interval is the line of the Diameter where the two combatants stand when they are equal in bodies, arms, and swords. The particular interval is the line of the Diameter of the particular circle chosen by the fencer, in which his opponent has no part, and the excess of the larger sword over the smaller.

JURISDICTION
Jurisdiction is a power that gives order to its own subjects; and this jurisdiction can either be considered in the free cause, without obstacles, or it can be considered in the cause that is subject to or limited by some accident, or resulting from the actions of its counterpart. When considered in a free cause, it’s ordinary for any part to have greater jurisdiction, and the reason is that there’s no opposition to impede it. If the cause is subject to or limited, the power is limited; thus, the jurisdiction that belonged to it is suppressed and limited to less. There is also resultant jurisdiction or power, which comes from the disordered actions of the counterpart, giving it jurisdiction it wouldn’t have if it acted with knowledge. The parts that make up a man have partial jurisdictions, and it’s necessary to know what belongs to each: the jurisdiction of the feet, the arm, and sword, and in the arm, the elbow’s jurisdiction, the wrist’s, and the shoulder’s, the body’s jurisdiction, the sight’s, and its visual lines, the whole’s jurisdiction when all its parts work in the proper order, and the whole’s jurisdiction when some part fails in the operation it was meant for, or in the way it should’ve been done; the intellect’s jurisdiction, which regulates actions and recognizes defects; and ultimately, there is no term that doesn’t have jurisdiction: the jurisdiction of appetite, of increase, of the abstract, of action, of aggregation, of the absolute, of accident, of the appropriate; so there’s jurisdiction of appetite, jurisdiction of increase, jurisdiction of the abstract, which has it over its inferiors, jurisdiction of action, jurisdiction of aggregation, jurisdiction by accident or of accidents, appropriate jurisdiction or of the appropriate medium: thus, the term jurisdiction is very universal since it encompasses universal terms.

Jurisdiction of the arm, in addition to its entire length, is the upper right angle formed at the touch or joint of the shoulder, like the neck, when it stands upright in an acute angle. The jurisdiction of the sword is defined by its length, without considering the arm. The profile’s jurisdiction is everything from the straight vertical line to the left.

SIDES
Sides are those considered in relation to a fixed place, where one puts their consideration or sight. For example, in swords, when angles are formed by looking at their point of contact, one observes if the four angles formed from the point of contact have equal sides, or if they are short or long. From this observation, one gains knowledge if they can be occupied, if they hinder future action, if one can remain in the aggregation of swords while the other follows, if, on the contrary, it does not want to, if it subjects even if it’s superior, or if it becomes subjected by adding the weakness of its sword to the strength of the opponent. There are also sides concerning each fencer, with respect to the place they occupy, since they can move to one side or another, for which there are measures. In swords, there aren’t only sides regarding their length, as mentioned, but also concerning the movements that one can or should make to one side or another, depending on where they find themselves. When making an aggregation of swords, there are sides; and if there is an increase or decrease, the sides change because the quantity is different, and the quality of the power is different. The sides must be formed by the fencer with intention, not by chance.

A side of the circumference (in a commonly understood way) is that part corresponding to the right or left side of a man. The side of a triangle, quadrangle, or square is each of the lines that make up such a figure.

LATITUDE
Latitude: this term is explained under the section Quantity.

LIBERTY
Liberty is the quality of the choice of means, and its opposite is necessity; and liberty is considered when the sword is not subjected with natural movement, taking this narrowly, as has been mentioned so far. But speaking of what fits within this term, it is certain that there is no free cause, having an opponent affirmed; and this even at the beginning of the battle, because if he affirms by occupying the right angle, which has the longest reach, being the longest line of the circle imagined between the two combatants, he doesn’t leave me the freedom to occupy it, if both have equal skill, because it’s easier to maintain than to acquire; and if he affirms revealing the inner part, he doesn’t leave me the freedom to go on the outside if he tries to maintain that posture: he’ll do it more easily, as said, moving over the center, whose motion cannot win by going around the circumference of the superior circle: and the same will be if he were to affirm revealing the outside, for the same reason, I won’t have the freedom to act on the inside if the opponent doesn’t want; and I will only have freedom in the attempt, or in the desire, but absolute necessity in not achieving: and although it seems that the opponent freely performs all the mentioned actions; but considering that the will has contracted to a particular, such as being attacked from outside or inside, to maintain that intent; wanting and opposing it, the motions on the center that have been mentioned are necessary, because with others he couldn’t achieve it: so he had freedom in choosing, and necessity in the way of acting, so that I wouldn’t achieve the opposite of his intention; and in this struggle (if it perseveres) which is a preamble to the battle, there’s great equality, because if the opponent manages not to go outside, which is what I want, I prevent him from going inside, which is what he desires: and if he deprives me of one act of will, I deprive him of another act of will; and in this, neither his will nor mine have freedom in achieving, but only in attempting. All this is in the preamble of where to attack the opponent; but then in the course of the battle, one must consider, in any position the opponent is in, that it limits the Diestro’s power, so that he cannot freely choose among all the tricks, and means of the Skill, which immediately seems to him; and the more it limits the power, the more it deprives him of the freedom to choose, as he has no jurisdiction over that posture. And speaking of the Atajo, which is what seems to most contradict this, it is said that there’s subjection: the Sword that is below is subjected, and the one that is above is subjecting; and what we say is that the Sword that is below is subjected, and the one that’s above is also, if there’s consistency; because the operation of the one above is that the lower one does not rise; and the operation of the one below is that the superior one does not descend, which is why they are consistent: and the freedom that the superior one has to rise, and move away, the inferior one has to lower, and move away; and the freedom that the superior one has to follow the inferior that descends, preserving the aggregation that it had with it, impeding its freedom to stop the movements wherever it wants, the same has the inferior, if the superior wants to rise to preserve the aggregation, and exclude it from the end where it directs its action, depriving it of the freedom of that act: so it is concluded that in the course of the battle between two Diestros, one never has total freedom, because it is deprived, and impeded in many parts; but speaking relatively, most of the time one is freer than the other, and when there is no aggregation, there’s more freedom: and freedom is also said in relation to what remains in what can be chosen; and the more the Diestro deprives his opponent of common freedom, it’s a more perfect way of acting, especially if he limits him to the necessity of only following one path.

LIBERATING
Liberating the Sword with a thrust is when the fencer (having previously diverted) passes their own sword, through a portion of a circle, below the other, until they leave the tip directed towards the point of greatest reach. Liberating the Sword twice is the same as making two semicircles, one from the inside to the outside, and the other from the outside to the inside, and vice versa.

LINE
A line is understood in two ways: Mathematical or mental, abstracted from matter, or Physical and real, objectified within it. The first is imagined as the flow of an imagined point; thus, both are invisible and indivisible. The Physical one is a quantity divisible solely by its length. It arises from the flow of the point and consists of many points continuous to it, using two as its extremities. It is the second part of a body, considering the first part consists of two points. Geometers consider lines in three ways: finite on one side and infinite on the other, finite on both sides, and infinite on both sides. In Fencing, where we use both types in various ways, the line serves as a genus, and we consider as its species or differences: the Cateta or Perpendicular, Circular, Collateral, Curved, Demicient, Diagonal, Diametral or common Diameter, particular, superior, inferior, Eliaca, Spiral, Finite, Infinite, Infinite-Finite, Physical-Flexible, Intellectual, Intermediate, Mathematical, Material, Mixed, Horizontal, Straight, Vertical, Hyperbolic, Ellipsis, Contingency, Touch, and Parallel lines. All of these will be explained in order as species of the Genus of Line that encompasses them.

Cateta Line, also called Perpendicular, is a straight line that falls onto another straight line, making the angles on both sides equal. In Fencing, it is the arm at the joint where it attaches to the body when held straight, making two equal and right angles, one below the arm and one above, at the neck. Circular Line is that which, after making a full circle, joins the end with the beginning, within which the circle is contained, and this is called the circumference or Periphery. For Fencing, it is considered greater and lesser, being the reverse and the cut. The human circular line touches at the feet and hands, with the legs and arms outstretched, and also made by the body when leaning far forward. The lesser circular line is considered in the chest or face. The Collateral Line in humans is considered at the origin of each of the arms and the chest, which perpendicularly goes down to the ground. Curved Line is the one that travels twisted, not situated evenly between two points, such as the turn of the circumference. Demicient Line is drawn in the parallelogram space, having taken on the longer sides, outside the angles where the diagonal should be, two equal quantities. Diagonal Line crosses the square and the rectangle or parallelogram from one angle to another, dividing them into two equal parts. For Fencing, it is considered in the square imagined on a fencer’s chest or face, where the cut and reverse of the species are executed.

Diametral Line is the one that, passing through the center of the circle and applying itself to its extremities of the concave circumference, divides it into two equal parts and is the longest that can be drawn within it, the other lines being parallel to it. The Diametral Line in a human is the one that passes through the middle of the forehead, mouth, and chest, and drops perpendicularly from the head to the feet. We also refer to it as the Vertical Line of the chest, of the sword, of the right and left sides, depending on which of the four mentioned parts it is situated. The Common Diametral Line divides the circumference or circle, imagined between the two combatants, and touches directly on the heels of both their right feet and corresponds to the heels of both their left feet when they assert themselves on right angles. The Particular Diametral Line is the one that, with a particular circumference, separates the fencer from the common one, on either side of it, in which the opponent has no part. The Upper Diametral Line of the circle, considered between the right shoulders of the two combatants, is when the arm and sword are asserted in a right angle. The Lower Diametral Line is the circle imagined on the ground between the two combatants and where the straight step and the increased step are given.

Eliaca Line is the one that encircles a column; and in Fencing, it is the one that encircles the sword with a movement that the sword makes against the opposite one, in the manner of a spiral. This is to make a revolution, starting at the tip of the sword and ending near the guard, as in the two general weaknesses, below or above the strength when they start to tighten or in a cross line. The Spiral Line, which some call Eliaca, is the one with which, in the manner of a snail, the sword encircles the opposite one, spinning around, without returning to the point where it began, until it reaches the body of the opponent where it ends.

A finite line is one that is contained within two endpoints, such as the Diametral in a circle, the Diagonal in a square, or the side of any figure. In Fencing, it refers to the sword of a combatant that touches the body of his opponent, making a right angle with the right arm and the right collateral line, so that the arm serves as one side and the tip as the other. An infinite line is a straight line that touches the circumference only at one point. It is called infinite because it can be extended infinitely in both directions if there were an infinite quantity. For Fencing, it is considered in two parts; the first touches the common circumference of the heel of the right foot, and the other touches the proper circumference and they serve for the trembling steps or tremors: the first serves the right foot, and the second serves the left. A line that is both infinite and finite is one that is contained by some endpoint on one side and can be extended or elongated on the other, like the sword in the hand, which cannot be elongated on the handle side, but can be infinitely extended from the tip if its quantity or material allowed.

A Physical Line is a material line that is tangible and can be divided because it is contained in matter: it is also called real and material. A wavy line is one that, on a flat surface, winds and turns, like a river on its journey or a snake on its path. In Fencing, it’s used to divert the thrust that’s aimed above the sword at the chest of the fencer. An intellectual, mental, or abstract line is the same as a mathematical or imaginary line. The Hypotenuse Line is the side of the right triangle that is opposite the right angle. In Fencing, it’s applied to the opponent when the arm is bent at the elbow, which in common Fencing is called Curled Posture or Iron Gate. The fencer, by the position of the sword, joins this posture, applying the force of his sword to the opponent’s weakness, striking him in the chest or face, thus forming a triangle with both swords. The arm and sword of the fencer is the Hypotenuse, opposite the right angle made by the opponent’s bleeding arm. The intermediate line is the one considered between any of the collateral lines and the diametral of the chest. It causes the right angle in the circumference and is also called transversal, falling between the diametral and a quarter of the circumference.

A Mathematical Line is an imagined one, which cannot be divided or even touched with the imagination because it is abstracted from all matter. Its understanding is crucial in Fencing, so much so that many times in some situations one couldn’t be defended without it. When combined with the Physical Line in the right way, they both create defense and offense with wonder. A Material Line is the same as the tangible Physical Line, as it exists in matter. In Fencing, this refers to the Sword, Dagger, Montante, and any other pole weapon. The Horizontal Line is the circular one that divides the lower hemisphere from the upper; and in man (as a microcosm) it bisects him in terms of his length. A Straight Line is the shortest extension from one point to another, the smallest of all lines with the same endpoints. In Fencing, we consider the Sword, Dagger, Montante, among others. A Vertical Line is one that directly corresponds to the head from the zenith; and in man, for Fencing, it goes down from the head to the feet. The Direction Line in the body is what we call the line that falls directly onto the foot supporting him; if balanced equally on both feet, we consider it to fall in the interval between them. We also call Direction Lines those that can be drawn unobstructed from one combatant to another. A Hyperbolic Line is one that is similar or analogous to a hill, or more precisely to a heap of wheat. It is used in Fencing in the description of the steps, both in the curved step mixed with trembling and strangeness, and in the transverse mixed with trembling and strangeness, and in the revolutions of the Sword. An Elliptical Line resembles an oval shape, divided into two parts with a diametric line. In Fencing, we see it in man, in the arch made by the thickness of the body and chest, since the back is almost flat. A Contingency Line, or Tangent, is a straight line that touches the convex circumference of a circle at one point. In the shoulder, it’s the one that crosses the chest, from the origin of one arm to the other, touching the circumference of the circle that is considered there. The Touch Line is when one of the swords manages to strike, touching one of the lines considered in the body of its opponent, which is also called the touch point.

Parallel Lines in Fencing is when both swords are equidistant on all sides from each other. If both combatants moved at the same distance, their swords would never meet.

LENGTH
The explanation of Length is in the same place as Latitude.

PLACE
The Place is where the fighters and swords are situated, as well as the proximity they can occupy. Contemplating this, before taking action, can be of significant importance to understand what potential can be achieved based on the location. Often, the position itself becomes the potential, restricting the freedom of choice and compelling action out of necessity. There are places of Origin, Through, and Destination. The place of Origin is occupied by the fencer and his arm, from where he intends to perform a maneuver or where it emerges. Through is the space between one fencer to another, through which he directs his sword, either based on the plans considered or with a particular aspect. In the Destination, the touchpoints come into play, and their considerations: whether the fencer occupies a rightful place or not, if the place is suitable for occupation, and if it is more contingent or necessary to occupy it. This can be understood by the size of the place because if it is tiny or indivisible, the outcome will have less necessity and more contingency, such as occupying the right angle on the opponent’s chest, which should be the longest line. Given that this line, in our imaginary circle, is considered indivisible, it becomes challenging to occupy. The wound of the quarter circle is in such a narrow place that it’s hard to occupy. This can be rationalized by understanding that as the spot where one tries to direct the sword has different parts of length – some at the beginning, others at the end – which have to be occupied along a physical line (and in a specific time frame). Given the narrowness of this place, even if the beginning of that spot is occupied, the opponent can divert the sword in the middle or end, pushing it out of that place, making it hard to achieve the intended action. Therefore, whether it’s a single touchpoint or the Through space, achieving the intended result becomes highly contingent. If both the Through and Destination places are both narrow in a single maneuver, the difficulty multiplies. These two factors converge in the wound of the quarter circle, making it more challenging than the right-angle wound. While no body can avoid occupying space, it’s essential to recognize the nature of the places being occupied, whether a place is chosen solely for defense or for both defense and offense. In this case, one must consider if the occupation is meant to be permanent or temporary. In the space occupied by the swords, it’s crucial to discern whether to occupy a place by extending or reducing, with or without addition, if it’s a place set up for intermediate action, or if it’s meant for direct and immediate action. Based on where they stand, the measurements of the distance between both tools or their tips, up to the touchpoints on the opposing bodies, need to be considered, observing where they need to pass and the space between. The amount of movements to be made and which will occupy the chosen place first need to be decided. Not just the occupied place (Destination) but also the intermediate spaces (Through) and the touchpoints need to be assessed for their security or danger. In another sense, a place is where things are positioned according to their nature. Or, a place can be a surface that surrounds and immediately contains the internal parts of a body. For Fencing, this is considered in the ways that follow: A place, or the end of elective or intentional choice, is where the sword is positioned for a wound, deflection, or subjugation, but hasn’t reached the spot where, according to the nature of the movement, it should end and rest. A place, or the ultimate end, is any of the extremities of the straight paths, where movements end, each according to its type, and its inherent or incidental action.

MATERIAL
Material, we have discussed this elsewhere, so it has already been explained.

MATHEMATICIAN
A Mathematician is a term that encompasses many categories, and the primary ones we use in this context are Geometry and Arithmetic. One contains measurements and the other numbers, and they are the main foundations of the art of fencing. However, due to their similarities or resemblances, we also refer to Astrology, as far as it includes aspects, and it is also relevant as it can aid a fencer’s understanding of Physiognomy. From music, we also draw upon the concept of consonance in many actions, without displeasing the ear, which perceives them better than the eye.

MAJORITY
Majority refers to advantages in any of the aforementioned things.

MEASURE
We will discuss measure when we explain the medium.

MEANS
Means. A mean is an entity through which the end influences the beginning, and the beginning reciprocates to the end, sharing equally in the nature of both. In essence, it is the likeness of the influence and reciprocity of the two extremes that it represents, constituting the substance of both and marking the union of form and matter. There’s a mean of union, mean of measurement, and mean of extremes.

Mean of Union is the link that binds or connects two things, or the union of them.

Mean of Measurement refers to the standard by which any quantity is measured, such as the rod, the span, the arroba, the pound, the azumbre, the quart, and the pint. The mind measures the quantity of virtue, considering between two or more, which has the majority, to whom more rules and reasons apply. Often where there is greater material quantity, virtue is lesser, which the mind also measures. Virtue is also a mean of measurement between two things, although in this, the mind plays a role as it makes a judgment about what the eye presents. The sword is also a mean of measurement. Mean of Extremes is that which equally distances from the two, or many extremes, and that which makes them known, like the common circle in the middle of the two combatants, and the center of the circle in between extremes, in relation to the points of the circumference, or that which partakes of two natures: like lukewarm water, or the compass, and mixed movements, which also share two natures. In the art of fencing, it is considered a genus and is differentiated by species or differences into common means of the combatants, common of movements, of common deprivation, of particular deprivation, dispositional, privative, of proportion, proportional, proportioned; and this is further categorized as absolute, particular, proper, appropriated, transferred, and universal or supreme.

Common Mean of the Combatants is where, after having broken the mean of proportion, they remain in equal disposition. It’s called not a proportioned mean, but a common distance. Common Mean of Movements Violent, Natural, Remiss, and Strange is the position where the sword stands at a right angle. Common Deprivation Mean is chosen by the fencer to not be under the subjection of the sword, or while gaining degrees to the profile. Dispositional Mean can either be appropriated by the opponent, or chosen by the fencer to be unassailable, and to attack if necessary. Privative Mean is precisely where the fencer makes it impossible for his opponent due to the instrumental cause, which is achieved by means of some shortcuts. Proportional Mean is when the bodies are upright and the arms are fully extended, this is to measure the swords, or any other weapon, ensuring the opponent’s weapon does not exceed the guard of the fencer’s sword. Intermediate Proportional Mean is a distance that lies between the means of proportion and proportioned, approached by any side of the circumference. Determined Proportional Mean is the specific distance required by any kind of technique from where it is executed, according to its kind, and the length of the weapon that is to execute it, and the one that is to receive it. Absolute Mean is one that has no relation to another; and in fencing it is that from where the fencer can execute all techniques and strikes within his capability, without the opponent being able to stop him. Particular Mean is a necessary position that the fencer chooses, from where he can only execute one of the five particular wounds, and no more. Own Mean is chosen by the fencer, independent of his opponent, and without the opponent having a say in its choice. Appropriated Proportional Mean is offered by the opponent with his movements and steps to be able to strike or make a concluding move. Transferred Proportional Mean is when the fencer takes it away from his opponent and claims it for himself. Universal or Supreme Mean in fencing, this is from where a concluding move is made on the opponent’s sword, with all the requirements of the Art, depriving him both of the instrumental cause and the efficient one.

MOVEMENTS
Movement is an act of the motivating power that man possesses, both as a whole and in his parts, to move towards himself or away from himself. Thus, it’s an imperfect act that is perfected in its end and rest. In fencing, we make various considerations with the distinction of natural, violent, accidental, circular, strange, oblique, mixed, remiss, cardinal, simple, compound, reduction, augmentation, diminution, diversion, corruptive, generative, concluding, and underway movements.

Natural Movement is the movement of the sword that descends directly to its center and is one of the cardinal movements. Violent Movement is the one with which one rises to the top from any term; and the second act for the cut or reverse, if free; and third, if it’s subject and one of the four cardinal movements. Accidental Movement: It’s with which some chance is removed from its center. An accidental movement is the one made with one sword on another, to move it, of whatever kind it may be. Accidental movement is the change from one place to another, forward, in a straight line, and one of the four cardinal movements.

Circular Movement is the one that perfectly, as much as the material of the arm allows, constitutes a circle, joining the end with the beginning, which is the formation of the cut or reverse of any kind. Strange Movement is the one made by the arm moving backward, moving on the shoulder joint or bending the elbow joint, and the one that one sword makes with the impulse of the other, of whatever kind it may be.

Oblique Movement is the mixture of natural and remiss movements, with which, from either side, it descends and moves away; and conversely, rises and moves away. However, if it only moves from one side to the other parallel to the horizon, without rising or descending, it is horizontal. Mixed Movement is the one that consists of more than one type.

Mixed Violent and Remiss Movement (in the person, their arm, and sword) is when it rises and moves away to one of the sides. Mixed Natural and Remiss Movement is when it descends and moves away.

Mixed Natural and Strange Movement is when it descends and the arm bends; and so with the others, where with a single action, it partakes of more than one straightness. Movement of Union, or Aggregation of Weapons, is when they together descend and ascend, move away, or return to the center, taking its name according to the natural kind, violent, remiss, or of reduction, with one aiding the other. Remiss Movement is when one moves away to any side, and the first act for the interception or reverse if it’s free, and second if it’s subject, and one of the cardinal ones. Cardinal Movement is the one that begins at one of the four main points, straight lines, or positions, that are considered in the person from top to bottom, one side or the other, and the front. Simple Movement is any of those made without the intervention of another. In fencing, we consider as simple the one that falls directly, the one that rises, the one that moves forward, the one that moves backward, the one that moves away, and the one that returns to align itself at a right angle, without mixing or combining with another. Compound Movement is that which is not singular because it partakes of another or others with which it mixes or combines.

A Movement of Reduction is with which from any of the sides the sword returns to the center and the right angle. A Movement of Increase in swords is one in which, having restraint or aggregation between them, one rises from lesser degrees of force to greater ones, and the internal angle then becomes of larger sides. A Movement of Decrease is with which the subject sword or only aggregated descends from greater degrees of force to lesser ones, and the internal angle of the agent becomes of smaller sides. A Movement of Diversion is with which the sword that is subjected moves away from the one holding it when, over it, it makes an accidental movement for a thrust, removing the movement in via. A Movement of Corruption is caused when the fencer thrusts and the opponent diverts, corrupting that form. Generative Movement is understood as the one that is caused when, having thrust and been diverted by the opponent, it generates or aids the fencer in the initial movements for the formation of a reverse or cut. Movement of Conclusion is to subject the guard of the opponent’s sword with the left hand, destroying the acts and tricks that are under its jurisdiction, and deprives the power to repeat them, sometimes removing from the hand the instrumental cause, and others (if appropriate and necessary for total defense) finishing with the efficient.

Movement in via is when the tip of the sword that is subject or subjecting directly points at the opponent’s body; so much so that with only the accidental movement it can wound with a thrust. Killing the movement is when, to the one the opponent begins, another of its kind is applied (if it allows mixture), bringing the sword to the end of the straightness that belongs to it, and when the natural movement opposes the accidental and violent one.

NATURE
Nature is the principle of movement and stillness in the subject, without there being priority in origin or distinct time; although there is a natural priority, such as being and duration, which according to nature, first considers the being, and its natural quality is duration, which is as ancient as the being of anything: and in this way, the figure is considered to be the nature of quantity. And appetite can be the natural quality of growth, taking growth as the subject; since it is not possible for there to be an increase in anything, to which the nature of desire does not also accompany, depending on the increase; and conversely, the increase can be the nature of the appetite if the appetite is taken as the subject: and thus one can reason in the other principles.

NECESSITY
Necessity is what is precise and cannot be missing in things or actions: there is a necessity in which one voluntarily places oneself to achieve the act that determines their will, like if one decides to make a cut and the sword is on the lower plane, there is a necessity to make a violent and natural movement, among others that intervene in its formation: and there is a necessity that arises from the actions of the opponent, which limits and constrains in such a way that it becomes necessary to do something specific, which we have discussed above in another term: and this is what is most important for the fencer to know, to put their opponent in this necessity so that they do not act by will, and their actions are not free.

NOVELTY
Novelty is any change for our subject or matter. Any change that occurs in the figure caused by the swords, arms, bodies, angles, places, and the rest brings about a novelty in the powers and in intellectual acts. This is because if one mind desires to make a movement of increase, it is different from the one that desires to aggregate: and the one who defends differs from the one who seeks to injure, in which it differs in terms of the acts, which is the matter it informs; and so it is with the rest.

OBJECT
In fencing, the object is the human body in which wounds are inflicted. Thus, this art is about one’s defense and offense against opponents, if it is precise in relation to it.

OCCUPATION
Occupation of an angle is to place the body within the capacity that exists between the lines that cause it.

Occupation of a line is when, in any of the things considered inside or outside the common or particular circle, the foot is placed directly on top, without cutting or making an angle on it.

OFFENSE
Offense is a natural offensive impulse, just as defense is a natural defensive and offensive repulsion. This was more extensively explained in the defense section.

OPPOSITION
Opposition: We have discussed this in the term Contrariety. Truly, not all oppositions are made with things that are perfectly contrary to each other. Even though the combatants are contrary and their intentions are, lowering and aiding in lowering isn’t opposing one movement to another, but rather aiding and harmonizing with it with another movement of the same type. The same is true for rising and aiding in rising, moving away and aiding in moving away; but it is to oppose its desire and to thwart its intention. For this, perfect contrariety isn’t necessary, but it is enough to make the action that wanted to produce different. With this consideration, it will be found that angles oppose movements, lines, and compasses; on the contrary, defense opposes offense, which is to oppose the part to the whole, and sometimes the whole opposes the part. In perfect opposition, which is contrariety, this is clearer, hence it isn’t discussed further. Opposition is when one strikes the opponent face-to-face, as much as the disposition of the body’s profile allows. Opposition of angles is when one opposes another of its kind and prevents the sword from making the movement it intended to make from that place. Opposition of compasses is when one opposes another of its kind or different.

ORBS
In fencing, we call Orbs the distance contained between different concentric circles that are considered in the lower plane with the distinction of Maximum Orb, Common Orb, Sword Orb, and Orbs of the means proportioned from the remote and near end, among others. Since in mathematical demonstrations, both universal and particular, we have to give an individual account of these Orbs and their description, no specification of each one is made here.

ORDER
Order is what power dictates in acting, or receiving, communicating, or the term in every kind of cause. This order is found in all the mentioned terms and in those that will be mentioned. The reason is clear because there is power in everything, in each one as it is, and these powers dictate the said order. This order is natural from the power, and they have an ancientness; so, among them, there is no priority of time, although there is one by nature, as we mentioned before. Parts are what compose the whole, be it physical or metaphysical.

PART
Part refers to the arm and the hand concerning the body, which is called the whole. The inner part is the capacity that exists from the line of the common upper or lower diameter to the vertical line of the opponent’s back, on the side of the circumference of the right hand of the fencer and the opponent’s left. The outer part is everything up to the same vertical line, on the side of the circumference of the left hand.

PARTICIPATION
Participation is communion with the opponent’s actions. So, in what the opponent chooses as his particular means, the fencer must see what there is in that action or means that can benefit him because there’s always something, especially in the beginnings or means of operations. It is essential that there’s something to take advantage of, and taking advantage of it is participation in that action. Whether it’s participation in the angle, the line, the movement, or the compass, or everything mentioned; to achieve this, profound knowledge is necessary.

STEP
Step in Fencing refers to the distance between the two centers imagined at the heels of the feet. This distance is created by the movement of one foot from one spot to another, without the other foot following. Therefore, a Step in its simplest form is taken with any foot from one place to another without moving the other foot from its spot. The measurement of these steps is determined from the center of one heel to the other. Steps in general are those taken alternately, walking with both feet in such a way that the body rests, moving the direction line over the center of one heel as the other steps. The most perfect and natural steps, in which the body is considered whole, strong, and of good posture, are those taken in such a way that the length of each foot creates a right angle on both sides of the vertical plane of the chest, which is imagined to run from the top of the head through the center of the chest. Moreover, a straight angle is formed at the intersection of these extended lines, between the foot taking the step and the other foot on which the body rests simultaneously. Less perfect steps are those in which, on either side of the vertical plane of the chest, the length of each foot creates an acute angle of twenty-two and a half degrees. At the intersection of these lines, a right angle forms between the foot that takes the step and the other foot that the body rests upon simultaneously. More imperfect steps are those taken on both sides of the vertical plane of the chest, moving the feet in parallel lines.

The most imperfect steps of all are those that, due to natural constitution, bad habits, or other subsequent incidents, are taken on either side of the vertical plane of the chest. They form an angle of sixty-seven and a half degrees with the length of each foot, and where these lines meet, an obtuse angle of 135 degrees is formed between the foot taking the step and the other foot on which the body rests at the same time.

PERFECTION
Perfection is anything that suits the subject well. In the fencer’s case, intention is his perfection because it suits him. Desire, if for a good thing, is perfection. Increase can be perfection on some occasions and decrease on others. Action can be perfection at times and imperfection at others. Allowing the other to act or begin to act is what suits him, so it’s his perfection. Joining can be perfection, and distancing can also be, depending on the situation. The same reasoning applies to other cases. See Goodness.

PERFECT
Something is Perfect when it is thoroughly completed, and it’s when it consists of all three parts. This must be found in all terms. See Complement.

PROFILE
A suitable Profile is to stand sideways and upright, so that only the depth of the body is visible to the opposing party’s line of sight.

PERMANENT
Permanent: this term is explained in Action.

PHYSICAL
By Physical, we mean everything real that does not exist due to understanding. Individuals possess a physical existence, while species and genera have a metaphysical one, as they only exist in the mind objectively or intentionally.

PLANES
After the main planes, which are the superior one, where one sword is higher than another, whether free or held; the upper horizontal, which is considered from one shoulder to another; the middle horizontal, which is considered to pass through the waist; and the lower horizontal, which is considered on the ground (where we also divide into another eight planes, for the use of compasses, dividing in them the Orb, which is described with the arm and Sword, as will be explained in its demonstration), we consider other planes, which we imagine in the delineation of the bodies of the fighters, dividing them, both in their length and in their width and depth. We refer to some as perpendicular to the Horizon, others parallel to the Horizon, and others oblique to the Horizon; and they are explained in the following way:

Eight Planes perpendicular to the Horizon

The first perpendicular plane, which we call the Primary Vertical, is the one that is considered to pass the two direction lines of the two fighters, or by the axes of the cylinders in which they are imagined, when they affirm at an Angle. The second perpendicular plane, which we call the right-hand side Collateral, is the one represented by the line coming out from the center of the arm until it corresponds in the lower plane to the transversal of the common circle inside. The third perpendicular plane, which we call Diametric, is the one that is represented by the line that goes down through the middle of the forehead and chest until it corresponds in the lower plane to the tangent of the common Orb. The fourth perpendicular plane, which we call the left Collateral, is the one represented by the line that goes down from the left side until it corresponds in the lower plane to the middle line between the infinite line and the one that goes backwards in the common circle. The fifth perpendicular plane, which we call the left Vertical, is the one represented by the line that goes down by the left side until it corresponds in the lower plane with the straight line going backwards in the common circle. The sixth perpendicular plane, which we call the left Sword Collateral, is the one represented by the line that goes down from the left arm, on the outside, until it corresponds with the lower plane with the other middle line, between the infinite and the foreign line. The seventh perpendicular plane, which we call the back Vertical, is the one represented by the line that goes down through the middle of the back until it meets the infinite line on the right hand of the common circle in the lower plane. The eighth and last of the perpendicular planes, which we call the right Collateral, also of the back, is the one represented by the line that comes out from the right arm on the outside, and goes down to meet the transversal line, which by the profile side is in the common Orb.

Nine Planes parallel to the Horizon

The first parallel plane to the Horizon is the lower plane, or the ground where the Swordsman is. The second parallel plane to the Horizon is the one imagined to pass between the lower plane and the knees. The third parallel plane to the Horizon is the one imagined to pass through the knees. The fourth parallel plane to the Horizon is the one imagined to pass between the knees and waist. The fifth parallel plane to the Horizon is the one imagined to pass through the waist. The sixth parallel plane to the Horizon is the one imagined to pass between the waist and the centers of the arms. The seventh parallel plane to the Horizon is the one imagined to pass through the centers of the arms. The eighth parallel plane to the Horizon is the one imagined to pass through the mouth or nose. The ninth and last of the parallel planes to the Horizon is the one imagined to pass through the top of the head.

Eight Oblique Planes to the Horizon

The first oblique plane is the one imagined to pass from the left side of the head to the center of the right arm. In this plane, cuts and half cuts, or Diagonal slashes, are executed.The second oblique plane is imagined to pass from the right side of the head to the center of the left arm. In this plane, reverse cuts and half reverse cuts, or Diagonal reverse slashes, are executed.The third oblique plane is imagined to pass from the center of the left arm to the right side of the waist. It represents the motion of the Sword in the formation of the Diagonal thrust. It also corresponds to this plane the formation that the Sword makes for cuts in the arm on the inside.The fourth oblique plane corresponds to the obliquity with which the Sword moves when attacking from the inside and executes the outside cuts on the arm, also called elbow cuts. Note that the most secure and strongest cuts will be when executed perpendicular to the elbow and wrist.The fifth oblique plane is imagined to pass from the left side of the waist to the right side of the knees. Although it doesn’t serve to execute wounds in it, it’s very important because it prevents the Sword that cannot immediately wound from the upper or lower part.The sixth oblique plane is imagined to pass from the right side of the waist to the left side of the knees. Like the previous one, it doesn’t serve to give wounds but has the same importance because it prevents the opponent from giving wounds immediately from the upper or lower part.The seventh oblique plane is imagined from the left side of the knees to the right foot and the lower plane. It serves to direct the cuts of slashes to the legs.The eighth and last oblique plane is imagined from the right knee to the left foot and the lower plane. It also serves to direct the reverse cuts to the legs.

PLENITUDE
Plenitude is the union of all degrees and perfections owed to a subject, without lacking any, and the gathering of all in a subject is the essence of fencing Skill. See Complement.

POSITION
A Position refers to any place where the body or sword is, and it is the same as posture.

POSTURE
Posture is a position of the body, arm, and sword of either of the combatants relative to their opponent. The posture of greatest power is in which the fencer has the most universal disposition for defense against the actions of the opponent, and to defend themselves if necessary, more than in any other disposition. Perfect posture is when the swordsman is based on a right angle, and makes another with the arm and body in its right vertical line; and from the tip of the sword to the left shoulder, it fits the definition of a straight line, with which everything is profiled. High posture is when the sword rises from the right angle to the obtuse directly, or leaning to any side. Low posture is when from the right angle it declines to the acute angle directly or leaning to either side.

POWER
Power is the virtue of the cause to act, receive, communicate, or terminate, as appropriate. It is a form by which an act exists and proceeds, and through which the understanding touches the object. Alternatively, power is the ability to actualize that which lies in the possibility ordered to the Agent who is to act, to act, and to the object that has to receive, to receive. Thus, power is both active and passive, and is considered and named by its acts, such as active when it acts, motivational when it moves, generative when it generates, corruptive when it corrupts, productive when it produces, dispositive when it arranges, privative when it deprives, determinative when it stops, subjunctive when it subjects, diversive when it diverts, impulsive when it pushes, expulsive when it expels, aggregative when it aggregates, segregative when it segregates: all being in the active, both proximate and remote. And for Fencing beyond what is mentioned, it is common, general, specific, and universal: and in common fencing, it is both active and passive.

Active Power is that strength, disposition, or natural virtue, which the Agent has, to act on its object from the active to the passive: and in Fencing, when through the appropriate means he strikes or subdues the swordsman, without being struck or subdued. Passive Power is the disposition the object has to receive the action of the Agent that works on it, doing on its part nothing more than resisting, more than wood, and wax less than both: and in Fencing, when a man is struck, unable to defend himself or strike. Proximate or next-to Power to the operation is when, by reason of the appropriate means, the swordsman can strike his opponent, setting a trap for him, not with more movements than necessary, without any contradiction between the power of the Agent to act and the object to receive, but it immediately finishes the work. Remote Power is when one has the sword free to act, but has no appropriate means for any wound; and if it has to execute any, it has to be mediate, not immediately. Common active and passive Power is when both equally act on each other; thus, both are agents and patients equally: this is found in the tricks of common Fencing. Specific Power is when the sword is subdued or diverted, and can be taken to any part desired; and leaving where it is to strike requires more movements than the trick demands. General Power in Fencing is when the sword is free, and it makes any trick (not with more movements than its kind requires) without considering this execution: it is also considered in the object, which must receive to receive, as in the agent to act, through the dispositions of the posture, and the profile of the body, or the jurisdiction of the arm. Universal Power is when the swordsman, having made a concluding movement, by subduing the opposing sword, can form and execute all the strikes he wishes.

PRELUDE
A Prelude is that part of a movement closer to its beginning, which lies between non-existence and existence.

PRESENCE
Presence is the actual existence of the subject, under the jurisdiction of the senses and powers of the soul, using its operations.

PRINCIPLE
Principle refers to the order of an actual effect, and it is from whom the effect emanates. It is distinguished from Power in that Power indicates the ability to produce, and is considered as it is; but Principle refers to the order of an effect, and actual, as mentioned. Therefore, the former is relative, and the latter an absolute term; and when talking about a principle, it is in relation to some effect that has proceeded from it, and is actual. Accordingly, as many causes as there are, so many are the Principles; and since there are primarily four causes, so many will be the Principles that intervene in the formation of anything. If one gives a compass, it is considered who gave it, in whom it was given, the form that was communicated to it, and the purpose for which it was done; and these are the principles of that effect: thus, man as the agent, the ground as the receptive matter, what is straight, curved, transversal, of trepidation, or strange, is the form; and the end, what primarily moved him to it. The same is considered in movement: who moves, what is moved, or where the movement is received, which is who is informed, what form was given to it, and for what end? The same is true for lines and angles; and the same is true, even if the movement is a very small part, since smallness does not take away its being an effect, and thus it must have causes and principles, as in the movement of increase, where the efficient principle is the arm, and who receives it is the opposing sword; and the being of increase is the form, because it is the difference, and in the end, it will be according to the occasion. The principle is also considered without looking at the causes, without seeing if the effect has first and last parts; without then considering with respect to the means, nor the end, even if it is mentioned. Speaking in this sense, the beginning is the material for the means, and the means for the end, since the means is made in continuation of the beginning, and the end of the means; and otherwise, neither the means nor the end will be achieved. Dividing the act into these parts is to consider it as composed of it, not as simple; and the understanding does this, gives it, or partial forms: and the purpose for which this is done is for the great effects that result from recognizing the power that corresponds to it at the beginning of the action of its opponent, in the middle, or the end; and the ways it must have to achieve participation in it, both in offense and defense.

PRODUCTION
Production is the dependence that the effect has on its cause internally as it is being made, which is referred to as emanation or production. This is not only found in material effects but also in the emanations or productions of the understanding. Thus, it can be considered in all terms.

DEPTH
Depth is explained in the term Quantity because it is one of its dimensions.

PROPERTY
Property is what differentiates one species from another. The property of humans is to be inquisitive and capable of laughter, while the physical and material body is characterized by gravity. There are also acquired properties, by which individual entities are distinguished from others: and the habit of any thing acquired with effort causes it to be considered its property if it has dissimilarity in it from others and not convenience; although this is more properly an accident.

PROPER
Proper is the same as Property, and it is explained as such.

PROPORTION
Proportion is a perfection of a part that speaks to its relationship to the whole, never straying from its end goal. The proportion of a Sword, and each of its dimensions, must be considered in relation to the person who will handle it, and to the end for which its actions are directed. A heavy instrument and a weak subject are not in proportion: thus, the swordsman with it won’t achieve his goal, which is defense and offense. A wide, soft sword isn’t designed for thrusting, and so it’s not suited for that purpose. A rapier isn’t designed for slashing, so it’s not proportioned for that. All the specific perfections that come together in a maneuver – movements, steps, angles, lines – they must all be in proportion to the end goal: thus it’s the function of a form to properly proportion it. In the art of fencing, it’s about the equality between two lines of the same type, in terms of quantity: so, in terms of length, none should exceed or be exceeded; this is divided into proportion of equality, and of inequality, as well as greater and lesser inequality. Proportion of equality exists between two quantities or numbers that are equal: in fencing, this refers to the balanced use of equal weapons, and the common point of deprivation. Proportion of inequality is between two unequal quantities or numbers: in fencing, this refers to the balanced use of unequal weapons, like a long sword against a short sword, or a very large body against a small one. Greater inequality is when comparing a larger quantity with a smaller one, whether continuous or discrete: in fencing, it’s the appropriate method chosen by the swordsman for the posture of the sword, either by blocking or by the profile of the body. Lesser inequality is when comparing the smaller quantity with the larger: in fencing, it’s the method of using a short weapon against a long one, and when for certain moves by the degrees of profile one moves slightly away from the common diameter line, or when with lesser degrees of force from one sword, one wants to control the greater force of another.

PROPOSITION
Proposition is the same as Trick.

PROSECUTION
Prosecution is advancing what has been started; and this prosecution can either be of one’s own action or someone else’s separately, or of one’s own and someone else’s action together. For example, the opponent’s sword drops, and mine does too, and I join it to continue its action of dropping; upon seeing it, it’s a prosecution of its action of dropping, and mine, which began before joining, even though the gap was so brief, it’s sometimes barely perceptible. There is the prosecution of one’s own action; and this can be a prosecution from the beginning, middle, or end, or it can be a prosecution of desire or intention, varying means when the first ones are not effective: even if these had their particular ends so perfect that their essence asks for no more, but since the intention is not achieved with them, the second ones chosen are in prosecution of the desire, which does not rest until its appetite is fulfilled; and once this is achieved, as the cause remains at rest, there the prosecution is made. Hence, if the fencer decides to strike someone with three blows, a slash, a backhand, and a thrust, even if the first has its particular end and therefore its consequent rest, the desire is only partly settled; thus, the second and third are a continuation of the appetite and total rest. There is prosecution in increasing and decreasing, prosecution of intervals, actions, joinings; there is prosecution in agreeing and in opposing, in differentiating, in arranging, in demonstrating; and the perfect prosecution is the one that always keeps the swordsman superior: so that, as the efficient cause, he produces the effects he intends on his opponent, as if on matter, or a receptive step of his forms.

POINT
Point is in two ways, Mathematical and Physical. The former is that which has no parts, is indivisible, and cannot be touched, not even in the imagination; and in this way, it is considered by the Mathematician. The Physical point, material and objective, is an essence of the natural term that is in the smallest part of the body; it is perceived by sight and imagination; it serves to gain knowledge and through it ascend to the understanding of the natural point. Otherwise said: Point is a real accidental quality, which does not make a species of quantity, but reduces itself to the species of Line, as its continuation, and is neither an essential nor intrinsic part: and because it is truly distinguished from the line, God and the Angel can separate it from the line, leaving a perfect Line. In another way: Point is that which signifies discrete quantity, whose terms are common; because when dividing a line by its length, it would be into Points, and each would not be the end of one part and the beginning of the other.

Point of touch is the closest part that the opponent offers of his body, where the swordsman’s sword reaches by the shortest path to inflict a wound, or to make a discreet, circular, or semicircular approach.

SQUARE
A Square is a figure enclosed by four equal sides and four right angles. For the purpose of the fencing, there are universal considerations of it, both in place and in the quantity of greater or lesser, and being common to both fighters, or particular to just one, and this being superior or inferior. The square in a person is the breadth or width of the chest, affirming itself as square, or aligning the body by its breadth. The common square is that which is considered in the common circumference of the flat surface, constituting the right angles because both fighters can equally use and benefit from it. The particular square of the fencer is that which is considered in the particular circumference he chooses, in which the opponent has no part. The greater square is the one that is considered in the circle of the chest, and where diagonal and descending cuts and reverses are executed. The lesser square is the one considered in the face, leading the thrusts towards it when it is in the closest touch point, due to some end point where the opponent positions himself; and in it, the half cuts and reverses are executed, as well as the diagonal cuts and reverses.

STILLNESS
Stillness is acquired when the cause has acted out all it desires, or the effect has received all it yearns for: one is called the stillness of the cause, and the other the stillness of the effect.

RAYS
Rays, or visual lines, are those emitted from the eyes by the visual power towards the body that is to be seen.

UPRIGHTNESS
Uprightness is each of the positions or extreme points that are considered in a person, where it is possible for him to stand firm. General uprightness are six: up, down, to one side and the other, front and back, and there can be no others except the intermediate or mixed ones. Mixed uprightness is when the sword is high and to one side; low and to one side; behind and to one side; and so on for the rest.

RECEPTIVE
Receptive is that which acts as a material, to which what it receives gives some new being, either accidental or essential, as appropriate. Sometimes the fencer receives dispositions that his opponent graciously gives him, and at other times he acquires them industrially.

RECOVERY
Recovery is to regain something that has been lost; and this can occur at the beginning, in the middle, or at the end of some action. Recovering from increase, decrease, aggregation, differentiation, correspondence, disposition, reach, and other things (which due to oversight tend to depend more on the fencer) if this is done before they are completely lost, being easier to obtain, indicates greater knowledge.

UNIVERSAL RULE
The universal rule is the shortcut for movements, over which one has power, as are also the right angle, the movement of conclusion, and that of diversion for its own.

BLOCKING
Blocking, materially this term is understood as blocking the blow of the opponent by placing in front of it the upper part of the body, the Dagger, Sword, or Shield, to terminate the action on these or similar instruments, which he intended to execute on the body, either as a slash or thrust. And this is as if receiving like receptive material. However, due to the contingency that this may not result in the blow being executed on these instruments, but on another part of the body, since it depends on the will of the one who shapes it, or because natural movement could overcome the forced one, or the perfection of the instrument and strength of the operator could break or penetrate the blocking instrument. Since the one who blocks only focuses on defense, not offense at that time, it is considered a weak action in good Fencing, something that does not aim to put the opponent on guard, forcing him to defend. Therefore, it is rejected and not used; and the damage that threatens is remedied with a diversion movement and other means that indicate defense and offense at the same time, removing the aforementioned contingencies, only by the addition of instruments, helping to lower, though not to the same part, which is diverting the place, nor resisting the force, but assisting or merely diverting the accidental movement, without assistance, as no more vigor is given to it. Since the blocking, in the common sense, is defense, and this is achieved by the fencer with diversion and assistance, they can be called blocks since they prevent the offense that the opponent intends to cause.

Universal block is the concluding movement, with which, in addition to depriving the effect of the opposing trick put into action, those in the will are deprived, and it gives general power to the one who performs it for all his actions. Block in general is the prevention of injury, by stopping, assisting, holding, deflecting, or diverting the sword that wants to wound. A perfect block must arise from the wound and can be of the species that the opponent forms, and it can be contrary. It is necessary to be so in the diagonal cuts, and in the half-reverses, and in the half-cuts.

REITERATION
Reiteration is the act of repeating an action once or multiple times. This is understood to be of the same type, but not the same in number. Because once the numeric form is corrupted, there’s no regression back to it in its potency, but rather towards its essence and species. This reiteration can be considered in the aforementioned terms, which provide a reason to consider it in specific matters.

DIAGONAL REVERSED
Diagonal Reversed is the one executed along the diagonal line of the square considered in the face.

VERTICAL REVERSED
Vertical Reversed is executed along any of the vertical lines considered in the human body.

CONTINUOUS REVERSED
Continuous Reversed is so named because when its natural movement goes downward, it finds an impediment where it was supposed to be executed; therefore, it continues as a thrust.

SAGITA
Sagita is the thrust executed against the natural, remiss, or violent movements that have the sword constrained, whether to form a cut, a reverse, another thrust, or to release from the constraint.

SATISFACTION
Satisfaction is a state of contentment that the swordsman enjoys, being certain that what they know is firm and true. This satisfaction can be purely theoretical, or combined with practical, with the former being partial and the latter total. This complete satisfaction is difficult to attain because one with knowledge of the terms and the science realizes that no one can be perfect. The potential indicates more external acts of fencing than the fencer can achieve in the short span of their life. Any slightest variation in any action makes it different. As seen in a movement of increase or decrease, any point causes a difference. In circular movements or parts of circles, there can be considerations of them being larger or smaller, resulting in almost innumerable differences. The difference in causes necessarily results in different effects, even if the difference is only accidental. The effect will correspond to the same accident as its cause; if it’s essential, then it’s essential. Those with more knowledge, though they aren’t satisfied that they know all there is to know practically since they haven’t practiced everything, enjoy satisfaction in defeating others who haven’t reached this knowledge. However, those who know less often feel more satisfaction because they’re unaware of what they lack, and this satisfaction only serves to place them in danger.

SECTION
Section (equivalent to segment or cut) is the point where the swords touch when one constrains the other or is aligned with it. Common section is when the point where the swords touch, constraining or aligning with each other, is equidistant from both opponents. Particular section is when it’s closer to one than the other.

FOLLOW
To follow the part to the whole is when a foreign step is given, and the arm follows the action of the body. To follow the whole to its part is when a straight step is given or when making a concluding movement, where the body follows the action of the arm.

SECURITY
Security is a clear term, but how it is to be achieved is difficult. Recognizing what is done, the duration it lasts, and which action is the safest to choose when there are many options, indicates great skill. Among the highest levels of security is depriving the opponent of their weapon, and the ultimate security is taking their life.

RESEMBLANCE
Resemblance is when two things look alike in some way, yet they aren’t the same. They can also appear identical in every aspect but remain distinct in number. It’s very challenging for things to resemble each other in every aspect due to the diversity of locations, the strength of the operator, and other factors intervening in the formation of tactics, lines, angles, tools, etc.

SEMICIRCLE
Semicircle is the same as half a circle or hemicycle.

SEMI-DIAMETER
Semi-diameter means half of the diameter.

SEPARABLE
Separable is a quality that denotes an accident, in which it is accurately verified, which can be separated from its subject without it being corrupted. It relates to the more and the less in quantities, lines, angles, movements, and compasses, and the lines of the angles. Because right angles are indivisible; if it’s even a point greater than a right angle, it will be obtuse and acute. Thus, what’s separable from the right or accident is only in the sides. This is what we call separable. However, in fencing, in terms of its purpose, which is offense and defense, many times these accidents constitute the preservation of the goal. Thus, in good fencing, such accidents aren’t separable. Also, the form can be separated from the matter, as the soul can be from the body, and this is the corruption of being, born from its separation.

BEING
Being is a level considered in every subject, first by nature, than by capability, and then by the action of the same thing, although there is no temporal priority among them. For as soon as something exists, it has the potential to exist, which is called inner potential. And the capacity for external actions arises at the same time, as it has an internal or entitative action, since it exists in actuality. There are other specific end actions, such as those of duration, perfection, and others. For at the very moment of existence, and it can last, there is potential, and it perfects the subject. These are internal actions corresponding to it, and without which no subject can exist. But the external actions of the potential of being, and the order it suggests, don’t arise simultaneously, hence they are called external. As each of the said terms is a thing, it will have being, power, and action. Recognizing these levels and the order they suggest in the external actions, each one of them, is the essence of the fencer, and the power to carry out their external actions accurately.

SIMPLE
Simple composition, or formality, is when the fencing move, whether a direct or reversed strike, half-reversed or half-direct, doesn’t consist of more movements or incorporate more angles than its kind requires.

SIMPLICITY
Simplicity, in strict terms, is what lacks composition of parts. In this sense, nothing in fencing is simple, because even if only the sword is considered and said to be a line, this line is composed of many parts. Any move, even if made with primary intention, isn’t simple, because lines, angles, movements, and compasses intervene in it, composing it, and they are necessary parts for its formation. Some are made up of various movements, essential preliminaries for the striker. But since in fencing there are general moves, and others taught separately from any combat, without the opponent defending, so that the prospective fencer gets used to where and how they should be executed, by which planes they pass, so that when in real combat they find themselves in those dispositions, they know what to do. In the midst of combat, considering the great variety of things intervening, knowing how to execute those moves is vital. It’s said that they should recall how and from where they executed them when taught separately from combat, reducing them to that primary simplicity. So, it’s a relative simplicity, not a proper and strict one.

SINGULARITY
Singularity is the act of distancing oneself from others in something, or in many things, being unique in those aspects. For example, the inventor of this Fencing was singular. Even though he used the same tools as those from common Fencing, as well as movements, angles, lines, and compasses, he applied and shaped them in a highly singular manner, inventing unknown moves. If there were only one person with a perfect understanding of what he taught and intended to convey in his writings, that person would be his unique disciple. If the explanations of these terms, as interconnected as they are, bring forth something new, the author of them would be singular, as would anyone in whom these properties are found. And if these properties are superior, their possessor will be singular in that superior capability.

SUFFICIENCY
Sufficiency is a qualified potential. While potential refers to the capacity to act, receive, communicate, or conclude, depending on its nature, it can be specific or total, complete or incomplete. However, sufficiency is an unlimited power, neither partial nor limited but complete, and requires nothing else for its external actions.

SURFACE A Surface is that which only has length and width. Its endpoints, limits, or extremes are lines when the surface is finite and not oval or elliptical. It is conceived or imagined to emerge or be generated by the movement of a line from one side to the other. Likewise, it is conceived in two ways: abstracted or separate from matter. Within it, there are concave, convex, and flat surfaces, all of which are of consideration in Fencing.

A flat surface is one that lies evenly within its lines (just as a straight line lies between its points). For the purposes of Fencing, it is the ground, where the circumference between the two fighters is considered, along with everything contained within it, and the specific surface of each one and the particular one chosen by the fencer.

A flat surface (in another extended sense) in Fencing refers to the sword when it is in a right-angle position. The techniques that belong to this posture are performed through it, facilitated by the binding or control.

A concave surface occurs when the fencer, without moving his feet, aims to reach his adversary by pushing. In such a way, while maintaining a precise touch in terms of a right angle, he aims to topple his opponent’s body, making him adopt the convex surface, its opposite. For if the fencer creates a concave surface at the front, he makes a convex one at the back; and the opponent, by forming a convex surface at the front, creates a concave one at his back. Thus, it will always be observed in the concave and convex surfaces that they go hand in hand; in a way that, being concave on the inside, it has to be necessarily convex on the outside.

SUPERIORITY
Superiority is the advantages that the skilled fencer has over the one who is not, and it consists of what has been mentioned.

CONTINUOUS CUT
A continuous cut in a thrust occurs when, due to an obstruction, the natural movement continues underneath, leading into a thrust.

TANGENT CUT
In Fencing, a tangent cut continued into a thrust is the one that, when for some reason it cannot be executed, is continued into a thrust through a semicircle, passing underneath the one causing the obstruction.

TERMINATION
Termination is an action that is not perfect or completed with respect to the purpose of the operator. It can sometimes be voluntary and other times necessary. Voluntary, as in when one can execute the techniques and only marks them by ending the actions at the end. The same can be done at the beginning or in the middle, but this doesn’t fall within the skill of fencing, as it changes the means different from the chosen ones. Actions are also terminated out of necessity, as can be seen when the opponent rises with violent movement, and upon blocking him, he stops against his will, which is to end his action of rising. The same applies to the downward movement, catching the natural movement very early, not in the act of descending, because resisting with the violent movement won’t be possible, or it will be very difficult. What is terminated is the action of descending to the body, which, when assisted, diverts to a different place. The same applies to the accidental movement with which the thrust is formed, as it ends with the diverting movement, not that the Sword does not move forward, but the straight line that it formed in the air, which was directed straight at the body, making it deviate its path and go in an oblique line away from the body. The same can be considered in many other things.

TERM
A term is called that which is the end of something and that which separates it from another. According to philosophers, it is that in which the proposition is resolved. In Fencing, it serves as a Genre, and has species like terms of Where, To Whom, From Where, Of Which, Of the Sword, Of the Lines, Of the Movements, Of the Width, Of the Length, and Common Term.

Term Adonde, which is the same as term To Where, is the point where the line ends, and the target where techniques are directed and their effects occur. Term to where and Adonde: the first one is common, which is the body where all the lines are aimed at, etc. as mentioned. The second is specific, which is the point where the sword should make contact, and where it should be directed, according to the type of technique or strike. Term from where and Dedonde: the first is common, which is the body from which all movements must be executed; and the second is specific, which is the point from which they originate, without which it would be impossible for them to exist. Term Adonde is the same as term to where.

Term Common in Fencing is the right angle, from which the beginning of movements is considered. Term of the sword is the right angle, or any other position where it can be touched, or to be able to act through it or with it, with addition, diversion, or control. Term of the lines is the body where they end by reaching it, making them finite on both sides. Term of the movements is each of the straightnesses or general positions, each according to its type, and the action that belongs to it. The terms of Width and Length are explained under Quantity. Term is each of the combatants for their opponent, from where the lines come out and where they are meant to end.

Term in Fencing is the limitation that the Agent has to act, and the object to receive, and by which the opponent is deprived of the choice of the suitable means to strike, and the same when the accidental movement is corrupted, through the control of the cut.

TIME
No matter how brief, anything done in fencing must be done in Time; because as it has to have first and last parts, just as it is divisible, it is done in time, which is said to be the measure of movements. However, some are so swift and of such short duration that they are called instantaneous actions, due to the brevity of the time in which they are executed and their short duration; this is unlike some wounds that are permanent and have assurance. Circular time is the same as a cut or reverse.

In fencing, everything is a thing composed of parts, and the total perfection of this is regulated by looking to see if any part that should be there according to its purpose is missing: such as looking at a tactic as a whole, a battle as a whole, and other things in this way. It is then necessary to look at the simple elements that make up the tactic, the lines, each movement individually, the steps, the angles, and the rest, through which one recognizes what was lawful, or the success.

TRANSCENDENCE
Transcendence is a term that signifies something very general and encompassing of everything else. In the abstract term, which has been explained, one will notice the nature of this term: also Perfection, Goodness, Appetite, Power, Order, Sufficiency, Action, Nature; and many of the aforementioned can be considered transcendental terms.

TRANSFERRED
Transferred refers to the tactic or strategy, which, chosen by the opponent, is taken by the fencer for hthemselves; and this is when the choice is in the making, not perfect. And he who transfers it, perfects it.

TRANSITION
Transition is the step given, or the place made by one thing to another in fencing, like the beginning to the middle, and the middle to the end; and this is considered in the movements, in the lines, in the steps, in the angles, in the formation of the tactics, and other things.

TACTIC
Tactic. This term is universal or general, because it doesn’t necessarily pertain to cuts, reverses, thrusts, half-cuts, or half-reverses; but to everything that is a crafty technique to harm a man without him realizing or being able to remedy it, and to defend oneself against it. It’s the same as a ruse or stratagem, and thus, a tactic is not a wound (as many authors claim), but a cause from which that effect or act originates. By definition, it is a concept from the understanding of the fencer, whose aim is their own defense and the offense of their opponent. It is the supreme genre, distinguished by the four precepts or general rules, which have jurisdiction and superiority over specific wounds, simple and complex, of first and second intention, through the choice of one of the four means of proportion: common, proportional, proportioned, and absolute. The first is solely for defense using the common means of deprivation. The second is to gain advantages over the opponent and wound him with first intention securely, and to take advantage of the movements initiated by the opponent and wound him with second intention if appropriate. The third, with its own proportioned means for wounding, without waiting for the opponent’s movements or delaying even for a moment; it has the strength of a specific cut, as it is known, that the proportioned means causes, at the very least, a disposition in the fencer, and deprivation in the opponent, or it wouldn’t be a proportioned means. The fourth has an absolute means, with the strength of a powerful cut, as he who has chosen it is disposed to wound with the injury he wishes; and the opponent, with such deprivation, subjects both the instrumental cause and the efficient one, as he is found concluded; in such a way that even if he wishes to abandon the instrumental cause and flee, he won’t be able to remain defended if the Diestro doesn’t allow it.

Each of the precepts or general rules has four distinctions, and each can be executed by the fencer using one of the aforementioned four means; and in addition to this, there are tactics, simple and complex, of first and second intention, due to the sword’s posture, the body’s profile, and the jurisdiction of the arm, of the far end and of the near end, in which its generality is recognized.

Tactic, or general rule, is one that encompasses under its jurisdiction the specific strikes of cut, reverse, thrust, half-cut, and half-reverse, of first or second intention, simple or complex, due to the sword’s posture, the body’s profile, or the jurisdiction of the arm. There are four of these, as mentioned before: the line in cross, narrowing, weakness below strength, and weakness above strength.

General Rule of Line in Cross is to form a portion of a pyramid below in order to join the opponent’s sword from the outer plane, to the extent that it can be communicated, bringing the swords to their direct right alignment, removing the direction of the opponent’s sword from the correspondence of the Diestro’s body; in such a way that he cannot be wounded on that path. It’s a rule that begins with the sword and ends with it; it can be executed in both first and second intention, as much through the degrees of profile as by the posture of the sword.

General Rule of Weakness Below Strength is to join the opponent’s sword from the outer side and, continuing (as in the general rule of the cross line) without stopping the revolution of a conical pyramid, the swords are brought to the Diestro’s left alignment, with his weak side below the strength of the opponent’s, to then strike with a thrust to the chest by the shortest path, leaving the opponent’s sword free, through the degrees of the profile that the Diestro would have gained to remain defended. It’s a rule that begins with the sword and ends with the body; but if the opponent moves on his center, he can strike and finish with the sword. This general rule is executed in both first and second intention by the two jurisdictions, depending on the position or alignment in which the opponent’s sword is found.

General Rule of Narrowing is to approach the plane of the opponent’s sword from the inside, making a revolution only with the center or axis of the wrist, forming a conical pyramid, and pushing the opponent’s sword towards the Diestro’s right alignment. As a result, the weakness of the opponent’s sword is positioned above the strength of the Diestro’s sword, without a direct line to immediately strike from that side. This tactic starts and finishes with the opponent’s sword and can be executed in both first and second intention across both jurisdictions.

General Rule of Weakness Above Strength is to approach the plane of the opponent’s sword from the inside; and by performing the same pyramid revolution as in the narrowing, one continues successively with another portion of the pyramid, separating the swords to the Diestro’s left alignment. Here, the Diestro will position the weakness of his sword over the opponent’s strength, to then strike with a thrust to the chest by the shortest path, leaving the opponent’s sword free, thanks to the degrees of the profile that the Diestro would have gained to remain defended. It’s a rule that begins with the sword and ends with the body; but if the opponent moves on his center, he can strike and finish with the sword. This general rule is executed in both first and second intention by the two jurisdictions, depending on the position or alignment in which the opponent’s sword is found.

A Specific Tactic is any of the five: such as a cut, a reverse cut, a thrust, a half-cut, and a half reverse. A First Intention Tactic is one that is executed with the sword, or through the opponent’s sword, provided he has not made any voluntary movement to strike, deflect, or control.

A Second Intention Tactic is executed after the opponent has made one or more voluntary movements, and it’s performed at the time when these are being executed or have just been completed, and the one which helps to form them. A Simple Tactic (in terms of the singularity of movement) is the thrust of the first intention by the sword’s posture, which is executed in the right collateral line, and also the one that doesn’t consist of more movements than those required by its form. A Compound Tactic exists in two ways: the first is the cut or backhand strike, and others that involve more than one movement, even for a thrust; the second is when the opponent prepares it, and the Diestro executes it, achieving it with the same movements. A Counterposed Tactic is one that the opponent helps to form, through the slow movements of weapon union (whom Don Luis called Mixed), even if it doesn’t consist of more movements or involvement of more angles than its kind requires: and when the opponent forms a cut and is struck with a reverse; and when a reverse and is struck with a cut; and against any of these, a thrust; and when he’s struck in the vertical line of the back. A Tactic to the Sword is when the opponent’s sword is outside the right angle, in one of the half divisions, and is sought after with the general rule that dominates the rectitude of that half division it’s in. A Tactic with the Sword is executed by leading the opponent’s sword with one of the general rules until having gained a degree of profile or arm jurisdiction. A Tactic by the Sword’s Posture of first or second intention with any weapon type starts with the opponent’s and strikes while holding it, until reaching the point of proportion or for the concluding movement if it reaches the near end. A True Tactic is a scientific composition of body, arm, and sword movement that the Diestro makes according to its kind, in order to defend and attack the opponent, if suitable.

A False Tactic is a composition of disordered movements of the body, or the arm, and sword, or all together, which is formed and executed without defense.

TRUTH
In fencing, truth is the act that reveals the virtue of the cause and makes it undeniable, because it unveils it to the eyes. It is found in the productions or emanations of effects and in their purposes. Even after these have been acquired, what results is stillness; but truth is also found in that stillness.

VIRTUALITY
Virtual is what substitutes in place of another, and after having become so, it enjoys its power as if it were. Weakness below strength, according to Pacheco’s rule, is understood with the aggregation of the sword, and virtually the same thing is done without aggregation, and the same effect arises from both positions. The angle is occupied virtually without the body having occupied it, and it produces effects as if it were occupied. The atajo is done with restraint, and virtually it forms without aggregation of the sword, and creates effects of restraint, impediment, and binding, which is called virtual. Increases and decreases can be made virtually without aggregation, which is how we consider them; and in many other cases, this term can be considered, running through the rest that have been mentioned, and it may be that in the virtual, some higher perfections and greater powers are found than in the actual.

VIRTUE
Virtue is taken as a sufficient power, without defects that hinder its operations, as was said in the term Sufficient.

UNITY
Unity is the primary foundation of the numeral, whether the numeral is of individuals, species, or genres; and unity sometimes consists of parts of the same species, like the natural movement that descends from above or higher up to the ground. It is one movement if it was continuous; but with parts, it could be divided into two or three, as determined by the Agent; but these component parts of this unity, or integrals, are of one species, and in the actual, it is one, being continuous; but potentially two or three. Unity can also be formed from different species, as seen in mixed movements, in which two natures come together to compose a unity, or a single movement with two virtues. And a tactic, which contains unity in terms of tactic, is composed of parts that belong to different genres, such as lines, angles, movements, measures, etc.

UNION
Union refers to the aggregation or adherence that one instrument has with another when they join, which is why it is said to have contiguity. In this sense, the hand is with the Sword: with this, increases and decreases are caused, and the opponent’s Sword is followed wherever it goes, as the movement arises from this mixture, union, or aggregation. Sometimes this is actual, and at other times only virtual. The virtual can even have greater perfections than the actual, as it is not so easily followed by the opponent. There is also a proper union, which is what unites two things making them one; and in this sense, there is no form applied to any material without this union, which they call the mode of union. To this material and form, external or accidental qualities are often united by the fencer, which are highly considered perfections since the victory often lies within them, achieving the intended goal. It is considered that when the movement of the arm and Sword, which forms a cut, is joined with the movement of the body with an external compass to spread the force; and the downward cut is something that joins it, and the application of more degrees of force is something that joins the act of descending, as it could be with fewer degrees, and moving to a safe place is a union. From these material and formal unions results a union of metaphysical degrees because it is a union of perfections of partial potencies, and of differences more sufficient for the task, causing greater stillness and security, as they all align towards the end.

UNIVERSAL
Universal is a complete understanding of everything related to fecning, both the material of tactics and forms, efficient purposes, instruments, timings of their operations; both in their principles, means, and ends of each tactic, as in the prosecution for the rest of the actual battle. It not only serves the aforementioned but also for the possible quality of the planes or places, contingency, or necessity of partial causes, and everything else that has been said.

ZERO
In fecing, Zero is the movement made by the fencer, seeking positions to strike or drawing the Sword from a dangerous place; by itself, it strikes, but it gives value to the following movement to strike. It is also called Assault.

CHAPTER FOUR.

IN WHICH THE PETITIONS, Maxims, and General Precepts, ARE INCLUDED.

PETITIONS OF THE REGIME OF THE ART OF the Sword.

I ask the enthusiasts and lovers of the true Art of Fencing to grant me that the perfect height of a man is two varas, which is equal to six tercias, or geometric feet. Each foot contains 16 fingers, making the entire figure 96 fingers. This is the height approved by sculptors and painters as natural.

They must also grant me that the sword, by which distances and measurements are to be regulated, should be in accordance with the standard of the Kingdoms of Castile. For by law and decree, it is forbidden for it to be more than five quarters, measured from the crossguard to the tip. Including the hilt and the pommel, which constitutes its full length, it has four tercias, or geometric feet, which is 64 fingers.

Also, as the most excellent sculptors concede that the arm, from the wrist line or back of the hand to the elbow, is one foot; and from there to the center of the arm, which is the shoulder, another foot, making it two feet in total; fencers should also agree. And by adding the 32 fingers of these two feet of the arm to the 64 fingers of the four feet of the sword, from tip to pommel, it sums up to the 96 fingers, which is the six geometric feet that constitute the height of a man.

And having determined that the proportionate middle is chosen, as far as when the arms are extended, the tips of the swords reach the wrist lines: they must agree that between the centers of the shoulders or heels of the right feet of the two combatants, there will be 8 geometric feet of distance. Because the sword has four, and with two from each of the arms, they sum up to the 8 that the diameter line of the common sphere should have.

Given that up until now the sword was divided into 12 parts by the ancients without any benefit or application, grant me the liberty to divide it into 4 equal parts. The use we will derive from these divisions will be most useful on the lower plane, for the selection of proportionate means.

If the entire sword is divided into four parts, one foot each, it will be evident that the parts closest to the guard are stronger than those near the tip, successively and proportionally, as we see in a balance or scale. To maintain balance, or to raise it, less weight is necessary the farther one moves from the fulcrum, which is the center of the arm.

The sword is better gripped by placing both the index and middle fingers within the guard, rather than not placing any finger or just the index finger. With both fingers, the sword is stronger and more prepared for all actions suitable for true Fencing.

The sword is stronger in the hand when the crossguards are perpendicular to the horizon than when they are parallel, either upwards or downwards. One must always keep in mind that when the sword is in the vertical plane of the chest, this rule should be followed: the crossguards should not deviate from this plane. But if the sword is in one of the other two planes, lateral or vertical, the crossguards can deviate from this plane and tilt towards the right hand, that is, they can move from the vertical up to 10 degrees, allowing the arm to be more relaxed.

When the feet are at right angles to each other, the body is better grounded, stronger, and more prepared to attack and defend.

When the feet are close to each other, they are more agile to perform steps in any of the eight directions found in Fencing.

Whenever the line of direction is between the two feet and close, one can step with whichever foot desired, and in any direction desired. But if it is over one foot, the other foot is better poised to take its steps in the desired direction than the one on which the line of direction passes.

It is easier and more natural to move forward than backward or in any of the mentioned 8 directions. It’s also more natural to move squared off rather than in profile since it’s an innate action that is performed regularly.

When either of the feet is parallel to the line of the individual circle, corresponding to the vertical plane of the chest, one foot can move a quarter part outwardly while the other remains fixed; they will be positioned at a right angle, which is the perfect posture that the feet should have.

When one of the two adversaries moves in any direction within his jurisdiction, the other can move in any direction within his own individual sphere.

The fencer is allowed, while in the middle of proportion, to move around the circumference of the said sphere in whichever direction they see fit to recognize the weak side of the strong side they intend to attack. Upon recognizing, without any delay, they can seize the opportunity, forming their strike.

Equal steps can be taken in equal times; and less time is required to take a step of two feet than one of three, and a step of three feet requires less time than one of four. The shorter the initial step, the more at ease the body will be to take another step afterward. The closer the movement is to the natural, the easier it is to execute.

The movement made by the arm for a thrust, when accompanied by the movement of the body to the same side, is more forceful than when the arm acts alone.

Equal movements can be made in equal times, and smaller movements should be made in less time.

Time should not be measured by the quality of the movements but by their quantity. There can be a single movement that takes more time than four. For example, the opponent might spend more time making a forceful or slow movement than the fencer in making a circle with the tip of their sword, in which they make four or five movements. Thus, movements should be measured by the line described by the imagined point on the sword and also by the disposition of the part that is to form the movement; that is, by its quantity and according to the speed with which it is made.

Not all pyramids that can be made with the wrist are equal; for some, less time will be spent than for others. This requires close attention, and the fencer should try to form the smallest pyramids possible, forcing their opponent to form longer ones. The longer the pyramid the opponent makes, the more time they will spend, which the fencer can take advantage of to form their strategies. The more the fencer impedes the opponent’s sword from entering their defenses, the better defended they are, causing the opponent’s movements to be larger and more deliberate.

Either of the two fighters can present whichever plane they choose to their opponent without the other being able to hinder them.

Just as it is suitable for the body to be upright and at a right angle to the horizon to easily move to its individual circumference, the arm should also be as much in the plane considered immediate between itself and the opponent. From the midpoint, it can better transition to the surface of the pyramid in which it is considered encompassed; that is, where it can be attacked by its opponent. In this manner, one will never need to make large movements to defend.

The upper part of the body, namely the shoulders (where wounds are typically directed), is not spherical and does not have equal width and depth. For this reason, the vertical right plane can be better protected with just the defensive pyramid formed by the guard, rather than the diametral plane where it opposes with its full width. From this, we infer which plane offers more defense, reach, strength, and weakness.

The body is organized such that the arm doesn’t have the same strength or reach across all four planes. When the fencer positions themselves so that the arm is in the vertical right plane, it has its maximum reach but is at its weakest. Moving to the right collateral, it gains strength; on the chest’s diametral plane, it’s even stronger. Reaching the left collateral plane, it has the most strength as the part is closer to the whole. However, in this plane, it has less reach than in others, and in the diametral plane, less than in the right collateral. Thus, there is a significant difference in having the sword on one plane versus another.

We can refer to any obstruction to the sword, whether real or virtual, as a shortcut without necessarily placing one sword over the other. The opponent’s sword can be hindered from either the lower or upper part if the opponent doesn’t know how to take advantage of their position.

For these propositions and the demonstrations we will make of them going forward, we must assume that the two fighters are equals and will duel with equal swords.

MAXIMS AND GENERAL PRECEPTS THAT are to be followed for the fortification of the intelligence and the exercise of the weapon, the Sword.

Fortifications are made, not only so that few can defend against many, but also so that few do not defeat many when caught off guard. He who builds a fortress must have knowledge, not only of the people who will man it, but also of the number and type of weapons with which it will be attacked, along with the strength of the assault, to proportionately set up its defenses: in the same way, a fencer must seek to have this understanding of his adversary.

All parts of the fortification must be proportionate; in such a way, that there is not one part that isn’t under regulation: and thus in those of our fortress, we will outline them so precisely and accurately, that there’s no need to change them at any time, or alter their form.

The distance an army chooses for its quarters when laying siege to a fortification is done with such proportion that they neither suffer damage from being too close to the fort nor waste more time than necessary on their approaches due to being too far. Thus, one of the maxims is that a fencer must choose this position with such attention that he is neither so close to the fort that he may be at risk, nor so distant that he cannot seize an opportunity his opponent offers. And for that reason, authors have called this the middle of proportion, which will be eight geometric feet in distance from heel to heel or the center of the right arms of the combatants.

The inner defense of our Fortress should be carried out with the guard and half of the Sword up to the hilt, and the offense should be achieved with the point and the edge; and this will not be alternated, because the parts of the Sword closer to and more interior to the center, or body of the fencer, are superior and have dominance over the outer parts of the opponent’s Sword. Knowledge of strength and weakness is essential; following in this, as in all else, the method that is observed in the military, since Fencing is nothing more than a reflection of these aspects, when one wants to launch an attack on a Fortress or Castle.

It is a well-known fact that, for the conquest of any Fortress, one always first seeks to recognize if it has any defect, in order to attack it on that side: the same must be done by the fencer, which is to recognize the Fortress he has to conquer, and after recognizing it, try to fight it on its weakest side.

It must be held as an inviolable maxim and general precept that wherever the fencer establishes himself with his body, he must place his feet at a right angle; meaning one heel directly opposite the other, and this even if they are more or less distant than the span of a geometric foot, which is the most regular distance: this will be observed from the farthest end. Also, on the upper plane, the arm and guard should be positioned in such a way that with one of the vertical, side, or with the tangent lines of the chest, a right angle is formed, or it approaches as close as possible to it; with this, his defense will be immediate; otherwise, it will be contingent. This should be understood from the far end, because in the closer proximity, it will be necessary for the arm and guard to be under the jurisdiction of some of the other angles.

Just as in a siege or encirclement, approaches are made only transversely and obliquely, to avoid damage from the Fortress; similarly, it is fitting that steps should not be taken along the line of the Diameter of the common Orb, because of the great risk of not achieving a beneficial and advantageous inequality over the opponent.

From the circumferential line, which is the median proportion, steps should not be of more than three feet from heel to heel, nor less. In the former case, if exceeded, there will be excessive distance, leaving the body dangerously exposed and out of proportion, making it awkward for the movements to be made afterward; and in the latter case, it will not reach to strike a blow, and if it does, it will be overextending forward. This is understood when operating from the farthest end; to move to the closer proximity and the concluding movement, the largest step should be four geometric feet, or slightly more.

The other circumstances and parts will be explained in the concept of our Fortress, which is its proper place, where it will be demonstrated graphically to the satisfaction of enthusiasts.

CHAPTER FIVE

WHEREIN THE GEOMETRIC DEFINITIONS ARE INCLUDED Applied to the Skill of the regimen of the Sword

In the clarification of the proper and necessary terms for understanding the regimen of this Art and its teaching, we have defined that the science of the Sword, commonly referred to as the Skill of Arms, teaches how to deliver a blow and defend against one from the opponent, whether with the Sword alone or with the other Weapons that usually accompany it.

The means by which this is sought are movements, both of the body and of the arm and Sword. All these movements together comprise what they call a tactic; thus, we define or describe the treta in the following manner.

A tactic is a combination of movements from either of the two combatants, directed at one’s own defense and the offense of the opponent.

The tactic that is formed from knowledgeable and suitable movements to achieve the intended goal will be perfect or true; and the tactic that lacks the necessary requirements for its perfect formation will be called false.

The way we must judge the perfection or imperfection of the treta is to examine all its components, which are the aforementioned movements.

We also defined that movement, according to Aristotle in the third book of Physics, is an action of the mover upon the moved thing.

To grasp the understanding of this action in Weapons, we need to first know the agent or mover, which is the Swordsman or his opponent, and the moved thing, which is the Sword, and in how many ways he can move it, along with the other parts of the body, in order to form some treta. Then, immediately, we must see the harmony and discord that may exist between these movements, both of the body and its parts.

Aristotle in the third book of Physics, speaking of movement, says that it seems to belong to the category of the continuous; and the continuous properly pertains to continuous quantity, whose species are Lines, Surfaces, and Bodies. Thus, it seems that Aristotle with these words wanted to suggest that the speculation of movement pertains to Geometry, the key to the mathematical sciences, whose role is to discuss continuous quantity and speculate its properties. This is clearly implied, since movement and quantity are so intertwined that we find nothing that belongs to quantity that can be moved without its movement causing a physical or imaginary quantity; for if it is a point that moves, its movement will cause a straight, circular, or mixed line, depending on the nature of its movement.

If it’s a line that moves laterally, with its movement, it will cause a flat, spherical, or mixed surface, depending on the nature of the line and its movement.

If it’s a surface that moves, it will produce a body, containing flat, spherical, or mixed surfaces, or parts of some and parts of others.

If it’s a body that moves from place to place, it will create a body of a different shape than it had.

The first three considerations, of the point, the line, and the surface, are very necessary in Fencing, as shown in its place; the last, which pertains to the body, is not used in this science because although the bodies of the two combatants must necessarily move to form their tactics, we do not consider the bodies that cause the movements, but that they move along certain straight or curved lines, according to the form of the movement. In this, they imitate the astronomers, who, although they consider those celestial bodies moving within their orbits, to regulate their movements they rely on lines, not on bodies. The same is done by those who deal with navigation; to regulate the movement of the ship on the surface of the waters, they rely solely on lines, which they call bearings (rumbos).

And given that all who have dealt with movements, both violent and natural, have done so under the speculation of continuous quantity, it will be good for us to imitate them in this. For if, through these imaginations, they have been able to regulate the movements of the stars in the heavens and the movement of ships in the water, it won’t be much to hope that, using the same means, we can regulate the movement of the sword in the air and the movement of the body on the ground.

This being so clear that it does not admit controversy, we will put all our effort into finding the way to facilitate the Art of Fencing through Mathematics, showing the use of some lines, surfaces, and bodies, which will serve us as a guide and north star for its perfect understanding. But before we can do so, we define some definitions related to Geometry, even though in the proper terms we have already specified a great part of them; but without figures, because of the complications that ensued. And in these definitions we now declare, it’s necessary to include them, so that later we can show the fencer their application in the Art of Fencing.

1. A Point (according to Euclid, Defin. 1. Book 1. of his Elements) is that which has no part.

Definition of the Point.

 

Among mathematicians, two types of Points are recognized: one is Mathematical or imaginary, an essence without quantity, abstracted from matter, and solely objectified by the understanding; the other is Physical, Real, or material, which, however small, can always be divided into divisible parts. This is marked with the letter A in figure number 1.

In the Art of Fencing, we also consider two types of Points: Physical ones, which are considered at the tips of Swords; and imaginary or Mathematical ones, considered at the intersection of certain imaginary lines, both on the ground plane (understood as the Floor) and on the bodies of the two combatants, or in the Air, with the lines we consider passing through the arms and Swords of the two combatants.

2. A Line (according to Euclid) is a length without breadth. Just as the Point is considered in two ways, one Physical and the other Mathematical, the Line will also be either Physical or Mathematical. For if the Line, according to Plato, is the flow or movement of the Point, if the Point is Physical, the resulting Line will be Physical; and if the Point is Mathematical, abstract from matter, the Line will also be Mathematical.

Definition of the Line.

 

A straight Line is the shortest extension from one Point to another, the smallest of all lines that have the same endpoints, or that which lies evenly between its Points. For example, the Line B.C., which resulted from the straight movement from Point B to Point C. The limits or ends of the Line are Points, like B and C, and are seen in figure number 2.

Of the Straight Line.

 

In the Art of Fencing, we consider the Sword, Dagger, and Montante, or their edges, as a Physical line. Whenever the tip of the Sword moves to a place where it can leave a mark or trace of its movement, such as on the ground, or against a wall, or on the body of its opponent, the line it causes with its movement will be Physical. And whenever it moves in the Air, even though strictly speaking it seems to be Physical, we will call it imaginary because it falls not under the sense of sight but under imagination; and such a line will be straight, circular, or mixed, according to the nature of the movement.

3. A curved Line is one that forms an Arch, and is not straight, as demonstrated by the letters D. and E. in figure number 3.

Of the Curved Line.

 

In the Art of Fencing, we consider it when the arm bends without making an Angle at the cut, and when the body is positioned in an arch-like manner, leaning forward or to the sides, making the Arch in depth; it is also considered on the ground plane, and particularly in the compasses, which derive their name from it.

4. A mixed Line is one that is neither straight nor circular. For example, the line F.N. is straight, and N.G. is curved, as seen in figure number 4.

Of the Mixed Line

 

In the Art of Fencing, it is formed with the Sword and arm when the arm bends without making an Angle at the cut; it is also seen on the ground for mixed compasses and for the concluding movement, representing it by the mixed compass of transversal and curved.

5. A wavy, tortuous, or Eliac Line is one that snakes like a River or serpent. It is divided into two types: one almost straight, and another that is winding; the almost straight one is H.I. and the winding one is K.L. in figure number 5.

Of the Wavy Line.

 

In the Art of Fencing, H.I. is considered when the tip of the Sword, with an accidental or strange movement mixed with slackening movements, describes portions of curved lines underneath the other Sword, to one side and the other; and K.L. is considered when also with an accidental or strange movement mixed with others, it forms curved lines without interruption in its course, or even when using the Sword to encompass the opponent’s Sword to restrict its freedom.

6. A spiral or volute Line is one that, in the manner of a snail, wraps around some columnar body without returning to where it began, similar to the turns the Sun makes between the Equator and the two Tropics. It is marked with the letter M in figure number 6.

Of the Spiral Line

 

En la Deſtreza ſe conſidera en muchas partes, y propoſiciones, como quando ſe forman las dos generales, flaqueza encima, y debaxo de la fuerza; y quando la Eſpada del Dieſtro figue à la de ſu contrario por la parte de adentro vnitivamente, haſta haer movimiento de concluſion, quedando hiriendo, formando el Angulo mixto: y tambien quando eſtando pueſto el atajo por de fuera en el extremo propinquo en la Eſpada del contrario, ſi eſte levantare el brazo, y guarnicion, incluirà, y rodearà el Dieſtro las Eſpadas por aquella parte, haſta dexar la contraria debaxo de ſu brazo derecho, y la fuya hiriendo por encima de la juriſdiccion del brazo, haziendo al miſmo tiempo movimiento de concluſion; y aſsi eſta linea eſpiral ſe puede formar tomando la Eſpada por la parte de adentro, y la de afuera.

7. Parallel straight lines are those that, extended infinitely and on the same plane, never converge. They are represented by the letters N.O. and P.Q. number 7.

Of the straight lines

 

In fencing, they are formed when choosing the middle proportion, according to the Art, to immediately set a block on the inside; they are also considered in many other propositions and cases, both on the lower plane and on the upper one. In the bodies of the combatants, the Vertical, Collateral, and Diametrical lines are parallel.

8. Converging lines are those that, drawn through a plane, converge, making a section, segment, or cut, as represented by the letters R.S. and T.V. that converge at X. number 8.

Of converging lines

 

In fencing, they are considered when two lines or swords join or one is subjected to the other; also in other propositions. These two lines are said to be non-parallel.

9. Elliptical line is similar to an oval figure, divided into two parts, with a Diametrical line, as shown by the letter Y. number 9.

Of the ellipse

 

In fencing, we consider it in the human body, in the Arch made with the bulk of the body and chest, because the back is almost flat.

10. The hyperbolic or parabolic line is the one that resembles or is similar to a mountain, or more precisely to a pile of wheat. It is represented by the letter Z. number 10.

Of the hyperbolic line

 

In fencing, it is used to describe the steps and is considered in the journey, both of the curved step mixed with trepidation and strange, and of the transversal one, mixed with trepidation and strange; and also in some revolutions made by the sword in the air.

11. A circular line is one that results from the movement of a point when it always moves at an equal distance from another point that is immobile: for example, if point A is fixed and point B moves always at an equal distance from point A, the line that results from its movement will be called circular, number 11.

Of the circular line

 

In fencing, these circular lines are formed with the arm and sword, and we also consider them in the upper and lower planes, as will be explained in the application we will make of them later.

12. Angles are the inclination of two lines that meet at a point and are not straight.

Definition of Angle

 

13. A Planar rectilinear angle is one that is contained by two straight lines, converging as marked by the two Swords C.E. at point D. number 12.

Definition of Angle

 

In fencing, we use the most generalized kind of Angle, as will be explained in each species: and we consider the rectilinear one anywhere the two Swords intersect or touch the Horizon plane; and also in the lower one it is caused, both in the lines we consider in it that serve us as directions, and when the transversal steps are given, mixed with trepidation, and strange; and in the imagined lines from one shoulder to the other of the fighters. A planar rectilinear angle is also formed for some propositions.

14. Planar curvilinear angles are those composed of curved lines, as marked by the letters D. in one, E. in the other, and F. in the third, in the figure number 13.

Curvilinear

 

In fencing, we consider them when fighting with double weapons, and also in the lines that in the lower plane describe the feet for different steps.

15. A mixtilinear angle is one that results from the touch of a straight line and a curve, as marked by the letters L. and N. that converge in M. number 14.

Mixtilinear

 

In fencing, when the arm is curved, and with the straight line, which is considered in the chest (whom we call of contingency) they constitute an Angle on the right side, or with the arm, and sword, constituting it in the grips: we also consider it in the lower plane for mixed steps.

16. A right angle occurs when a straight line, falling upon another straight line, makes the angles on either side equal to each other: each of the angles is called right, and the line is said to be perpendicular to the other: for example, the line C.D. is said to be perpendicular to the base A.B. and makes the right angles, number 15.

Right

 

In fencing, it is considered when the right arm is not affirmed, as it arises in the body, without participating in any of the extremes from top to bottom, to one side or the other, the body being the line A.B. and the arm, and sword C.D. and these right angles are also considered and formed, both in the lower plane and in the touching of the swords.

17. An obtuse angle is greater than a right angle, as the sword rises from the letter C, which was considered a right angle, to the letter B, num. 16.

Obtuse

 

In Fencing, it is considered when the arm raises to the high straightness directly, or leaning together to either side; in a way, that the arm and body are not parallel to the Horizon plane, as C.D. indicates, but are found as demonstrated with D.B.

18. An acute angle is less than a right angle, as the line of the arm and sword drops from the letter C.D. where it was considered to be right, to the letter B, where it is acute, num. 17.

Acute

 

In Fencing, low postures are made with it; so, the arm is not fully united to the body, nor the hand and Sword to the thigh, as indicated by the letter B.

19. Surface is that which has only length and breadth, and in the same way that we consider the line caused by the movement of the point; we also consider the Surface caused by the movement of the line: and as the line is divided into three differences, straight, circular, and mixed, according to the nature of the movement of the point; the Surface will also be divided into three, according to the difference in the movement of the line, which is called flat, spherical, or mixed, and the ends of the Surface are lines.

Definition of the Surface

 

20. A flat surface is one that is equally between its lines and is caused by the lateral movement of the straight line when it moves equally: for example, let’s suppose that the line A.B. moved entirely from where it is, to D.C. equally, and directly by the shortest path, it will have caused a flat surface, bounded by four straight lines A.B.-A.C.-C.D. and D.B. and we call this type of Surfaces flat, for brevity.

Of the Flat Surface

 

In Fencing, this Surface is demonstrated in the lower plane, and also in the upper one, imagining a contact line from one combatant’s shoulders to another’s, for when they face each other, the bodies are squared, and the Swords in parallel lines, pointing the tips to the left shoulders, and considering in them a point of contact, will have formed a flat Surface.

Also, the surfaces, if composed of curved lines, like the arches of Buildings, we will call them concave on the lower part, which is indicated by the letter A, and convex on the upper part, where the letter B is, as shown in figure number 19.

In Fencing, this surface is considered when the body leans extremely forward, or backward, or to the sides, and also in the description of curved compasses, which if the foot left a trail, this surface would be perfectly formed.

Also, the straight line would cause a flat surface, if, with one end fixed, the other moved around it; as in the following figure, which is called a circle, and is defined by Euclid in this way.

21. A circle is a figure contained by a single line, which is called circumference, indicated by the letters A.D. to which, from a point within it, all the lines that go to the circumference, being straight, are equal to each other; and this point is called the center, as indicated by the letter B. in number 20.

Definition of the Circle

 

In Fencing, we consider different circles: such as the upper, the lower, common, particular, and others, according to the positions of the combatants, and the proportions that are made, as we will explain later.

22. The diameter of the circle is a line, passing through the center, terminates on both sides in the circumference, and divides the circle into two equal parts, as indicated by the letters A. and D. and half of the Diameter is called the Radius, number 21.

Of Diameter

 

In Fencing, we consider the line of the Diameter, both in the lower plane and in the upper one, and in the body of the combatant.

23. A semicircle is the same as half a circle, being a figure contained by the Diameter, and half of the circumference, indicated by L.Y. number 22.

Of the Semicircle

 

In Fencing, we consider it, both in the formation of many tricks and in the execution of some blows.

24. A portion of a circle is a figure contained by a straight line and part of the circumference, greater or smaller than half of it: it is called a larger portion or segment, indicated with A.B. and a smaller portion or segment, indicated with C.D. number 23.

Portion of Circle

 

In Fencing, we also consider these portions for the formation of strategies and execution of strikes, depending on the path that the Sword follows, as everything is manifested in the Treatise of strategies, and in many other propositions, where its application will be seen.

25. A quarter of a circle is one of the four parts into which the entire circumference is divided, indicated by the letters A.B.C. in number 24.

Quarter Circle

 

In Fencing, it is useful when, by taking the opponent’s Sword from the inside, one strikes with a thrust in the right vertical: and when taking it from the outside, one strikes above the Sword in the Diametral of the chest: this quarter of a circle is also considered in the formation of other strikes and in the lower plane, as the common circle is divided into four, as is the one considered in the man’s chest.

26. Concentric circles are those described with only one center, like A. and B. that are described with the center M. num 25.

Concentric Circles

 

In Fencing, these circles are evident, as the maximums include those that are caused by the revolution, which is caused by the divisions of the arms, and Swords, and all are concentric; which serve as a guide or compass, both to regulate the measures of the means of proportion, as proportioned, giving them a fixed quantity to the compasses, as will be explained in its place.

27. Eccentric circles are those that have different centers, and the larger one includes the smaller one in this figure, because the larger one has the point A. as its center and the smaller one has the point B. which interval is included by the larger one, num. 26.

Eccentric Circles

 

In Fencing, they are considered when the Swords, and bodies are unequal, as the circle described by the larger one, and with the larger one, will include the one described by the smaller one: and it is also considered in the lower plane, as the circle, to whom we give the name of Maximum, will include the common one, which is imagined between the right feet of the combatants, and they have different centers.

28. Tangent circles are those that, touching at one point, do not intersect, like the circles A. B. of number 27.

Tangent Circles

 

En la Deſtreza ſe manifieſtan eſtos circulos en los Orbes, que de las diviſiones de los brazos, y Eſpadas de los combatientes, conſideramos en el plano inferior; pues el Orbe, ò ciruclo que deſcribe el Dieſtro con ſu punta de Eſpada, es contingente al que deſcribe el brazo del contrario; y à eſte reſpecto en las demàs diviſiones de la Eſpada, como ſe verà en ſu proprio lugar.

These circles are also seen with perfection in the formation of the vertical cut and reverse cut, which in their execution touch in the vertical middle of the Zenith E., going through the forehead to the chest, and to the ground F., as shown in said number 27.

Also, the straight line touching the convexity of these circles is called the line of contingency, or tangent, marked by the letters C.D. of the same number 27.

Any straight line drawn within the circle, which is not a diameter, is called a Chord, like the A.B. of figure 28, and the portion of the circumference it subtends is called an Arc, like the C.D., and the Line that bisects the Arc and the straight line is called the Sagitta, marked by the E.

Before entering the declaration of the other Surfaces, we will discuss some necessary figures for their understanding, which are caused by the flat Surface; and since we talk about figures every step, we will put here the definition given by Euclid book 1. Defin. 14. for them.

A figure is the surface contained beneath one or many boundaries; one with a single boundary is a Circle; one with two boundaries is a Semicircle, or a larger or smaller segment; one with three boundaries is a Triangle; one with four, a Quadrilateral, etc.

Definition of Figure

 

Rectilinear Figures are those contained by straight lines. Trilateral Figures are those contained by three straight lines.

Rectilinear and Trilateral Figures

 

Multilateral, or Polygonal Figures, are those contained by many straight lines.

Multilateral

 

27. A Triangle is a closed surface with three lines and three angles, it takes its name according to the lines and angles; thus, when it consists of straight lines, it is called a Rectilinear Triangle, if of curved lines, Curvilinear, and if of two straight and one curved line, Mixed, as was said of the angles.

Definition of Triangle

 

There are three kinds of Rectilinear Triangles, which are named by the length of their sides, or by the opening of their angles, in this way.

Rectilinear

 

Among the Trilateral Figures, the Equilateral Triangle is the one contained by three equal straight lines, as demonstrated by the letters A.B.D. in figure num. 29.

In Fencing, we use it for many things, both for self-defense and for offending the opponent; particularly for the perfect attack on the inside, considering one of its sides as the arm, another one as the line of contingency of the chest, and the other imagined from the hilt of the Sword, to converge on the left shoulder.

28. An Isosceles Triangle is contained beneath two equal sides and a base that is unequal, as appears in the figure, because C.X. is equal to X.R. and unequal to both sides C.R. as shown in number 30.

Isosceles Triangle

 

In Fencing, it is important in many cases, applying it more or less, as in the previous figure: and in the lower Plane, its consideration is crucial for the true understanding of the steps, for if one is to strike, one must walk by one of its sides, or Perpendicular, that is considered in it, as will be seen in our universal demonstration of the Circle.

29. A Scalene Triangle is contained beneath all three unequal sides, like P.T. which is greater than T.R. and this is less than R.P. and is manifested in number 31.

Scalene Triangle

 

In Fencing, we use it, both in the lower Plane and in the upper one, for when we make the rigorous assault from inside, through a block, we consider the longest line to be the one we imagine coming from the tip of the right foot, converging with the opponent’s tangent; and the shorter one, the one that comes from the right heel, converging on the shortest path with the same tangent, and this tangent is the third side.

In the upper Plane, we consider in this assault the longest line to be the one imagined from the tip of the Sword, to the shoulder to the received line, or hilt; and the other line, which closes the triangle, is the Sword.

30. A Right Triangle is the one that has a right angle, as manifested in number 32. with the letter B. and the line that is opposite C.D. where its extremes converge, causing acute angles: is called Hypotenuse, being opposed to the right angle B. for whose discovery Pythagoras offered the sacrifice of a hundred cows to the Goddess Minerva.

Right Triangle

 

En la Deſtreza ſe forma eſte Triuangulo en muchos propoſiciones de la Eſpada, y Daga, quando ſe combate deſde el extremo propinquo, y con la Eſpada ſola ſe vè quando el contrario encoge, y baxa el brazo al Angulo agudo, y la punta de la Eſpada ſube al obtuſo, y el Dieſtro aplicando ſu eſpada con la graduiacion neceſſaria, ſea por de dentro, ò por de fuera, encamina herida de eſtocada, ſirviendo ſu eſpada de linea Ipotenuſa.

31. An oblique triangle, or obtuse-angled triangle, is one that has an obtuse angle; this is shown by the letter A. in number 33. Its application in Fencing is detailed in the preceding sections.

Oblique Triangle

 

32. An acute triangle, or acute-angled triangle, is one that has all three angles acute, as is shown by the letters M.C.P. in number 34.

Acute Triangle

 

Its application in Fencing is also covered in the preceding triangles, through the knowledge of the lines that compose them.

33. Among the quadrilateral figures, the square is the one that has all four sides and all four angles equal, as is demonstrated with the letters P.B.C.D.

Definition of a Square

 

If a straight line is drawn from one of its angles to the opposite angle, it is called a Diagonal, and this line will divide the square into two right triangles of equal surfaces, as shown by the line drawn from C. to B., all in number 35.

In Fencing, we consider the Square in the chest of each of the combatants; and also the Diagonal line that divides it from one angle to another; as well as the Quadrangle, or Parallelogram, which we consider on the face, where all the Diagonal wounds of the upper plane are executed.

34. A parallelogram is a flat figure, contained by four lines, of which the opposite ones are parallel, its species are the Square (already mentioned), the Rectangle, the Rhombus, and the Rhomboid.

Of the Parallelogram

 

A rectangular parallelogram is one that has all four angles equal, and only the two opposite and equal sides, like V.K. and C.D. in number 36.

Of the Rectangular Parallelogram

 

In Fencing, we consider it in the lower plane, and it will be seen in our universal demonstration of the circle, and also in the face of each of the combatants.

35. A Rhombus is an equilateral figure but not a right-angled one, composed of four equal sides, like the square: they differ in that their angles are unequal, and if two Diagonal lines are drawn from one angle to another, they will not be equal, and its sides are equidistant and of opposite contradiction, because the angles A.B. are obtuse, and C.D. are acute, as verified in number 37.

Definition of Rhombus

 

In Fencing, this figure serves for some propositions of the French doctrine, since when they affirm, they bend the knees to balance the body equally; and in this manner, it is seen perfectly if both heels are joined, as it is often executed in the progression of the battle.

36. A Rhomboid is a figure that has its sides, and angles, equal to the opposite ones, but it is neither equilateral nor rectangular; it is similar to the Rhombus, except that the opposite sides are longer, like A.B. is longer than C.D. and to the line designated by the O.O. dividing it from one angle to another, we call it Diagonal; and to the line that divides it into two Rhomboids, as indicated by the letters M. and M. we call it Diametrical, number 38.

Of the Rhomboid

 

And in Fencing, when the two combatants affirm themselves in a part of both postures (square, and profile) and the Swords are directed to the left shoulders, or collaterals of the same side, this figure is observed.

37. The remaining four-sided figures, which are not the aforementioned, are called Trapeziums; of this species, some are more irregular than others, the most regular one has two equal sides, like S.V. and the other two opposite sides parallel, like P. and N. in the figure of number 39.

Definition of Trapezium

 

In Fencing, when the combatants affirm themselves in square, and the tips of the Swords are pointing, one to the Diametrical of the chest, and the other to the left Collateral.

38. An Irregular Trapezium is the figure demonstrated by the letter Q. in the figure of number 40.

Irregular Trapezium

 

And in Fencing, it is useful in the doctrine of Beautiful Spanish; for when we affirm ourselves in it, the body slightly collapses, bending the knee in such a way that the thigh forms one side, and the leg forms another; the third side will be the distance that should exist from the left foot, which sustains the body, to the right one; and the fourth side will be the right leg and thigh, which will be without forming an Angle: this figure is also considered in other cases, which will be referred to when we discuss this doctrine in the third Book, which deals with all the strategies.

39. There are other figures with many sides, each having its particular names: like the one with five sides, which is called a Pentagon, the one with six sides Hexagon, the one with seven sides Heptagon, the one with eight sides Octagon, and so forth, infinitely.

Figures with Many Sides

 

Of these figures, some are called regular, and others irregular; the regular ones are those that have equal sides and angles; and the irregular ones are those that have unequal sides and angles.

The lines that contain these figures are called sides, those that divide them in the middle are called Diametric; and those that pass through the opposite Angles are called Diagonals.

Of these figures with many sides, we only use the Pentagon in Fencing, both the regular and the irregular, in this manner.

For the regular Pentagon, when affirming ourselves with the body in the French posture, equally on both feet, one heel will be distant from the other the same amount as the length of the thigh or leg; because from the birth that the thigh makes in the fork to the knee or bend, we consider one side; it is indicated by the letter A. the second side, equal to this, we consider from the knee, down to the ground; it is indicated by the B. the third is the other thigh, indicated by C. and the fourth the other leg D. the fifth, and last side, is the imagined one from one heel to the other; it is indicated by the E. figure, number 41. And for the irregular Pentagon, when the interval from one heel to another, is of greater, or lesser length, than the sizes referred to.

40. When dealing with any angle in a triangle, the lines that comprehend it are called sides, as demonstrated by the two C’s. And the line that is opposite to the angle A. is called the base, like the letter D.F. And the line that is drawn from the angle A. perpendicular to the base, is called the Perpendicular; and the parts of the base are segments, the greater D. and the lesser F. num. 42.

Of the Sides in the Triangle

 

Following the understanding of straight, circular, and mixed lines, and of right, obtuse, and acute angles, and of the flat Surface, which we have divided into different figures, both of three, four, five, six, and more sides; we now move on to the understanding of the curved Surface, which is divided into spherical, and mixed.

41. Spherical Surface, according to Euclid Defin. 12. of book 11. of his Elements, is formed by the revolution of half the circumference over its diameter: he does not say it in express words, but it is inferred from the definition he gives of the sphere, in this form.

Of the Spherical Surface

 

A sphere is a solid figure, contained by a single surface, to which, from a point that is inside, all lines drawn to the circumference are equal to each other; and the description, or formation of the sphere, is made with the revolution of a semicircle, over its fixed diameter, until it returns to the place where it began.

He does not specifically declare that the surface is caused by the movement of the circular line; but as said it is inferred, because the line with its movement causes surface; and he says, that the sphere, as a body, is contained by a surface, which cannot be other than the one described by the line of the semicircle C. and C. that moves over its diameter A.B. num. 43.

42. Mixed surface is the one caused by a straight line, moved circularly, or by the circular line, moved straight; as seen in the surfaces of the Cylinder, and the Cone, or conical Pyramid, and it is inferred from definitions 16. and 18. of Book 11 of Euclid, who says.

Mixed

 

The Cone is a solid figure, formed by the revolution of one side of a triangle, around another that remains still, like the triangle A.B.C. where the side A.B. moves around A.C. and causes the conical surface, and the whole triangle, being a surface, causes the body contained in the conical surface, figure number 44.

The same is seen in the following figure, which is called Cylindrical, which is caused by the revolution of the side A.C. in the parallelogram A.B.C.D. around B.D. this side causing the Cylindrical surface, in which the body of the Cylinder is contained; where it is seen, that this surface is called Mixed, as it is composed of two movements, or two different types of lines, one is circular, and the other straight, being formed by the revolution that the straight line makes around the other side.

It is also caused by the movement of the circle A.G.E. if it moved straightly from top to bottom, which can be more easily considered, if some circle moved straightly through some soft mud, in which it would have caused a Cylindrical surface, which they call Mixed, figure num 45.

There are other infinite differences in mixed surfaces, but these two are the most necessary in Fencing, as will be seen in their place.

43. Solid (according to Euclid, definition 1. of Book 11 of his Elements) is what has length, width, and depth, and its limits are surfaces.

Definition of Solid Bodies

 

In the same way that the line is divided into straight, circular, and mixed, and the surface into flat, spherical, and mixed; also, the bodies are divided into three differences: namely, those that are comprised of flat surfaces, such as the five bodies called Regular, and other infinite ones found in nature, those that are understood under mixed surfaces, of which there are many; but among all, in Fencing, we need to consider three of them, which are the Sphere, the Cylinder, and the round Pyramid, which although demonstrated, we will declare again, in this manner.

44. A sphere is a solid figure, contained by a single surface, from which, from a point within it, all the lines drawn will be equal to each other, as shown in figure number 46.

Definition of the Sphere

 

The description, or formation of the sphere, is made by the revolution of the semicircle, keeping its diameter firm and immobile, until it returns to the place where it began, as already explained.

45. A cylinder is a solid figure, formed by the revolution of a parallelogram around one of its sides, which remains still, until it returns to the place where it started: its axis, or axle, will be the side that was immobile, or the base of the parallelograms, as in this figure number 47.

Definition of the Cylinder

 

The parallelogram A.D., moving around B.D., caused the cylinder A.E. Its axis is the line B.D., its bases are C.H.E. and A.G.F., which were caused by the revolutions of the lines A.B.C.D. around the points B.D.

46. The cone is a solid figure, contained by two surfaces, one flat and the other mixed; it is formed by the revolution of triangle A.B.C. around or along the side A.C., which remains immobile, until it returns to the same place where it began. The side that remains immobile is called the axis, and the base is the circle that describes the base of the triangle, number 48.

Definition of the Cylinder

 

Apollonius of Perga provides another description of this Pyramid, saying: If from a point a straight line is drawn to the circumference of a circle, which is not in the same plane as the point, and the point remains fixed, the line moves along the circumference of the circle, until it returns to the same place where it started, or began to move: the surface described by the straight line is called a conical surface; the vertex, the point that does not move; the axis, the line drawn from the vertex to the center of the circle; and the Cone, what we call Pyramid, is what is contained by the conical surface, and the circle, and the circle serves as its base.

Another Description of the same Pyramid

 

For example, let point A. be in a different plane than circle B.C.D., draw a straight line from A. to B., a point on the circumference of the circle, and with point A. fixed, move the line A.B., or the extremity B., along the circumference of the circle B.C.D, it will describe a conical surface, its vertex will be A., its axis A.E., its base the circle B.C.D., and everything contained between the circle and the surface will be the Cone, or conical Pyramid, as shown in figure number 49.

These three bodies are of great consideration in Fencing, as will be mentioned in their place: the first, which is spherical, is not only used to consider the movements made within the jurisdiction of a sphere, which is formed, or considered formed with the movement of the Sword; but it also serves to consider some horizontal, vertical, and oblique planes, along which the Sword must move, for the formation of strategies that resemble the circles considered in the celestial sphere.

El Cilindro nos ſervirà para repreſentarnos vn Caſtillo, en que conſideramos pueſto el Dieſtro, que tambine ſe formarà del movimiento de la Eſpada.

The Pyramid is also very necessary, because its consideration and its formation not only serve to defend the fencer, but also give him knowledge for the offense.

Lamina primero del Libro ſegundo

 

First Plate of the Second Book

 

CHAPTER SIX

PRACTICE, AND USE OF THE COMPASS that the Fencer MUST know.

Having understood the definitions, or geometric principles that have been referred to, we will now discuss the use of the compass, or the practice of some problems necessary for our intent: so that the expert does not lack knowledge of the appropriate rules in the construction of the figures of the true Skill; as it is so precise, both for its own use and just in case, as it usually happens, he gives a lesson to a King, Prince, or Lord; and this one, being fond of Mathematical disciplines, asks him, before or after handling, or exercising, geometric reason for what he has been taught, or will be taught: and so that the Master can satisfy his desire, giving him full satisfaction, demonstrating the Propositions of true Skill, without the Compass, and the Rule being an obstacle, it is convenient to keep in mind the following rules.

PROPOSITION I. PROBLEM

Given a straight line, divide it into two equal parts

Let the given line be A.B. figure 1. Center the points A. and B. and with any interval, as long as it’s greater than half of the line, describe four portions of Circles, and let two of them intersect at point C. and the other two at point D. and from point C. to point D. draw a line, let it be D.C. which will divide the line A.B. into two equal parts, at point E. as demonstrated in the Proposition 10 of book 1. of Geometry by Euclid.

APPLICATION I.

In the Art of Fencing, this construction is used when it is necessary to divide the common Diameter Line in half; and if it is needed to execute it on the ground, the fencer will do it by taking a string, and having one of its ends fixed at the ends of the line: with the other end, and a pencil he will describe the crossings, as was done with the Compass; and having made the intersections on both sides, he will draw a line, which will divide the common Diameter in half.

If he doesn’t find a string at hand, he should position himself at an angle, and above a right angle, in the mean proportion, and placing the other Sword by the shoe as a plumb line, letting the pommel reach the ground, and making a revolution on the heel of the right foot, until he returns to the place where he started, the pommel will have passed dividing the circle into two equal parts: and drawing a straight line from one division to another, the Diameter will be divided in half; and if he does not want to make the revolution, he should move his arm and Sword, both to the right side and to the left; until the pommel of the hanging Sword is perpendicularly over the circumference, and he will find it has fallen on the fourth part of the Circle on both sides: and if he draws a line from one to another, it will divide the Diameter in half, creating four right angles at its center.

Shoe here refers to the leather cover added to the tip of the blunted sword for practice

 

PROPOSITION II. PROBLEM

To divide a given straight line into as many equal parts as desired

Let the line F.G. figure 2. be given to divide into five equal parts: draw another undetermined straight line H.I. and with any opening from the end H. five equal distances will be taken on it, and where they end, which we will suppose is I. an arc will be made with the same opening of one of the five parts, towards K. this point of intersection will be made K. and through this intersection, and the point H. the line H.K. will be drawn undetermined: now take the opening of the given side G.H. and with it from H. the arc E.L. will be described. I say, that the chord E.L. will be the fifth part of the proposed line G.F. as is clear from the 2nd Proposition of book 6. of Euclid.

Note, that as it was divided into five parts, if it is desired to divide into more or fewer parts, so many will be taken on the H.I. working in everything else that has been said.

APPLICATION II.

This proposition of dividing a line into as many parts as desired is found to be restricted in the practice of our Fencing, regarding having precise quantities, by which to govern all the demonstrations: which are regulated by the divisions that we have made of the body, arm, and instruments, in this way: The length of the man in six parts, or Geometric feet, from the sole of the foot to the zenith of his head; the arm in two feet, from its origin, to the wrist line; the Sword in four feet, from the pommel to the tip; the whole Cross in one Geometric foot, from the end of one quillon to another; the hilt, or guard of a quarter of a foot, or four fingers of Semidiameter, whose measures, and instruments serve as a base, or flat scale, to construct, or fabricate on the lower plane, or ground all the figures of Fencing, without needing any other divisions: so the fencer will use these instruments, and a string for whatever he needs to construct on the flat surface, or ground.

PROPOSITION III. PROBLEM

To raise a perpendicular to a straight line, given a point on it.

Let the line A.B. be figure 3, and the point be C. Then from the side C.A. take the line C.D. and equal to it the line C.E. Let the point E.D. be the centers, and with any interval, as long as it is greater than half of the line D.E., describe two portions of circles, that intersect, and let it be at point E. From which, and point C. draw the line C.E. which is perpendicular to the line A.B. as demonstrated in Proposition 11, book 1, of the Geometry of Euclid.

APPLICATION III.

This construction is applied in Fencing when on any point of the eight in which the line of the Diameter of the common circle is divided, or in any intermediate of its divisions, it is desired to raise a perpendicular, to ascertain the quantity of some of the means, or distances, or even if it is desired to raise them on the tangents that pass through the heels of the right feet, the perpendiculars of the Isosceles triangles, which are in the proportionate means, both by the posture of the Sword, as well as by the profile of the body, this operation can be done on the ground, drawing with a string its crossers, in the same conformity as it has been done on paper with the compass, and the rule.

PROPOSITION IV. PROBLEM

To raise a perpendicular to a straight line at one of its ends.

Let it be at the end F. of the straight E.F. figure 4, where the perpendicular is desired to be raised. For this purpose, it will be discretionarily extended towards G. and making with any opening from point F. the equal distances F.G.F.E. and with any larger opening from points G.e. the intersection H. will be made. Draw the H.F. which will be perpendicular to E.F.

This is understood when there is capacity, so that the line can be extended to the part where the perpendicular is to be raised. But if the proposed point is at the end of the line, and it cannot be extended on that side, we will use this practice.

Let the line A.B. and the proposed point on it be A. Take any point outside the line, with the condition that, when extended, it does not coincide with it; and let it be, for example, the point C. Center the same point C. and with the interval C.A., which is the distance from the point taken outside to the end of the line where the perpendicular is to be raised, describe the circle arc E.A. D. which cuts the line A.B. and if it does not cut it, extend it until it cuts: and in this example, let it be at point D. From which, through point C. draw a line, which cuts the portion of the circle at point E. From which to the proposed point A. draw a line, which is perpendicular to the line A.B. because the angle E.A.D. is right, as demonstrated in Proposition 31, book 3, of Euclid.

APPLICATION IV.

This construction serves in Fencing for when at the ends of the line of the common Diameter it is necessary to raise perpendicular lines, which extended on one side and the other serve as infinites, passing through the heels of the right feet of both combatants, to give through them the trepidant compasses.

PROPOSITION V. PROBLEM

To draw a perpendicular to a line from a given point outside it.

Let the proposed line be A.B. figure 5, and the point outside of it be C. From which, with any interval, describe a portion of a circle that cuts the proposed line in two parts, or points, and let them be D. and E. Divide the line D.E. into two equal parts, at the point F. Draw the line F.C., which is perpendicular to the line A.B. as demonstrated in Prop. 12 of book 1 of Euclid.

APPLICATION V.

This construction is applied in Fencing for when, from any of the proportional means, touching the wounds of first intention, it is desired to determine the amount by which each one deviates from the line of the common Diameter. This operation will be done on the ground, by fixing the end of a cord at the center of the heel of the foot that took the step, which is the point that is found outside the line; from which, and with any interval, or amount of cord, a portion will be described; and by dividing the divided portion in half, a perpendicular will be drawn from the point of division to the given point outside, whose length indicates the amount by which that proportional mean is separated from the line of the common Diameter.

PROPOSITION VI. PROBLEM

To draw a line parallel to another given straight line.

Let the line be C.D. figure 6. With a discretionary interval, and from any point on the line, such as from A.B., the arcs E.F. will be described. Through the endpoints of the circumference, the tangent E.F. will be drawn, which will be the parallel line that is being sought.

APPLICATION VI.

In Fencing, this construction is observed when, after drawing the infinite line that touches the heel of the right foot, to use it as a guide for the trembling steps that correspond to it; it becomes necessary to draw another line parallel to it, extending from one side to the other of the heel and tip of the left foot, so that this one can be used as a guide for the steps that belong to it.

PROPOSITION VII. PROBLEM

Given a point outside an indeterminate straight line, draw a line parallel to the given line through that point.

If the line H.I. figure 7 is given, and it’s requested to draw a parallel line to it passing through point G, a perpendicular G.K. will be drawn from this point (as previously taught). Using its interval, from any point on the line, let it be L, the arc M will be described, and the tangent M.G. will be drawn, which will be the parallel line that is being sought.

APPLICATION VII.

This construction follows the same course as the preceding one, considering that the given point outside the line is the heel of the left foot, and the perpendicular that drops represents the distance between the two heels. Using this interval and describing the portion of the circle, or arc, in the same way that was observed on paper, the tangent touching the left foot will be drawn, which will be parallel to the one touching the heel of the right foot.

PROPOSITION VIII. PROBLEM

Given a straight, finite line, describe upon it an equilateral triangle.

Let’s consider the line segment A.B. in figure 8. Using the distance between its endpoints, intersections will be made at point C. From there, lines C.A and C.B will be drawn, resulting in the formation of an equilateral triangle, which is also equiangular or has equal angles, as demonstrated in Proposition 1 of Euclid’s Book 1.

APPLICATION VIII.

In fencing, the construction of an equilateral triangle is not commonly practiced on the lower plane. While on the upper plane it is considered for certain attacks, and to allow the body, supported by its constituting lines, to pass beneath the angles created by the swords’ contact at their near end and the concluding movement, it is never rigorously an equilateral triangle. However, stating that it is equilateral helps differentiate it from the isosceles and scalene triangles and also distinguishes the action of each.

PROPOSITION IX PROBLEM.

Given three straight lines, two of which are equal and the third either greater or smaller, describe an isosceles triangle.

Let’s consider the equal lines D.E. in figure 9 and the unequal line F.G. Using the endpoints and the length of one of the equal lines, an intersection at point H will be made. By drawing lines H.F and H.G, the desired isosceles triangle is formed.

APPLICATION IX.

In fencing, these isosceles triangles are described both by the posture of the sword and by the body’s profile, as demonstrated in my universal explanation. The vertices of these triangles are the proportional middles used to transition from them to the proportional endpoints of all injuries. The smallest of its three sides has a length of six geometric feet, which are found in the tangent of the opposing right foot, from its right heel and the proportional middle, to the first orb of its sword. From these points, straight lines are drawn to the proportional middle of the right-hand posture of the sword, which is on the tangent of its right foot, three feet away from the proportional middle.

PROPOSITION X. PROBLEM.

Given three straight terminated lines, and unequal, such that the sum of two is greater than the other, describe a scalene triangle.

If the three lines A.B.C. figure 10 are given, and wanting to form a triangle with them, take one, let’s say C, and set it as the base from D to E. With the length of B, from the endpoint D as the center, draw an arc towards F. And with the length A and center E, intersect at F. Afterwards, draw the lines F.D and E.F, and you’ll have the desired triangle.

If the intention is to form a right triangle, given the two lines that form the right angle and terminated, let’s say C and B, set one like C from D which will be the base, and raising a perpendicular at one of its ends D.F equal to B, draw the line F.E, called the diagonal, and the triangle will be formed.

But, if one of the lines forming the right angle is given, like C, and the diagonal A, all you have to do is set C as the base D.E, and raising an indeterminate perpendicular at D, take the length of the diagonal A and from the point E make the intersection F. From there, draw the line F.E and the triangle will be formed.

APPLICATION X.

This construction (as also revealed in the universal demonstration) is found in the same preceding isosceles triangle; since dividing the smaller line in half, which is the tangent of the opponent’s right foot, and from its division raising a perpendicular, which when extended divides the angle formed by the two larger lines at the proportional midpoint of the fencer, it will be seen that with this line or perpendicular, the isosceles triangle has been divided into two right-angled scalene triangles; all their lines are unequal. For example, the smallest, which is the base, is three feet long, from the heel of the opponent’s right foot to his proportional profile midpoint. The other, which is the perpendicular, is eight feet, from the fencer’s proportional midpoint to that of his opponent. And the largest line, opposite the right angle, serves as the hypotenuse; it starts from the proportional midpoint and the opponent’s right foot and touches the fencer’s proportional point, where it meets the perpendicular, as seen in the universal demonstration.

PROPOSITION XI. PROBLEM.

Describe a square on a given terminated straight line.

Given the line G.H. in figure 11 to form a square on it, raise the perpendicular G.I. from the endpoint G, which should be of the same length as G.H. Using this same length from the endpoints I.H., create the intersection at K. From this, draw the lines K.I and K.H. which form the desired square, as demonstrated in the Proposition 46, Book 1 of Euclid.

APPLICATION XI.

In fencing, the construction of the square is made in the same manner as was practiced in the first application, dividing both the common diameter and the circumference in half. From these points, drawing from the proportional midpoint and centers of the right feet of the combatants, the four straight lines, which we call transversals, until one meets the other in the fourth part of the circle, both due to the position of the sword and the profile of the body, we will find the desired square inscribed within the common circle.

PROPOSITION XII. PROBLEM.

Given two unequal terminated straight lines, describe a right-angle parallelogram.

Let the lines A.B. be given in figure 12. Take one of the two lines, let it be A, and place it from C to D. Raise a perpendicular from one of its endpoints, C.E., equal to B. Using this length, create an arc from point D toward F. Then, with the distance of C.D. and from endpoint E, intersect at F. Draw the lines F.D and F.E, which will complete the desired figure.

APPLICATION XII.

In fencing, this right-angle parallelogram is described using two terminated and unequal straight lines in the following manner. Let the first line be the common diameter, with a length of eight geometric feet. Let the second, unequal to the first, be the portion of the tangent, which goes from the proportional midpoint, and the center of the right foot, to the proportional position of the sword of the fencer, with a length of three geometric feet. Now, raising a line at this endpoint, or proportional midpoint, which is perpendicular and equal to the common diameter, it will meet at the proportional midpoint of the profile of the opponent with the portion of their tangent, completing the desired figure. And another right-angle parallelogram, equal to this one, is found in the profile of the fencer.

PROPOSITION XIII. PROBLEM

Find the center of a circle.

To determine the center of the circle A.B.C.D. in figure 13, choose three arbitrary points on its circumference, let’s say E.F.G. Draw lines from one point to another, such as E.F and F.G. Divide these lines in half, as previously demonstrated, with lines D.B-C.A. extended until they meet at a single point, let’s say H. This point H will be the sought-after center.

APPLICATION XIII.

If, in the practical application of fencing, one wishes to find the center of the common circle, it is quickly and easily done, both because the sword acts as a semidiameter of it and because, assuming the two fencers are firmly positioned at the midpoint at a right angle, if from that plane, through the primary vertical, they naturally lower their arms and swords to the acute angle until the tips touch the lower plane or ground, it will be found that they precisely occupy the center of the common circle.

PROPOSITION XIV. PROBLEM

Given a straight angle, divide it into two equal parts.

Let the straight angle be A.B.C. in figure 14. This angle is to be divided into two equal parts, which can be achieved by taking two points on sides A.B. and A.C. equally distant from point A, let’s say they are D. and E. Using a compass with the distance between these two points, or another larger or smaller distance, describe two arc portions which intersect at point F. Draw a line from point F to point A, which divides angle A.D. into two equal parts, as demonstrated in Proposition 9, Book 1 of Euclid.

From this, it follows that a straight angle can be divided into four equal parts, then eight, sixteen, and so on, doubling the divisions.

If there’s a need to divide an angle into three equal parts or another proportion that isn’t doubled, it can be done by dividing the arc of the circle enclosed between the two lines forming the angle as required. For example, if we need to divide angle A.B.C. into three equal parts, we’ll take points on the lines A.B. and A.C. that are equidistant from point A, let’s say N.D. Divide them mechanically (this is sufficient) into three equal parts at points S. and O. Drawing lines from these points to point A will divide the angle into three equal parts. The same can be done for any other non-doubled proportion.

APPLICATION XIV.

In fencing, we see right and straight angles divided into two equal parts, both on the plane below and at the proportional midpoint. The right angles that meet at the centers of the right feet of each fencer, formed by the common diameter line and the internal tangent, are divided into two equal parts or angles of 45 degrees by the transversal lines that form the square inscribed within the common circle.

In fencing, we also use divisions of 3, 5, or more equal parts, or another proportion that isn’t doubled, as seen in the same straight angles of 45 degrees. These are formed at the center of the right foot by the common diameter and transversal lines that divided the right angle into two half-right angles.

For the fencer to move from his midpoint to the proportional positions of the thrusts, for some, it is necessary to deviate from the common diameter by half a foot, for others one foot, and for others one and a half or two feet. In this respect, we divide the angle into the necessary parts, whether even or odd.

PROPOSITION XV. PROBLEM.

On a straight line, describe an equilateral and equiangular pentagon.

Given the proposed line A.B. in figure 15, divide it at the point C such that A.C is the larger segment and C.B is the smaller. Extend line A.B on both sides until lines B.E and A.D are equal to the larger part A.C. Using A. and D. as centers and with the distance of the proposed line A.B, describe two arcs that intersect at point F. Do the same from points B. and E. and they intersect at point G. With the same distance, describe two other arcs from points G. and F. and they will intersect at point H. Draw lines to these points, and you’ll have constructed the equilateral and equiangular pentagon A.B.G.H.F, as demonstrated in Proposition 10 of Book 4 of Euclid.

Alternatively, one can describe a pentagon, or any regular polygon, inside a circle. Suppose we want to describe a pentagon. First, describe a quarter-circle, let’s call it A.B.C. Divide this quarter-circle into five equal parts. Take four of these five parts, and draw a chord, or straight line, A.S. from their endpoints. This line will be the side of the equilateral and equiangular pentagon inscribed, or constructed within, a circle whose radius is A.B. The reason behind this method is as follows: By dividing a quarter of the circle into five equal parts to make the pentagon, the entire circumference will consist of twenty of these parts. The line A.S. is the chord of four of these parts. Therefore, the combined length of the four equal parts A.S. will have the same proportion to the entire circumference as one part has to the five parts into which the quadrant A.B.C. was divided. Thus, A.S. is the side of the pentagon. Using this method, one can inscribe any shape in a circle. For instance, if you wanted to inscribe a seven-sided figure, you’d divide the quadrant into seven equal parts and take the chord of four of these parts as one of the sides of the seven-sided figure. This reasoning applies to the pentagon and all other figures similarly.

APPLICATION XV.

The pentagon is seldom or never described in the lower plane. If ever used in fencing, it’s when the body is evenly balanced on both feet, distanced proportionally from heel to heel. One side of the pentagon is determined by the distance from one heel to the other, and the body provides the other four sides—legs and thighs—when the body is evenly leaning on both legs, bending the knees until it’s in a stance position, as described in the geometric definitions and the application of the pentagon in fencing.

For other shapes with more sides, such as the hexagon or octagon, they are commonly used in fencing, especially to describe and demonstrate body exercises or movements, as will be seen in the third book.

PROPOSITION XVI. PROBLEM.

Given a point on the circumference of a circle, draw a tangent to it.

Let there be a circle A.B.C. as shown in figure 16, and let the given point on its circumference be A. Draw a line from this point to the center, forming the radius A.D. From point A, erect a perpendicular line A.E., which will be the desired tangent.

APPLICATION XVI.

This construction is also very straightforward in the practice of fencing. Given any point on the circumference, whether of the common circle, specific circle, or the maximum one, the lines (both the diameter and others that divide it) serve as a guide for drawing tangents. In fencing, the tangents always pass through the centers of the feet of both combatants when they are in the mean proportion, or in the proportional points if one steps into the sphere of the sword of their opponent.

PROPOSITION XVII. PROBLEM.

Given a point outside a circle, draw a tangent to it.

Let’s consider figure 17, where a point F is given outside the circle. Draw a line from F to the center of the circle, which we’ll call F.D. Bisect this line at point G. Draw a semicircle D.C.F., which intersects the given circle at point C. Draw a line from this point to F, which will be the desired tangent, and it will be perpendicular to the radius D.C., even though it is not necessary to draw this radius.

APPLICATION XVII.

This application is the same as the previous one, and even more straightforward. Any given point outside the circle to draw a tangent will end up pointing to the center of the foot that touches the circumference. Given the two corresponding and clear points, the one outside and the one on the circumference, in this operation, all you have to do is draw a tangent from one point to another. If the given point outside is in a place where a tangent cannot be drawn that touches the center of the foot on the circumference, it will not be necessary for the use and practice of fencing.

To truly understand and universally apply the art of fencing, it’s essential to have knowledge and practice in the foundational principles of geometry, as already explained. Alongside this, one must also practice and be familiar with the exercise of weapons, as will be evident throughout this treatise. This stands in contrast to the opinion of many who are presumptuous in this art and claim that there’s no need for geometry when engaging in combat. Such individuals disdain geometry simply because they lack understanding of it. It’s evident that someone who possesses both theoretical and practical knowledge in a science will use it more effectively than someone who only has practical experience. The latter is not in control of what they practice; instead, the practice controls them. Since geometry provides the theoretical foundation for the art of fencing, someone who fully understands it will master the art. Conversely, without this understanding, the art will dominate the practitioner. For this reason, and to avoid an extensive focus on geometry, I have only provided the basic rudiments, as these are the aspects most commonly addressed in fencing. Subsequently, I’ve included the practice of certain geometric problems that are essential for our purpose. If enthusiasts wish to delve deeper into advanced geometric concepts, they should study it more extensively.

For a better understanding of everything discussed and the benefits that can be derived from it, I will present the proportions of both the body and the sword based on measurements by Albrecht Dürer. Then, I’ll present the idea of our Stronghold and its structure. Once familiarized with its marvelous concept, we’ll start discussing all the lines, surfaces, and shapes we need to consider, caused by the movement of the sword. Afterward, we’ll explore the utility of all these concepts in the practice of fencing.

Lamina ſegudno del Libro ſegundo

 

Second Plate of the Second Book

 

CHAPTER SEVEN

EXPLANATION OF THE MEASUREMENTS AND Proportions of the human body most necessary for the use and practice of the science and skill of weaponry

Albrecht Dürer, in his book on the symmetry of the human body, presents two methods to teach how to measure and proportion its figures. The first method involves dividing its height into many aliquot parts, such as half, third, quarter, fifth part, etc. The second method is through the use of specific characters, whose explanation we’ll address in due course. Typically, to apply these rules in practice, Dürer relies on the second profile and the third reverse perspective. However, in the context of fencing, we commonly refer to the first as “Profile,” and the second as “Square.” We won’t assign a specific name to the third perspective, which is viewed from the back, as it isn’t typically used in this discipline. Of these aliquot parts, those used to measure the figure’s height will be found in the margin, while those used for width and depth will be located within the figures themselves, each labeled with a number corresponding to its value. We only need to mention a few of these measurements here, specifically those relevant to our framework: the full height of the figure, the length of the arm alone, the arm’s length with the sword, the distance between the centers of both arms, the length from the centers to the ground, the distance from the body (or its center point, the navel) to the ground, its maximum width, and its greatest depth.

The commonly accepted height for a perfect figure (as referred to by painters and sculptors as “from the natural”) is two yards, which equates to six geometric feet. If we further divide each foot into 16 fingers, the total height of the figure becomes 96 parts or fingers. Using these measurements, we’ll examine the two variants provided by Dürer in his books. To standardize these measurements, we’ll use the more familiar unit of fingers, which will allow us to precisely and easily determine each part’s exact value.

In Dürer’s first book, on page 3, there’s a profiled figure alongside an arm with its hand. Next to it, there are four measurements: two larger ones and two smaller ones. The first of the larger measurements, which runs from the upper part down to the elbow, is denoted as ²⁄₁₁. This suggests that if the figure’s entire height were divided into eleven equal parts, this section would represent two of those parts. To get a better grasp of this fraction, we can convert it into our standard unit of fingers. By multiplying the fraction’s numerator, which is 2, by the figure’s total height, which is 96, we get 192. Dividing this by the fraction’s denominator, 11, we get 17. ⁵⁄₁₁ fingers, which slightly exceeds one foot, as the length of this part up to the elbow.

The other larger part, which extends from the elbow to the fingertips, is marked with the number 4. This indicates that this section constitutes a quarter, or one-fourth, of the entire figure, which is a foot and a half or 24 fingers. This measurement aligns closely with what cosmographers assign to the ulna or cubit, as can be seen in works by Pedro Apiano and many other authors. However, since our current intention is only to examine the arm’s length without mentioning the hand, we’ll subtract from this quarter, which amounts to 24 and ⅗ fingers, and the remainder will be 14 and ⅖ fingers. Added to the previous 17 ⁵⁄₁₁, the total comes to 31 and ⁴⁷⁄₅₅ fingers, which is just slightly less than two feet. Thus, we can conclude that for a figure that is six feet tall, the arm will be two feet, or one-third of the total height. This measurement starts from where the arm originates up to the line known as the Receta.

The distance found between the two centers of the arms is one-fifth of the total height, which corresponds to 19.2 fingers. The distance from the centers of the arms to the lower plane will be determined by subtracting 18 fingers (the value of the longer of the two lines facing the head with the numbers 10 and 11) from the total height of the figure, which is 96 fingers. The remainder will be 78 fingers, which is five feet minus two fingers.

The maximum width is ³⁄₁₀, which, converted to our measurement, makes 28.8 fingers. The maximum depth is one-sixth of the figure, which is one foot. The distance from the center of the body, corresponding to the navel, to the lower plane, is five-fourths, or sixty fingers. This is the same length given to regulation swords, according to the kingdom’s law. This can be verified with the figure on page 4, seen from behind. If you subtract 36 fingers (one-tenth and three-elevenths of the total height) from the top of the head to the navel, the center of the body, the remaining length is the 60 fingers we mentioned earlier, which equates to the five-fourths length of a sword from the tip to the hilt or guard.

This same length can be found from the center of the right shoulder to the tips of the fingers of the left hand, with the arm stretched out in a straight line with the shoulders. This can be verified by adding the first three parts: the length we assign to the elbow, the distance from the elbow or joint to the center of the same arm, and the distance from center to center. In total, they amount to just over 60 fingers.

In the same book, on page 7, Albrecht presents another figure of a man. From the given method, the measurements determined are as follows: the arm length is 33 fingers, with an additional ⅗ of a finger. The distance between the centers of the arms is 16 fingers and an additional ²⁄₁₁ of a finger. The distance from the arm centers to the bottom plane is five feet. The maximum width of the figure is one and a half feet, and its maximum depth is 13 fingers with an additional ⁵⁄₇ of a finger. The height from the center of the body to the bottom plane is 61 fingers, which equates to five-quarters plus one more finger. The distance from the center of the right arm to the tip of the left hand is 59 fingers and an additional ⅓ of a finger, which is slightly less than five-quarters.

On page 10 of the same book, Albrecht showcases another figure whose arm length is slightly less than 32 fingers. This is because only 16 parts out of 401 (considering a finger divided into 401 parts) are missing, which is negligible in practice. The distance between the arm centers is one foot. The height from the arm centers to the bottom plane is five feet. The figure’s maximum width is 21 fingers and an additional ⅔ of a finger, its maximum depth is 12 fingers and an additional ⅖ of a finger, and the height from the center of the body is 61 fingers.

On page 14, another figure is presented, whose arm measurements are nearly identical to the previous one. The distance between the arm centers is one foot, its height from the bottom plane is five feet, the greatest width is 21 fingers and ⅔ of a finger, and the greatest depth is 12 fingers with an additional ⅖ of a finger.

Lastly, on page 18, the arm’s length is noted to be 32 fingers and an additional ²⁄₁₁ of a finger. The distance between the centers is 16 fingers minus ²⁄₇ of a finger, the height from the arm centers to the bottom is five feet, the greatest width is 21 fingers, and the greatest depth is 12 fingers.

We could continue with the explanation of the Symmetry found in the figures of Albrecht’s second book, but it doesn’t seem necessary to delve into the multitude of examples when just one will suffice for the authority we seek. What we need to note in this book, as in the previous one, is that there is so much proportion and correspondence in the length of the sword with these figures, that it seems either these figures were adjusted to the measure of our sword, or those who made the mark took it from the symmetry of these figures.

In the second book, he uses certain characters (in place of numbers), which are as follows: 𝑪Ɛ⎳٪ The first, 𝑪, represents one-sixth of the entire figure, which is one foot or 16 fingers. The second, Ɛ, is one-tenth of the first, equivalent to one finger and ⅗ of another. The third, ⎳, is one-tenth of the second, corresponding to ⁴⁄₂₅ of a finger. The fourth, ٪, is a very small quantity, as it’s one-third of the third, amounting to ⁴⁄₇₅ of another finger. Using these measurements, he calculates his figures. On pages 4 and 5, he shows how the human body fits within a circle that spans from the feet to the tips of the hands when the arms are raised to the level of the head. The center of this circle is the navel, which is located the same distance from the lower plane as the sword’s length, which is three feet, three-quarters, or sixty fingers. The same is found on pages 58 and 65.

This measurement is equal to the five-quarters, which by kingdom law is the mandated length of the sword, from tip to hilt or quillons. From this, it follows that the sword is the exact measurement of the radius of a circle in which the man is encompassed as if spherical; because if one places one quillon in the center, which is the navel, they can describe the circumference of this circle with the tip of the sword. This is demonstrated by Albrecht on page 54, where the close correspondence and proportion of this instrument with the one who is to wield and govern it is recognized.

It’s also found that if four fingers of grip are added to its length, the entire length, along with the arm, will be six feet, which is the height we’ve determined a life-sized figure should have. Thus, the sword by itself not only defines the realm of the swordsman, but accompanied by the arm that wields it, matches its height. Another property or excellence found in the sword is that its length determines the greatest stride a swordsman can take, measuring the distance between the two feet when they are as far apart as possible. Anyone can test this. If geometers and geographers have set the geometric stride to be five feet, it’s because they count one solid foot along with four empty feet. However, this stride isn’t accepted in the art of fencing since it would require an extreme extension of the body.

Having verified the precise measurement of the whole man, his parts, together with the length of the arm and sword for the defense and conquest of this imaginary castle, it won’t be difficult to determine the jurisdiction required for the use of both things. But before starting this work, we need to recall three essential things observed in any real and regular fortification.

The first is the distance to be set from the center of the square to the side or angle of the inner polygon. The second is the distance from the inner polygon to the angle of the outer polygon. The third is the one the enemy must choose when intending to lay siege to the square.

The first distance must be such that the polygon can accommodate a sufficient number of people who can defend the square, in addition to having space for military exercises and for retreats when necessary. This inner polygon is defended by walls, embankments, parapets built on the curtains and bulwarks. The distance from the first, or inner, polygon to the outer one is defended by the most manual offensive weapons available in the square, such as muskets, grenades, etc., currently. This distance should not exceed the reach of the square’s most powerful weapon, which is the cannon. This distance has changed since the invention of gunpowder, as previously it was much smaller. In the past, an army would immediately reach the counter-scarp, but now many days pass, many people die, and much ammunition is used before they can reach the ditch. Not only this distance but the entire form of fortification has changed with gunpowder, though the main principles remain.

Our fortress will have no need to change over time because the perfection of the weapon with which it will be defended and conquered is such that its form admits no change or alteration; it encompasses everything found in offensive and defensive weapons. Artillery and other firearms are weapons of great precision and have impressive effects, but their role is solely offensive without any defense. Defensive weapons, such as breastplates, parapets, walls, and embankments of castles and fortified cities, have only defense as their function. But the sword alone has the preeminence of both tasks: to offend and defend simultaneously. The offensive aspect seems easy, but to offend while remaining defended requires more skill and appears challenging. The reason for this is that the most essential part, the defense, is based on fortification, and the required finesse is almost all imaginary. It’s no wonder that those lacking knowledge of its concept find its defense perplexing.

Some may find this thought extravagant, but I am confident that once they see our concept, they will admit that this is the only way to understand a science that has been so intricate until now, as everyone knows. And these teachings will not only serve to grasp the art of fencing but will also be of great interest to those who understand military precepts. Since the objectives, which are to conquer or not be conquered, are the same, the means to achieve those objectives must have much in common. Here we will detail the form and structure of this castle in more depth, with its plan, elevation, and perspective. Then we will explain all its parts, with the necessary mathematical demonstrations to make evident how the swordsman can form this fortification with the perfection represented here. I don’t mean he can create it all at once, for as much as that’s impossible, it’s unnecessary. It will suffice that he can form a defense and put his opponent in a position where he can’t achieve his intention. In this context, we can apply the adage that says:
It is in vain to do with more what can be done with fewer.

CHAPTER EIGHT

EXPLANATION OF THE IDEA OF OUR Fortress, its structure, and the strong resemblance it has to the Real Forts and Squares, through which the use and practice of the Skill of Weapons is facilitated.

Let’s imagine that the fencer is firmly positioned on the right angle at K.L., and at a right angle with his arm and sword P.G.K. Let’s assume his line of direction is A.H. and that the six geometric feet, which is the combined length of his arm and sword G.P., is divided into three parts at the points N.O.P. The first section G.N. from the center of his arm to the center of the hilt of the sword is a length of two feet and a quarter. The second N.O. is one and three-quarters feet, which is from the center of the hilt to the midpoint of the sword, considering from the pommel to the tip. The third section O.P. is two feet, which is half of the sword’s length to the very tip.

From each of these points G.N.O.P., we imagine perpendicular lines dropping to the lower plane K.C.D.E. On the line H.E., the common intersection of the primary vertical plane A.B. and the lower plane B.H., being all parallel to each other and to the line of direction A.H., four parallelograms are formed: the first A.K., the second A.C., the third A.D., and the fourth A.E., all four being encompassed by the parallelogram A.E.

Let’s imagine that, with the swordsman positioned in the aforementioned manner with his arm and sword, he makes a revolution around his line of direction A.H., along with the four parallelograms. By Definition 21 of Euclid’s Elements, he will have created four contiguous and concentric cylinders.

The first is G.K.M.L., whose base is K.M.L., formed from the parallelogram A.K., which encompasses the swordsman. The second is N.CC.Q., with its base as CC.Q., formed from the parallelogram A.C. The third is O.DDD., with its base as DDD., formed from the parallelogram A.D. The fourth is P.EEEE., with its base as EEEE., formed from the parallelogram A.E.

Just as these four parallelograms are contiguous and contained within the parallelogram A.E., the four cylinders they create are also contiguous and encompassed by the largest one, P.EEEE. All of these cylinders have two surfaces, one interior and another exterior, except for the swordsman’s cylinder G.K.M.L., which only has an exterior surface.

Since in this construction we couldn’t depict the bases of these cylinders in their entirety, due to the elevation, we deemed it clearer to show them fully in the figure that is placed on the plane beneath this one, with the perpendiculars extended to intersect with their diameter F.F. From the divisions they cause on it, the necessary understanding for their comprehension and explanation arises.

The circle K.M.L., which is closest to the center of the figure, represents the base of the swordsman’s cylinder, created from the revolution of the parallelogram G.K.M.L. Its diameter of one foot corresponds to the distance we’ve determined between the centers of the arms.

The immediate circle CCCC. represents the base or foundation of the cylinder that was formed by the revolution of the parallelogram A.C. Its radius, H.C., is two and three-quarters feet, and its full diameter is five and a half feet.

The circle DDDD. represents the base of the cylinder, formed by the revolution of the parallelogram A.D., and its radius H.D. is four and a half feet, and its full diameter is nine feet.

The circle EEEE. is the base of the cylinder, formed by the revolution of the parallelogram A.E., which encompasses the others. Its radius is six and a half feet, and its full diameter is 13 feet. The bases of all these cylinders are concentric to one another.

To these bases and circles, another circle of four, BBBB., follows. It’s located eight and a half feet from the center of the figure and is concentric with the aforementioned circles. Its diameter is 17 feet, and the space between this circle and the adjacent one, EEEE., is two feet. Following this last circle is another, FFFF., concentric to the others, with a radius of nine and a half feet and a diameter of 19 feet. The distance from this circle to the adjacent one, BBBB., is one foot. In this space, at intervals, there are smaller circles marked with the letter b.

Now, it is fitting to show the resemblance that this idea of our Fortress has with the fortifications of the Plazas.

In any kind of fortification, attention is first given to the site that is to be fortified, to the people and the weapons, to the material with which it will be built, and to the form it will take.

The site for fortification can be on flat land, on a mountain, or on a hill, which has aspects of both, or on the sea and its ports.

Regarding the people, not only is attention given to those who will defend the Plaza, but also to those with whom it can be attacked. It is commonly believed that one fortified individual is worth six of the besiegers. There are authors who claim that one of the fortified is worth ten of the besiegers. Based on this consideration, the capacity of the Plaza is determined, not only in terms of housing but also to ensure there is sufficient space for the handling of weapons, both near its circumference on the inside and in the center of the Plaza. The designated space is often called the “Plaza de Armas” or “Weapons Square.”

The weapons used to defend the Plazas are either purely defensive, like walls and bastions, or offensive. The latter is subdivided into smaller arms, like arquebuses, muskets, etc., and larger ones, which are different types of artillery: cannons, half-cannons, culverins, half-culverins, sacres, etc.

With the primary weapons, the walls, the inner polygon is defended. The so-called outer polygon is defended with the second set of weapons, whose jurisdiction extends to the range of the musket. With the third set of weapons, the territory within their range is defended, and these compel the besiegers to set up their circumvallation line far enough from the Plaza so as not to be harmed.

The material used to build the Plazas can be earth, stone, or brick, and for ships constructed for sea warfare, which are called warships, wood is used. These ships are also mobile fortresses designed for both defense and offense.

The shape of the Plazas can be circular, as they were traditionally made, or polygonal, as experience has shown is necessary for them to be defended from the weapons now in use. These can be triangular, quadrilateral, pentagonal, etc. These variations are seen in fortified cities, citadels, or castles, and field forts, shaped like stars, pincers, and redoubts, half-moons, etc. Others are used by the besiegers to fortify their quarters and circumvallation lines.

In the same order, we will go on to explain the resemblance that the idea of our Fortress has with the aforementioned.

Firstly, the location is considered, and the fencer cannot choose it, as he must fight wherever his opponent confronts him. However, to elucidate our idea, it has been convenient to select a flat terrain, as depicted in the previously explained figure. This serves to better clarify our point, much in the same way that, to teach irregular fortification, one must first understand regular fortification, the principles of which one should strive to maintain as much as possible, even when presented with irregular situations.

Regarding the people who must defend and storm our Fortress, according to our propositions, it boils down to two combatants. For the sake of clarity, we assume that one has to defend this Fortress against his opponent, who wishes to conquer it.

Although it’s observed in fortified places, as mentioned, that one fortified individual might stand against six besiegers, this shouldn’t be applied to our fencer. It’s not that he can overpower six opponents. What he can do, however, is with a slight movement, whether whole or partial, counteract the complete or partial moves of his opponent, granting him a significant advantage, perhaps even greater than a ratio of one to six, as demonstrated in some of the scenarios we addressed.

La Plaza de Armas de eſte Fuerte ſe proporciona por la cantidad de la longitud del brazo, deſde el axis de ſu cilindro, y parte dèl, correſpondiente al centro del brazo, haſta el centro de los gavilanes, como ſe vè en el eſpacio que comprehende el circulo dos CCCC. en el qual no ſolo ſe puede mover el Dieſtro ſobre ſu centro; pero tambien dar ſus compaſes con mucha facilidad à todas partes, para las operaciones à que le obligare el contrario.

The weapons used to defend this Fortress are the sword and its guard. Within them, two types of defenses are identified: one is solely defensive, consisting of the guard and the strong part of the sword up to its midpoint. With this stronger part, the defense of the space from C to D in circumference is formed. We aptly compare this to the inner polygon of fortresses, as both focus primarily on defense. The other half of the sword, from the midpoint to the tip, defends the outer space in circumference from D to E, enclosed between the two circles DDDD and EEEE. We aptly liken this to the outer polygon of fortresses. Just as this outer space or polygon in fortresses is defended by smaller weapons like arquebuses and muskets, our Fortress is defended with the cut and thrust of the sword. And just as besiegers can’t approach fortresses without danger due to the range of these weapons, so an opponent can’t break the range the fencer maintains with his arm and sword without danger.

The space from circle E. to B. is what we compare to the area defended by the Artillery with its range from the Fortresses, because within this jurisdiction and space, the fencer can reach and wound his opponent easily using a compass, without leaving the Fortress or changing its position. And for this reason, just as the Artillery forces the besiegers, to avoid danger, to establish their encircling line at a distance, and with such proportion, that it’s not just the Artillery that can harm them for having come too close, but also considering that if they are too distant, they will waste more time than necessary approaching the Fortresses through their trenches: with these same considerations, we have determined in our Fort this distance, so that the one intending to attack it neither risks too much by being too close, nor wastes excessive time if too distant, waiting for opportunities presented by the carelessness of the Diestro not maintaining his Fort with defense. And for these mutual conveniences, and the possibility of going on the offensive without changing the position of his Fort, we say that this distance between the two opponents is (and we appropriately call it) the true mean of proportion, as it is where both have security and an equal disposition to approach each other, given the length of their swords, and the ease with which each can take their steps.

The outermost circle FFFF is imagined to be outlined by the left foot of the opponent, and with the center of his right foot, he describes the inner circle BBBB. He stands perfectly on a right angle at F.B. in this middle proportion relative to the fencer (Dieſtro), each establishing their fortress without any difference.

In the space from B to F in circumference, there are little circles marked with a b, representing the base of the opponent’s cylinder when the fencer stands on a right angle at K.L. Thus, his line of direction M.H corresponds to the center of his fortress’s figure H, as is clearly shown.

The substance of our Fortress is partly physical and partly mathematical: the physical part is the sword and its guard, and the imaginary part is everything considered in the figure presented in perspective and in plan. Yet, for the fencer, it functions as if the whole fortress were actually made of steel and iron, just as the guard and sword are, given the possibility he has to position it anywhere for his defense. To clarify this, it’s noted that in fortresses there are essential and incidental parts, and these same elements are found in our Fortress.

The essentials of fortresses are walls, embankments, bastions, moats, etc., and these are constructed before any enemy lays siege. The incidental elements include tenailles, half-moons, traverses, redoubts, counter-batteries, counter-mines, counter-approaches, etc., and these are often constructed when an enemy sets up camp, opposing their plans.

The essential part of our Fortress is the sword with its guard, which are ready before the occasion to fight arises. The incidental part involves the fencer positioning it in areas as needed to counteract his opponent’s intentions. From this capability emerges the idea of our Fortress as if it were entirely made of steel and iron. And because we’ve demonstrated some of this in explained cases, it follows that with these essential and incidental parts, this concept has enough substance that we can appropriately say it bears a great resemblance to real fortresses and strongholds.

Regarding the shape of our Fortress, it is exceedingly perfect, as can be seen in the perspective figure, and even clearer in the one laid out flatly. This design encompasses the ancient style of fortifications that were circular, as well as the modern method of fortification, which uses angles similar to bastions, both in the inner polygon and the outer. Immediately next to them is the appropriate space with its surrounding area, suitable for the weapons of both combatants.

However, since we have already explained these spaces and the Parade Ground at the beginning of the previous chapter, and the entire figure, both in perspective and flatly, and successively what each part is and serves for, and the concept of this Fortress, we now only have left to explain the angles of the inner and outer polygons that we imagine in the figure and how vital it is to understand their purpose, which we explain in the following manner:

The angles of the outer polygon serve as a guide for the position the opponent’s sword on its sides, either on one side or the other; by doing so, it ensures his defense so that it doesn’t point towards his body and cylinder. This can be achieved in various ways.

Firstly, when the fencer stands balanced with his opponent in the middle of proportion, as depicted in the figure, he can, through a Atajo either from the inside or the outside, and also from both sides at a sharp angle with greater strength, manage to place his opponent’s sword on the sides of his angles using any of these four universal methods to interact with the opponent’s sword.

Another way is when the opponent places his sword on any of the sides of these angles, sometimes interacting with the fencer’s sword and other times not, voluntarily.

Another method is when the fencer forces the opponent to position his sword on any of the sides of these angles, through an attack either from the inside or the outside, to execute his strikes at the moment of deviations.

And the last method is when the Diestro takes a step to one side or the other, blocking the path corresponding to his opponent’s sword to launch an attack. This action causes the opponent’s sword to end up on one of the sides of these angles. Most of the time, the Diestro is in a position to strike, or at the very least, forces the opponent to make movements out of necessity. Taking advantage of these, he can immediately attack.

The angles of the inner polygon are also imaginary, like the others. When following the precepts of this science, they serve as if they were physical and real, allowing the Diestro to position his opponent’s sword on either of its sides through various means.

The first method assumes that the Diestro waits for his opponent to attack him, ready to execute any of the five types of wounds that are possible. If the attacks were thrusts and were aimed above the guard, with a slight upward movement, he will ensure they don’t target his torso, face, or head. If the opponent’s thrust is aimed at any side of the guard, with just a minor movement of it, he can place his opponent’s sword on any side of these angles, achieving the same defensive effect. If the thrust is aimed at the lower part, under the jurisdiction of the acute angle, the opponent’s sword, if intending to strike, will have to pass through the weaker part of the Diestro’s sword, be it from the inside or the outside. Also, with minimal movements, he can defend and position the opponent’s sword on any side of the angles of this polygon. If the opponent forms circular or semi-circular feints from the upper plane, aiming to strike the Diestro, he can also, with very short movements of his guard, defend against them, regardless of their type. If the opponent attempts these types of attacks in the lower plane, under the jurisdiction of the acute angle, the Diestro can also defend against them with greater strength in his sword and very short movements.

The space between the outer Polygon (end of the Orb of the Diestro’s Sword) and the mean of proportion B, although primarily designed for the opponent to move in order to approach the proportional means of the tricks, doing so transversally, resembles the trenches made by the besiegers of the Fortresses obliquely, so that the bullets from the Artillery cannot directly target them. The opponent, to avoid the risk of equality and the danger of attacking along the Diameter line, moves on the sides of the Angles, which we also imagine in this space. The sides of these Angles can also be used and are advantageous, just like those of the previous Polygons, because many times it happens that the opponent, with the sword in hand, voluntarily places his arm on its sides on both parts, especially for a trick, whose name is to Call. It also happens that he places his arm on its sides due to the attacks of the Diestro. At other times, the same occurs when the Diestro uses one of the four universal methods from the mean of proportion to position the opponent’s sword on one of the sides of the outer Polygon’s Angles, and the opponent voluntarily, at the same time, places his arm on one of the sides of the Angles that are in this third space, making it easier for the Diestro than he might have otherwise managed. Thus, it’s not a stretch to say that the Angles in this space form a third Polygon, because from what we’ve mentioned about them, it’s evident that the same effects can be achieved as if they truly were one.

With this in mind, we can confidently say that our idea of our fortification is even more favorable to the Fencer than real fortresses and strongholds are to besiegers, as they don’t offer as many defensive and offensive positions.

Note that this idea of our stronghold, which we’ve conceived for the Fencer, is also imagined for his opponent without any differences. This implies that if both are right-handed and each knows how to defend in their stronghold, one cannot offend the other. Because no matter how they move, whether around the center of their particular circle or from place to place, they will bring these positions with them, and only through negligence can an offense occur.

Someone might argue that this treatise is not essential for Fencing, thinking all this elaborate construction of our Fort to be superfluous. But to clarify for those who question, we reply that it is the fundamental basis of all Fencing, upon which its mighty mechanism relies, as will be demonstrated later. We position it here after having explained in the preceding chapters what is necessary for understanding and practicing the Art, its Method, Definitions, specific terms of this science, the Requests, Maxims, and general Precepts to be observed, and the Geometric Definitions that the enthusiast should bear in mind, along with their adaptation to Fencing, and the practice and use of the Compass. Without this knowledge, one would proceed blindly, and many terms, such as Cylinder (in which we envision the fencer), how to contemplate it, how many and what kinds can be formed by his arm and sword with its rotation, according to the divisions in which we partition its quantity, etc., would remain unclear.

So that the curious might better visualize what we want them to conceptualize, we’ve prioritized their benefit over our efforts, offering them this Fort with its adaptation to our science, and providing them with a thorough understanding of the potential it offers for both defense and offense. This is for those who are protected by its bulwarks, angles, and lines of fortification, both internal and external, to achieve the desired goal, which is where the aspirations of our well-founded doctrine lie.

Just as in Mathematics, its practitioners are allowed to conceive of Spheres, Circles, and other lines to regulate movements, whether of the stars in the sky or ships in the water, I believe I too have been permitted to shape ideas to adjust the movements of the arm and sword in the air, aligning them simultaneously with the feet on the ground. If the former serves for contemplation and utility, the latter serves, no less profitably and notably, for the preservation of the minor rational world, or Microcosm, as the Greeks called it, which is the well-organized fabric of the human body. And if those are suited to their purpose, such as imagining routes or paths for navigation, so too are the ideas we conceive for weaponry, as there’s nothing more appropriate for man’s defense and offense than considering the siege and conquest of a fortress. Here, it should be noted that just as Astronomy contemplates those different spheres in which the bodies of planets move, seeing them as complete without anything material in them other than the bodies of the planets forming them through their movement, so too should Fencing consider its fort completely, even though there’s nothing material in it other than the Sword, which describes and shapes it through its movements. Moreover, in this, we have conformed to the rules most accurately observed by the Military in its wise operations.

Lamina tercera del Libro ſegundo

 

Plate three of the second book

 

CHAPTER NINE

BRIEF EPILOGUE, OR COMPILATION OF THE most essential points of the Art of Fencing, and the manner of discussing it; whose foundation will show it to be a science subordinate to Mathematics, arguing in this way.

The Queen of Mathematics, which is Geometry, has as the object of her demonstrations and evidences four kinds of continuous quantity: the Line, the Angle, the Surface, and the Body, as evidenced in the Elements of Euclid, of Apollonius, in the books of Archimedes, Pappus of Alexandria, and countless others, etc. The Art of Fencing is founded on the consideration of these same four kinds of continuous quantities of Lines, Angles, Surfaces or Planes, and Bodies caused by the movements of the Sword, as evidenced by all those who have written on this subject, and was specified in the Prologomenon I wrote in the Book of Science, whose repetition should not tire the Reader, because it also fits here: from which it follows that the Art of Fencing is one of the Mathematical Sciences, subordinate to Geometry. At the very least, it is shown that the purpose of the Art of Fencing is to defend oneself or to wound the opponent if it serves in defense; and this must necessarily be through the movements of the Body, and of the Sword and arm; these movements cannot be made without the formation of these four kinds of quantities; hence the Art of Fencing is based on these kinds of quantities.

The minor point is proven with the clear demonstration that every continuous quantity with its movement sometimes causes another quantity of the same kind as itself, and sometimes of a different kind; for example, the line that moves laterally causes a Surface, which is of a different kind than the line; but if it moves straightforwardly it causes a straight line: the Surface, when it moves according to its length, or width, causes a Surface; but moving according to the variety of its movement, and of its ends, which are lines: bodies also cause the same effect; for example, the Sphere, when moved on its axis maintains its same shape; but however else it moves straightforwardly it causes a Cylinder; and the Point, which is not a quantity, moving in any way causes a straight, circular, or mixed line.

In the Art of Fencing, the tip of the Sword represents a point, which when moved necessarily creates a straight, circular, or mixed line, depending on the type of its movement it will create a line or a flat or curved surface; and this surface with its movement will also create volume; and the Angle is formed from the intersection of the lines that are considered in these three types of quantity: thus it is clearly proven that movements cannot be regulated without first paying attention to the quantity that is formed from them, because to treat the Sciences methodically, what is first in resolution, is last in composition: all of this assumed, in order for us to speak on this matter with order and clarity, it will be necessary, according to Aristotle’s doctrine in his Analytics, starting by considering the Art of Fencing by its main objective, which is to wound or defend, we will find that it must necessarily be through the movements of the body and the Sword, which is the most universal thing found in this matter; then delve into the specifics, which is to consider in how many ways these movements can be, so that we take individual notice of each one: and considering well the power of the body and the arm, which is who has to move the Sword, we will find that each one can move in two different ways, namely straight or circularly; when the body moves straight it can be forward, backward, to one side, and to another, and by the mid-divisions, which come to be eight paths, or directions, that are considered for the steps; and when it moves circularly it can be by the circumference of three different circles; namely, its own, that of the middle of proportion, whose center the opponent occupies, and the common.

The Sword can move straight or circularly: straight will be when it goes in a straight line: circularly, when with the center of the arm, elbow, or wrist, it describes some circles with the tip of the Sword: this circular movement is considered in two ways, one when the Sword, forming a circle with the tip, moves on a plane: and the other is when it moves on a curved surface, forming Pyramids: the Planes can be vertical, horizontal, and oblique, as we will inform the fencer throughout.

Note that from the perfect knowledge of these Planes and Pyramids, one achieves the total perfection of this science, because not only do they regulate the movement of the Sword in the air; but also that of the body on the lower Plane, always having to find such a correspondence between the whole and its parts, that it is necessary to have only one north as a guide, and this is found in the speculation of the Planes and Pyramids.

CHAPTER TEN

DESCRIPTION OF DIFFERENT FIGURES, through which the straight, circular, and mixed lines that can be considered, both from the movement of the body and the Sword, are shown. Their use is of utmost importance for the true understanding of the Art of Fencing.

First Figure, Plate Four.

Let’s assume that with the length of the Sword A.B., which is four feet, a circle B.C.D.E. is described on the ground, whose center is point A. The circumference that is described with the tip of the Sword, moving around the pommel that is at point A, will be a very mysterious circle in Fencing because it determines the distance that should exist between the two fighters, which is from point D. to point B. being eight geometric feet; and this Circle will be called the Common Circle, because in it the opponent has as much jurisdiction as the Fencer; and if the Fencer is in D. and his opponent in B. having equal or marked Swords, they will have chosen a midpoint of proportion, as is demonstrated by the two figures of this fourth Plate.

Second Figure, Plate Four

This same circle, which has been explained, shows the jurisdiction of each of the two fighters, because if each one places the pommel of the Sword at the end of the Diameter that corresponds to him, and each forms his own particular circle, he will see the jurisdiction he has in this common circle to make his moves, because we will show that they cannot be greater without discomposing the body. This is what is made evident by this second figure with the three circles, one with its common center between the two fighters, and the other two have their center at the end of the common Diameter C.D.

The two particular circles each contain within them three other concentric circles, which are caused by the revolution of the divisions of the Sword. For greater ease (although others imagine it divided into 12 parts), we consider it divided into four parts, each one being a third, or a geometric foot, which is the same, as demonstrated both by the preceding figure and by this one.

In each of these circles, either of the two fighters can make his moves in the way he wishes, because the quantity of its Semidiameter, which is the length of the Sword, determines the size of the move that either of the two fighters can make without discomposing the body. And although the movements that each can make, moving from the center to the circumference, seem infinite (since there are infinite lines that can be drawn to it from the center), given that sailors, despite having such a vast horizon, only consider 32 directions to steer their ship and take it to any part of the world; we will be satisfied with eight, since the circle in which the fencer moves is very limited. Each of these directions serves to make his moves and has its own particular name, as will be verified by the third figure, which we will explain very clearly in this way.

Third Figure, through which the straight movements or steps that the body can make on the lower plane are made evident.

The same circles described in the previous figure are drawn here, with the concentric circles divided into eight semidiameters, as represented by this third figure. Through it, one will understand the straight steps, assuming the fencer is positioned in the center at letter A, taking his steps in this manner.

The step taken along the line A.B., which goes straight to his opponent (whom we also assume is positioned at letter B), will be called ‘straight.’ The step taken along the line A.F., moving backward, will be called ‘alien’ or ‘strange.’ The step taken along the line A.C. will be called ‘transversal to his left hand.’ The step taken along the line A.I. will be ‘transversal to his right hand.’ The step taken along the line A.D. will be ‘trepidation to the right hand.’ The step taken along the line A.H. will be ‘trepidation to the left hand.’ The steps taken along the lines A.E-A.G. will be called ‘trepidation, and strange, to the right or left hand.’ The use of each of these steps will be explained in its place.

Plate four of the second book.

CHATPER ELEVEN

IN WHICH BOTH THE Proportional Means, as well as the appropriate positions that the Fencer should choose, are Demonstrated

In addition to these circles, which display the jurisdiction the body has to take its steps, and the one given to the Fencer’s imaginary fortress, we imagine other circles to show the jurisdiction and reach of the sword when the Fencer stands with it at a right angle.

Let’s assume that the line A.B. is the distance of the diameter of the common circle, which is eight feet, or the length of the sword twice over. Divide it into eight equal parts, each one being one foot. Take the distance A.C. to be six feet, which is the length of the arm and the sword, and draw a circle with this interval. This will be the circle of the sword’s jurisdiction, which from now on we will call the Orb of the Sword. Continue drawing the remaining circles passing through D, E, F, G, and H. Each one of these circles serves to recognize the jurisdiction of both the Fencer and his opponent, to take their steps for tricks. The circle passing through B represents the position the Fencer should be in to have chosen the middle of proportion, as we will show in its place; the outermost circle shows the circle the left foot should create when, while profiled or squared off with the opponent, the right foot moves inward.

The space between circle B and circle 6 is the distance from the proportional middle to the appropriate distance for thrusts and has a jurisdiction of two feet, which is the least the opponent can move to go from one middle to another.

The delineated space between the sixth and fifth circles is the place for the proportional means for thrusts. The space between the fifth and fourth circles will be for the proportional means to form cuts, reverses, half cuts, and half reverses, and to establish the most powerful bind.

The space between the fourth and third circles is where the opponent should stand to make the Fencer make a concluding move; however, not anywhere within it, but on the side that corresponds to his right side, as will be explained later. Understand that the opponent will occupy the distance from one circle to another with his foot, and these spaces, for brevity, we will call Orbs from now on.

The third circle is of great importance in Fencing, because it shows the place of the proportional means that the Fencer should choose to move easily and safely from the middle of proportion to the appropriate positions.

The second circle shows how far the Fencer’s sword’s pommel or the opponent’s tip reaches in the upper plane when the opponent stands in his middle of proportion. It also shows the smallest step that can be taken to move from the middle of proportion to the appropriate position along the diameter line, which is the shortest line, though it is the least safe path.

The first circle is the one in which the Fencer is considered positioned and is called the Fencer’s Particular Circle.

The outer sphere, which is between the right and left foot, is called the Maximum Sphere, and of the means of proportion.

Note that we consider just as many Spheres for the opponent, and in the same way that the Fencer is in the middle of all these Spheres or circles, the opponent, assuming he is equal to him, will also be in the middle of his own.

But now, if we consider our Fencer positioned at the center of his circle at A, and imagine that the Sphere of the Sword, with all its circles, its straight lines, parallel planes, would be always rising parallel to the horizon until it reached the level of his head, we would find that the outer circle and Sphere of the Sword, with its perpendicular movement, would have created a cylindrical surface, like a tower or a castle. And that the other inner circles would have done the same. If these circles were real, as they are imaginary, the innermost ones, up to the sword guard, would always be stronger and offer more resistance, because the sections of the sword are stronger the closer they get to the guard. But we would also find that if there were many sword tips around the entire outer circle, one would have to admit that there would be much resistance in the conquest of this castle: the part of it that is between the sixth and fifth Sphere would be defended with the tip of the sword and the edge; the other part, which is from the fourth to the second, touches from the second, or middle division of the sword to the pommel, and looks more to defense than to offense.

The inner cylinder 1 will be like a column, in which the Fencer is considered positioned so that the surface of his body can be considered with some regularity, to imagine on them some lines that serve the direction of the tricks.

The straight lines that divide all these circles into eight equal parts, with their movement, would have caused four vertical planes, which, intersecting the inner cylinder where the Fencer is considered to be, create on its surface eight lines. Imagined on the Fencer’s body, each one has its particular name.

The line corresponding to A.B. will be called Vertical of the chest, because for better understanding, we consider that the Fencer is directly facing his opponent, who is at B. The line corresponding to the part of the plane passing through A.2 will be called Right Lateral. The line corresponding to the part of the plane passing through A.8 will be called Left Lateral. The line corresponding to the one passing through A.3 will be called Right Vertical. The line corresponding to A.7 will be called Left Vertical. The other three lines correspond to the back; the line corresponding to A.4 will be called Right Lateral of the back. The line corresponding to A.6 will be called Left Lateral of the back. The one corresponding to A.5 will be called Diametral of the back.

The consideration of these planes, these spheres, and these lines is of such consequence in Fencing that almost all its excellence lies in them. As we have shown, Fencing is nothing other than movements, both in part and as a whole, and these movements are regulated by lines and planes. All the lines, planes, and surfaces we imagine here are so proper that they all derive not only from the symmetry of man but also from the true measure of the sword, the weapon with which one must attack and defend. Thus, the great utility that can be drawn from this figure for understanding this science is clearly recognized.

With this figure, the Fencer will easily see how he can form his movements with the sword, shifting it to different planes, and at different angles, and immediately afterward the correct positions in which he can stand.

Using this figure, he can examine the strength of his arm and sword in any of the planes where he might place it, to make use of this knowledge for the occasion in the formation of the technique, and to attain the true understanding of the matter through its cause.

By this figure, he can examine in which of these planes his body will have a greater disposition to take his steps, to understand how his opponent might when he sees him positioned, and make judgments about the immediate disposition he might have to act.

One can use this figure to become accustomed to the selection of both the means of proportion, as well as the proportionals and the proportioned. The mean of proportion is found between circle 7 and 9 and closely resembles what they call the encirclement of fortresses, or the cord set by those who lay siege at such a distance that they are neither too close to the fortress, risking considerable damage, nor too far away, which would cost them a lot of time to approach.

The same principle applies to this mean of proportion, whose distance must be such that it is not so close to be easily injured with a small movement, nor so far that one could attack it without being noticed.

The proportioned means are found in different areas: either they are for thrusts and lie on the circumference of the Sphere of the Sword; or they are for cuts or reversals, half-cuts, and half-reversals and are on the fifth Sphere; or they are for finishing movements and are on the fourth. The third sphere is where the proportional is, as mentioned above. To better understand these means and their etymology, we will clarify these terms and try to provide some rationale that has led authors to use these names of proportion and proportioned, and for us to add the term proportional.

Plate five of the Second Book.

CHAPTER TWELVE

Etymology of the Means of Proportion, Proportionals, and Proportioned; and the circular movements that touch the body in the lower Plane.

Euclid, in book 5, Defin. 6. of his Elements, says that proportion is a similarity of ratios; and in Defin. 3. of the same book, he says that a ratio is the relationship one quantity has with another, as to how it is equal, greater, or lesser than it. Even though, according to this definition, there cannot be a proportion among less than three quantities, the terms ratio and proportion are still often conflated, contrary to Euclid’s intent or purpose. Authors call it the means of proportion to the distance chosen by the two combatants because this distance is proportional to the weapons they use for fighting.

Euclid refers to a mean proportional when among three quantities the same proportion is found from the first to the second, as from the second to the third. The one that lies between the two extremes is called the mean proportional. For example, with the numbers 9, 3, 1 of the first figure, 3 will be the mean proportional between 9 and 1 because there is the same proportion from 9 to 3 as from 3 to 1. The same understanding applies to the numbers 8, 4, 2 from the second figure, where 4 is the mean proportional between 8 and 2.

In the circle, or semicircle, there exists a unique property: whenever a perpendicular is raised from any point on the diameter and terminates on the circumference, it will always be the mean proportional between the segments of the diameter. For example, in the semicircle A.D.B. indicated by the third figure, if the perpendicular C.D. is raised from point C, it will be the mean proportional between A.C. and C.B. This can be inferred from the corollary of proposition 8 in book 6 of Euclid’s Elements. One can empirically test this, finding that if A.C. is 1 and C.B. is 9, then C.D. will measure 3.

The second example can be seen in the fourth figure. In the same manner, given that E.G. is 2 and G.F. is 8, G.H. will be 4, serving as the mean proportional between the two segments, based on the same referenced proportion.

Now, we will show in the fifth figure that follows, how in the common Orb, which is considered between the two combatants, we find these same proportional means that converge at a point, which we call the proportional middle.

Let the circle A.B.C. have a diameter of eight feet, which is what we call common, where the two combatants stand with their right feet; and let the other external circle of the left feet be D.E.F. with a diameter of 10 feet. Draw a tangent I.A.H. from point A to the inner circle, which will be perpendicular to the diameter D.F., according to proposition 16 of book 3 by Euclid. Based on the aforementioned reason, it will serve as the mean proportional between the line D.A., which is one foot, and the line A.F., which is nine feet. The same will apply to the line H.K., perpendicular to the other diameter G.E. that is 10 feet. The line K.E. is eight feet, K.G. is two feet, and the mean K.H. will be four feet, being equal to and parallel to the radius of the common circle A.L., as can be verified in figure number 5.

And because at point A is the mean proportional, and at point K is the proportional mean for the atajo, as will be shown in its place, with our proportional mean being at H, it can be seen that all three means are located at the angles of a right triangle, whose base opposite the right angle is A.K., measuring five feet. Due to such a large distance of five feet, especially with the left foot positioned at D, it seems nearly impossible to take such a large step, which is almost six feet, to move from the mean proportional to the proportional mean. This is the reason that has prompted us to search for a mean between these two extremes, arranged in such a way that what cannot be achieved with one step can be easily and safely accomplished with two, as anyone can verify by drawing a figure on the ground in the required manner, to practice the necessary exercises to easily find these means, both in proportion, and in proportionals and proportionates.

Warning for this and for the seventh.

Take note that, in addition to the absolute necessity of understanding this mean, it offers a great ease to transition from it and choose all the proportional means for all the maneuvers. Although many may appear evident, we have nevertheless reduced them to a total of nine so as not to deviate from what our predecessors have left us. Our intention is to simplify this subject, not obscure it, as will be explained in these two diagrams, numbers 6 and 7. Thus, the six means presented in diagram number 6 are from the distant end and are located on the circumference of the Sphere of the Sword. They lie along the sides of two isosceles triangles and their perpendiculars, specifically, at the intersections of these straight lines with this circle and are used for thrusts.

Two of them, present in diagram number 7, are used for cuts, reversals, half-cuts, and half-reversals. They are located at the intersections of the perpendiculars of these triangles and the fifth Sphere of the opponent’s Sword, and are also useful for the most powerful bind. The ninth, also present in number 7, is for concluding movements and is situated in the opponent’s fourth Sphere and on its tangent from the common inner circle. To better illustrate all of this, the diagrams will be explained in the following manner.

Explanation of Figure number 6.

Let there be a common circle A.M.B. with a diameter of eight feet, and the outer circle of the left foot of 10. Let’s consider the Sphere of the opponent’s Sword to be at point B, which intersects its tangent N.B.E. at E.N.

Draw the lines C.E. C.D. C.B., and the isosceles triangle C.B.E. will be formed, with its base B.E., its perpendicular C.D., and its vertex C, which is our proportional mean. We also consider another isosceles triangle on the other side of the Diameter I.N.B., with its base N.B. also of 6 feet, its perpendicular I.O of 8 feet, being equal to the Diameter A.B. Each side and perpendicular represent a path from the means of proportion to the proportional means, and these means are determined, that is to say, those of the distant end in F.G.H. by the jurisdiction of the opponent’s arm, and in K.L.M. by the jurisdiction of the body.

Point F. represents the means for maneuvers of the first intention, or for the fourth circle. Point G. is for the full circle. And point H. is for the general moves of weakness above, and strength below by the jurisdiction of the arm.

Also, the mean at point F. is useful for the general constriction by the same jurisdiction. And point G. for cross line. Point K. from the other triangle of the jurisdiction of the body, serves for the general constriction by this jurisdiction. Point L. serves for the cross line. And point M. serves for the two general moves, below and above strength.

Explanation of Figure number 7.

In this figure num. 7, the point T. serves as the means for cuts, reversals, half-cuts, and half-reversals, whether diagonal, vertical, or horizontal, by the jurisdiction of the body.

The point R. serves the same purpose by the jurisdiction of the arm, and also serves as a proportional mean for the most powerful block, from which one can move to the conclusion motion.

The point S. also in this figure number 7, serves as a mean for the conclusion motion; and we will provide a more detailed and precise demonstration of all these means in a demonstration that we will conduct for all of them, which we will call universal.

WARNING

Let the fencer note that even though we have identified these proportional means, we do not intend to suggest that merely positioning oneself in these positions is sufficient to attack the opponent without other considerations. If the fencer doesn’t apply their defensive pyramids at the same time, they would have achieved nothing. For instance, in the siege of a castle or fortress, little would it matter to have a breach open for assaulting the place if the offenses from inside the fortress are not neutralized. Similarly, it would matter little to a fencer to have chosen these means if they do not hinder their opponent and remove the threat, always covering themselves and forcing the opponent to point their sword away from their body. This will be further clarified when we delve into atajos

From this, it follows that the proportional mean should not be understood merely as the position we indicate for each technique, but rather when, along with the body’s movement, both straight and circular, the sword’s movement also aligns, preventing any potential threat from the opponent, from the moment one moves away from the proportional mean until one is able to attack the adversary without receiving harm. Otherwise, this distance would be termed common to both. Hence, we will need to explain all the movements that serve to set these impediments, which we will call atajos, even though interception and impediment are the same thing in their common sense. Simultaneously, we will address the potential attacks from each of these positions to offend the adversary.

However, before delving into these, it would be best to first conclude with all the movements that concern the body in the lower plane, due to the significant correlation between the movements of the lower plane and those of the upper or intermediate plane, through which the sword must move. As we have already discussed the straight body movements, which are the straight and transverse steps, etc., that are made along those eight lines we call directions, we now need to address the body’s circular movements, performed in three different circles.

Figure num 8.

The first circular movement is made within its first particular circle, which is the first of those that make up its Orbs, and is performed without moving the center of the heel of the right or left foot, forming with the tip of the same foot a circle, as seen in this figure num 8. This movement is called motion about the center, and this movement serves to oppose the steps or movements that the opponent might make around the circumference of the maximum Orb, as seen in the same figure. When the opponent is at B, and moves around the circumference B.C. to C, the swordsman, to oppose him, will move the tip of the foot in A.C. The same will be for A.D.

Figure num 9.

The second circular movement that the swordsman can make is around the opponent’s maximum Orb, which is the Orb of the means of proportion, and is called curved step because it’s taken along the circumference of a circle. This step is used to seek an advantage over the opponent, if they neglect to make the proper opposition with the motion about the center. So, if the swordsman, being on the circumference of the maximum Orb, takes a curved step from B. to point C. by the profile of the body, or to point D. by the posture of the Sword, and their opponent, who we assume is at point A. in this figure num 9, doesn’t make a motion corresponding to those lines, the swordsman will have gained an advantage for all the propositions of our Fencing.

Figure num 10.

The third circular movement is the one the swordsman will make through the common Orb, which is considered between the two combatants, as seen in figure num. 10. Where the swordsman is at A. and his adversary at B. If he takes a curved step around the common circle from B. to S., he can take his from A. to C., ensuring he always remains in the middle of proportion.

Figure num. 11.

Another step is called mixed, and transversal and curved. This is because part of this step or movement is made in a straight line, and part is made along the circumference of a circle, which is the opponent’s fifth, as seen in this figure. Here, the swordsman is at A. and his opponent at B. If the swordsman takes a transversal step along line A.D. from the middle of proportion A. to the proportioned middle D. for the atajo, and without setting the left foot next to the right, goes on to position himself on the opponent’s tangent; and having set it, he will move the right foot to point E. along the circumference D.E., positioning the heel’s center on the tangent, and with the foot’s length, he will occupy part of the circumference of Orb 5, as shown in the figure.

The same will occur if the swordsman goes to make this concluding movement from the proportional middle C. because the step he takes from C.D. will be transversal, and the remainder from D.E. will be curved. Therefore, this step, or movement made with the right foot along the straight and circular line, will be called mixed transversal and curved for the concluding movement. This will be done much more easily and safely from the proportional middle C. than from the middle of proportion A., as we will demonstrate in its place.

And here we have concluded with what pertains to the lower plane, which is the ground. To regulate body movements, we will describe other geometric figures that facilitate understanding the movement of the Sword and arm in the Air.

Lamina ſexta del Libro ſegundo.

 

Plate six of the second book.

 

CHAPTER THIRTEEN

On the movements of the sword, and the arm in the Air

Just as we have considered in the body three types of movements, which are made either on planes, or circles, or lines, or mixed surfaces; similarly, in the Sword, we consider three other types of movements: some on planes, some on circles, and others on lines or mixed surfaces. And just as the body makes some circular movements on its own center and others on different circles; likewise, in the Sword, we consider movement on its own center to regulate the position of the guard in the formation of techniques, and we consider it moving on other circumferences, some larger and others smaller. Just as we don’t emphasize mixed movements for the body, we also won’t dwell on the infinite curved movements the Sword can make, always following learned scholars who wrote about celestial movements. Although most planetary movements are mixed, they represent all of them through circles to make the complex and challenging easily understandable.

To explain the movements of the Sword, we need to use some terms accepted by mathematicians, rather than inventing new ones. We mimic authors who have written about weapons, who have introduced many such terms, like calling cuts vertical, horizontal, diagonal, etc. Every time the tip of the Sword moves, it will do so on a plane, or a circle, or a mixed line. To explain this more easily, we’ll discuss the different possible planes. Opticians have noted these to represent all the differences in planes and lines found in the universe, and even those imagined in the heavens. They depict the movements of the Sun, the Moon, and the Firmament through lines painted on planispheres, astrolabes, or walls. And since there are no planes or lines on earth that aren’t parallel to those considered in the sky, we will explain all the differences in planes or circles they’ve considered in the celestial sphere. This way, we can know what type of plane we’re making and which it’s parallel to, consequently understanding its type.

Besides the ten main circles considered in the sphere, the six major ones are: Horizon, Meridian, Equatorial, Zodiac, and the two Colures, Arctic and Antarctic. Beyond other circles called Hourly and Position, etc., there are circles called Verticals or Azimuths, and others of Altitude, etc. To satisfy understanding, I will present the following demonstrations, the layout of which the Swordsman will find in the seventh plate.

FIGURE ONE

All the circles of the sphere are either parallel to the Horizon, or perpendicular to the Horizon, or oblique to the Horizon. The circles parallel to the Horizon are called circles of Altitude, or almucantars, as are those represented by these straight lines parallel to the Horizon A.E.B.

The Reader should be aware that circles, both large and small, depending on the various projections, are sometimes represented as a circle, sometimes as straight lines, and other times as ellipses or ovals.

In the Sphere, these circles are used to determine the altitude of the Sun or the Stars above the Horizon; that is, how much a celestial body is distant from the Horizon or from the Zenith, which is point C. The same circles could be considered in the inner hemisphere A.D.B.

In the Art of Fencing, as already mentioned, a horizontal plane or one parallel to the Horizon is considered, which is the ground. To determine the position of the sword’s tip or its guard, or more specifically, how far it is from the lower plane or the upper plane (a plane that passes through the centers of the arms of both combatants), some planes parallel to the Horizon are taken into account, as will be explained in due course.

FIGURE TWO

The circles perpendicular to the Horizon are called verticals because they pass through the Zenith, and all are maximal. Although there can be infinitely many, astronomers divide them into three types, as follows:

The vertical circle that directly faces Noon and the North is called the First Vertical.

The vertical circle that passes through the noon point is called the Meridian, and it intersects the first vertical at right angles, directly facing the Horizon and the West.

Any other vertical circle between these two is called the Declining circle, and this declination is understood from the first vertical: thus, if this circle deviates by 30 degrees from the first vertical, we will say it declines by 30 degrees, or it has 30 degrees of declination from Noon, or from the North, to the East, or to the West. For example, in the second figure, A.B.C.D. is the Horizon, where A. is the noon point, B. is the West, C. is the North, and D. is the Horizon.

The circle represented by the line D.B. that faces point A. on one side and the North on C. on the other is called the First Vertical and passes through point E. which represents the vertex.

The circle or plane represented by the line A.C., which passes through Noon and the North, is called the Meridian. It is at right angles to the first vertical because it spans the entire quarter-circle D.A., directly facing the Horizon at D. and the West at B.

The circle represented by the straight line F.G., which also passes through the vertex E., and deviates by the arc D.F. of 30 degrees, will be called Declining by 30 degrees. The same will be true for any other circle, like the one of H.I. that declines by 60 degrees. The part facing the East, because it is seen from the North point, will be said to decline from the North-East. The other part facing the West, because it also looks at the noon point, is said to decline from Noon to the West, depending on the arc considered between it and the first vertical.

FIGURE THREE

The same demonstration is presented in the third Figure, imagining the Meridian circle as a circle, the Horizon as a line, and the First Vertical as a line as well; however, the Declining circle is represented as an Ellipse. For clearer visualization, I’ve used the same letters in both figures. However, to explain the Nadir, I’ve added the letter K in the third figure.

But to explain the other three types of circles, or planes, that we have yet to discuss, it’s essential to know that every circle, both major and minor, has its Poles, and the line joining them is called the Axis or Axle, upon which it moves or is imagined to move.

The Pole on the surface of the Sphere is a point that is equidistant from all parts of its circumference, much like the center on a flat surface is equidistant from its circumference.

In the second figure, the Pole of the Horizon A.B.C.D is point E, representing the Zenith, or Vertex; and because it’s represented on a plane, not on the surface of the Sphere, there’s no other point that can be the Pole in this type of projection but the center.

The First Vertical, represented by line D.B., has its Poles at A. and C., which are the Noon point and the North, and they are equidistant from the circumference represented by D.B. because anywhere there’s a quarter-circle, like A.B., A.D., C.B., C.D. Its Axis will be the line A.C.

The Poles of the Meridian, represented by A.C. for the same reason, will be the two points D.B., the true East, and the true West, and its Axis D.B.

The same is represented in the third figure, where A.C. is the Horizon, its Pole will be point E., Vertex, and the Nadir at K. The Poles of the Meridian are D.B. corresponding to its center; the Poles of the first vertical are the same A.C. The Poles of the declining circles will be on the Horizon and will deviate from the Meridian by the same amount of their declination.

All of this will be better understood through a tangible Sphere, but nonetheless, with this understanding, I’ll attempt to explain the other three types of Planes: those that lean towards the Horizon, those that decline from the Horizon, and those that both lean and decline simultaneously.

FIGURE FOUR

In this figure, let’s assume that the circle A.C.B.D is the Meridian, A.B. the Horizon, and C.D. the First Vertical. If the First Vertical, moving over the Poles of the Meridian that corresponds to point G, and if the line C.D. were to incline with point C. moving from C. through C.B. to F. and point D. moving along the circumference D.A. to E., this circle would be called Inclining to the Horizon, by as many degrees as the arc B.F. represents.

FIGURE FIVE

If the Meridian were to move over the Poles A.C. of the First Vertical and were to incline towards the Horizon, or if the Horizon were to move over the same points A. and C., it would come to represent some circle, such as A.F.C.G. Even though it is inclined towards the Horizon, to differentiate it from the previous one, it is called Declining to the Horizon.

FIGURE SIX

However, if the Declining circle were to incline towards the Horizon, approaching it, this circle would be called both Inclining and Declining, like the circle C.G.F.I. In addition to the decline measured by the arc G.H.G.I, it also has an inclination, which is measured by the arc C.D.

FIGURE SEVEN

From all that has been mentioned, it follows that all the distinctions of planes can be reduced to seven, which are Horizontal, First Vertical, Second Vertical or Meridian, Declining, Inclining to the Horizon, Declining from the Horizon, and both Inclining and Declining together.

Let’s now see how we can apply this to the Sword, and if any utility can be derived from these concepts.

We have already stated that the movement of the tip of the Sword can be considered as moving across the surface of a Sphere. For this reason, it can be called Spherical. If the circle A.B.C.D. &c., formed with the Sword, when the Fencer stands firmly in position I at right angles, were to revolve around its center, or were considered to move around its Diameter A.D. or C.G, it would create a globe, as already defined in the Definition of the globe. This globe would precisely be called the globe of the Sword, and its jurisdiction because it is formed from the particular circle of the Sword. In this globe, we can consider the same seven distinctions of planes, through which the Sword can move for the formation of any technique.

The first will be the horizontal, formed on the upper plane A.B.C.D. &c.

The second will be the circle represented by the straight line C.G. Since it passes through the vertex I, the Pole of the Horizon and Zenith, and is considered to pass through the center of the opponent’s right arm, it will be called the First Vertical. This plane with the Sword will be caused upwards or downwards, creating in that plane the three Angles, called Right Angle, Obtuse, and Acute, or the three postures or alignments, named Forward or Front, High, and Low.

The circle represented by the line A.E., which in the celestial globe would be the Meridian, here we will call it the Second Vertical. This plane can always be caused when the Fencer raises his arm perpendicular and moves his Sword to one side and then the other. This movement will rarely happen, but another movement with the Sword alone, placing it perpendicular and the arm straight can be formed. Although this circle, passing through the center of the arm, is seldom used, another circle, passing through the wrist and parallel to it, can be understood as the Second Vertical. If not this, another circle, passing through the middle of the Sword and dividing the common circle in half, will serve as this and will be very useful to regulate the movements or position of the Sword in any of its alignments or postures, as an example.

FIGURE EIGHT IS GIVEN AS AN EXAMPLE

If the circle A.B.C.D. were the common circle, considered between the two combatants, with the Fencer at D. and his opponent at A., the circle or plane that passes through A.D. would be the First Vertical plane; and the one passing through B.C. would be what we call the Second Vertical, which will be infinitely useful for the formation of Pyramids and to consider the position of the sword, both of the Diestro and his opponent.

The circles or planes that, passing through the Vertex I., deviate from the First Vertical, such as D.H. and B.F. in the previous figure, will be called Right Declining or Left Declining, depending on the direction of the decline. They will form every time the Diestro, having moved his sword away from the First Vertical plane, such as from I.C. to I.D., raises it upwards or lowers it downwards, creating in this plane the three angles: Right, Obtuse, or Acute, or the three positions they call high and to one side, low and to one side. The movements made by these planes are called violent to go up and natural to go down. The same understanding applies to the planes that can be formed on the left hand.

The plane called Inclining to the Horizon will form every time the Diestro is positioned at a right angle in his First Vertical plane and moves his sword to the Acute or Obtuse angle of one of the declining planes. For example, being on I.C. at a right angle, if one moves to the plane I.D., not with a horizontal movement but oblique to the high posture of the line or Plane I.D., the created plane will be inclined to the Horizon. If from there one returns and moves to the low posture of the plane I.B., it will also be through the same plane inclining to the Horizon. However, this movement is made to form the cuts called Diagonals. So, I do not intend to change the accepted terms, but only to make clear that there isn’t a movement that cannot be regulated and adjusted with the sword if we pay attention to it. Because any movement made with the sword must necessarily be through one of these seven planes. If we understand them well, we will be able to recognize the nature of any movement that composes any tactical move.

The Declining Planes from the Horizon will be formed every time that, with the Diestro positioned at an acute angle in his First Vertical plane, he moves his sword to the acute angle or low posture of some declining plane, to the other side. This movement is sometimes used to strike at the shins or to form other variations of tactics, as we will see in due course.

This is what I have deemed appropriate to say for now about the different planes that can be created with the sword. Although at present this may seem somewhat confusing and unclear, the Diestro will later see the clarity and distinction that the use of these concepts will provide in both the theoretical and practical aspects of the art of fencing.

FIGURE NINE

The optical artists have also identified seven different planes and lines to represent on a canvas, through perspective, all visible things, especially architectural structures. Even though there’s some variation compared to those considered in the Celestial Sphere, these lines and planes can be compared with the canvas they are to be represented on. Let’s explain with an example:

Imagine the canvas upon which a painting is to be made is the square A.B.C.D., considered perpendicular to the horizon, and the line that they refer to as the plane, where the ground is imagined to meet, is the line A.B.

All lines falling perpendicular onto A.B. are called Direct lines, like the line E.F.

Lines parallel to A.B. are called Adverse, like I.G.

Lines that deviate to one side or the other from E.F. are called Declining, like E.H. All these lines are considered in the horizontal plane or parallel to it.

If the direct line E.F. were to rise from one of its endpoints, either F. or E., leaving the other endpoint on the ground, it would be called Inclining to the Horizon.

If the adverse line were to rise in the same manner, it would be called Declining from the Horizon.

If the declining line E.H. were to rise as mentioned, it would be called both Declining and Inclining simultaneously. All these three different lines are oblique to the horizon. And the line perpendicular to the horizon is called Erect. Thus, we have these seven different lines. When applied to the sword, they are considered in the following manner:

Every time the Diestro stands opposite his adversary such that his sword is parallel to the horizon, and its tip points directly at his adversary, so that it’s perpendicular to his body, we’ll say the sword’s line is direct.

Every time he deviates from this parallel alignment with the horizon, and it reaches one of the declining planes, either to one side or the other, it’s said to be declining.

Every time, while maintaining its parallel alignment with the horizon, he crosses it in front of his body in such a way that it forms a right angle with his adversary’s sword, which is on the common diameter, it’s called Adverse.

If, while standing at a right angle on his initial vertical plane, he raises or lowers the tip without moving it to one side or the other, this line will be called “Inclined to the Horizon”, which will be when it’s at an obtuse or acute angle.

Whenever holding the sword at an acute or obtuse angle, if he moves it away from the initial vertical plane and takes it to one or another declining plane, it will be called “Declining and Inclining simultaneously”. And every time, if he inclines it while it’s adverse, it will be called “Declining from the Horizon.” And if he raises it so high that it’s perpendicular to the horizon, it will be called “Upright”.

Everything that has been said about the lines will be understood about the planes because as the planes are considered contained by lines, according to the nature of the lines by which they are understood, they will take their name: so, if a plane is contained by direct lines, it will be called “Direct”; if by declining lines, it will be called “Declining”; if by inclining ones, it will be “Inclining”; and the same for the others.

What has been said so far about the lines that can be considered in the sword must be attended to in the lines that are considered in the arm’s line, and each of its parts, because to specify the position, both of the entire arm and of the part that is between its center and the blood groove, as well as the remaining part between the blood groove and the wrist, we must consider the same differences in lines.

But as it is difficult to regulate the declination and the very different inclination that these parts can have, I have found it more appropriate to use the same method that astronomers use to mark the place of some star or comet in the sky; that is, by means of some vertical circles and others horizontal, because if once we determine the position of the sword tip, that is, in which declining or vertical plane it is, and then there’s a way to determine its height in that plane, and we would do the same for the pommel, we won’t lack the knowledge of the true position of the entire sword.

The vertical planes that I have considered, to know the declination that the sword has from the first vertical plane, are nine, and they begin to be counted in the following manner.

TENTH FIGURE

Let the individual sphere of the fencer be A.B.C.D., or the larger one, and let A.C. represent the right and left vertical plane, or the plane that passes through both the right and left verticals, and B.D. the one that represents the plane that passes through the vertical of the chest and back. Divide the fourth C.B. and B.A. into equal parts with the lines E.F.G.H. and these will be the planes corresponding to the collaterals, as already mentioned. Divide each arc into two equal parts at K.L.M.N. and draw lines from the center: these lines will represent the vertical planes that we need to regulate the movement of the sword, in relation to how much it deviates from the first vertical plane; and for easier understanding, we will call the plane corresponding to the right vertical represented by the line I.C. as “First” and the one immediately following it, represented by I.K., as “Second”. The plane I.E. between the right collateral and the chest vertical will be called “Fourth”. The vertical of the chest will be called “Fifth”: and so on for the rest up to the left vertical plane I.A., which is the 9th.

If these lines rise with the entire circle upwards to the level of the head, they will not only mark the vertical planes that we need to consider, but will also display and mark the main vertical lines and their intermediates on the surface of the fencer’s body, as seen in the figure, where the line C.A. representing the right and left vertical plane, forms with its movement on the surface of the cylinder, which represents the fencer, the lines O.T. for the right vertical and S.V. for the left vertical.

The collateral planes E.F.G.H. create the two lines P.X. for the right collateral and R.S. for the left collateral. And the chest’s diametrical B.D. causes the chest’s vertical, or Diametrical Q.Y., as seen in the same figure; and the intermediate dotted lines cause their intermediate lines to the verticals and collaterals.

For the consideration of the planes parallel to the horizon, we’ve imagined that as the circle of the lower plane A.B.C.D. rises parallel to the horizon, it leaves its traces in certain places, as represented by the lines that are drawn parallel to the line 1.9. of the lower plane; and this is done for clarity, and I’ve imagined another nine planes, including the lower plane: and this is to consider the height at which the sword’s tip will be from the lower plane, and we are grading it in this manner.

The first will be the lower plane, or the ground on which the fencer stands. The second will pass through the midpoint between the lower plane and the knees. The third through the knees. The fourth between the knees and the waist. The fifth at the waist. The sixth between the waist and the centers of the arms. The seventh through the centers of the arms. The eighth through the mouth or nose. The ninth at the top of the head.

Curious readers will note that to determine the fixed position of the sword’s tip, it is not enough to just mark the vertical and horizontal plane where it is located. Astronomers do this to determine the position of the fixed stars, all of which are considered in the Firmament. However, these two circles are insufficient to determine the true position of the planets, which are in other lower heavens. To do so, it’s necessary to know the distance, which is found by measuring Parallax, or the difference in appearance. To precisely determine the position of the sword’s tip, hilt, or elbow, it is necessary to determine the distance of each of these points to the direction line, considered to pass through the middle of the cylinder in which the fencer is considered. This is easy but not necessary because the elbow already has its determined length from its center. If we determine its horizontal plane, it can only be one, and thus it will serve as a common place for that point. If, in addition to this, we determine its vertical plane, it will also be common, and it cannot be in different verticals at the same time. Therefore, at the intersection of these two planes, which will be a straight line, the center of the elbow must be located. The location along this line will be determined by the arm’s length from the center to the elbow or the “sangria”.

Having determined the elbow’s point, the same can be done for the center of the guard, thus precisely knowing its place and position for the same reason. These are the three things required: the intersection of the two horizontal and vertical planes, and the determined place on that line, knowing the distance from the elbow to the wrist. Once this is determined and the elbow’s location is known, the wrist’s location will be known through a circle formed by the length from the elbow to the wrist.

The same logic follows to determine the position of the sword’s tip. However, since the sword can rise much higher than the head, we can imagine another four planes above the mentioned ones, each one foot apart from its lower counterpart, totaling four feet, which is the maximum height the sword’s tip can reach in the formation of tactics. Thus, with these planes, there will be no position or straightness, both of the arm and of the sword, that cannot be explained to be able to declare with specificity the perfect formation of tactics, both in their beginning, middle, and end.

Lamina ſeptima del Libro ſegundo.

 

Plate seven of the second book.

 

CHAPTER FOURTEEN

FOR A BETTER UNDERSTANDING OF THE movements, Angles, and straightnesses of the arm and Sword, in confirmation of what has been demonstrated, it is further facilitated in the following figures and explanation.

Although what has been said so far about these planes seemed sufficient to regulate the movements of both the arm and the Sword; nonetheless, I have deemed it appropriate to add another speculation, which will not seem of lesser utility than the aforementioned, rather one with the other will greatly facilitate this work.

Sailors, for the governance and good direction of their Ships on the Seas, not only rely on the courses set parallel to the Horizon, but they also use an instrument which they incline between their sight and the Pole, to observe the movement of the Stars near the Poles, to know through this observation the height and position in which they find themselves: they do the same for the movement of the Moon, considering it parallel to the equinoctial circle, to know in the middle of the Sea the directions the waters flow in the crescents and wanes of each day; and all this has been done by Geographers to avoid the multiplication of instruments, so as not to burden them with different uses, imaginations, or rules.

We must do the same, using to observe the movement, place, or position of the Sword of the Fencer or his adversary, imagining in the middle of the two combatants, a circle perpendicular to the Horizon; and in the way that the particular circle, which is considered in the lower plane, is divided into eight courses or paths, to govern the movements or compasses of the Fencer on the ground; this circle will also be divided into eight equal parts, to regulate the movement of the Sword in the Air.

The parts into which this circle is divided are as many places where everything necessary for the understanding of the operations that pertain to the arm and Sword can be found, such as the types of Angles, the types of movements, and the six simple straightnesses, as well as the four types of mixed straightnesses, which are imagined in the Air, in imitation of the places we have considered on the ground or lower plane, to regulate the movements of the body. Following in these imaginings, as already mentioned, the Sailors, who not only rely on the courses to govern the movements of the Ships over the surface of the waters; but also use the same considerations and terms in the Air, to regulate the movements of the Stars: all in order for the perfection of their voyage, and to reach the port they have destined; and since in a vast sea men have been able with these imaginings to find a way to conduct themselves to any part of the World, avoiding the risks of shallows, and reefs, and other dangers; greater ease must be granted to us in the understanding and application of these same considerations in the movements of the body, which a man can make with his arm and Sword, to avoid the risks and dangers that he has with an adversary, also opposed with a Sword in hand, because with the movements of the body, which we call compasses, and motions on its center, and those of the arm and Sword, with admirable artifice, one passes to the formation and execution of all the tricks, harmonizing the upper movements with the lower ones, according to what the nature of each one demands for its greater perfection, causing the two precise effects of defense and offense: this being supposed, let us come to demonstrate the circle, explaining in it what we have offered, and it will be in the following form.

Let the Circle E.F.G.H. &c. be placed perpendicularly on the lower plane A.C.B. and let it have its semidiameter of five feet. which is the height we suppose a man of perfect stature has from the center of the right foot to the center of the right arm; so that, being affirmed on a Right Angle, and at a Right Angle with his arm, and Sword parallel to the Horizon, it passes through the center of this circle, and divides it in half; and for better clarity, we will accompany this demonstration, which is in plan view, with another that is in perspective, and the two combatants affirmed in their means of proportion in Angle, and on Right Angle, the Fencer in A.N. and the adversary in B.M. having between the two centers of the arms, and of the right feet eight feet of distance, which distance is divided in the middle at C. a straight line C.D.E. is considered perpendicular (which will coincide with the line M.N. which is considered passing through the centers of the arms of the two combatants) and will pass through the middle of the Sword of the Fencer, so that it is perfectly affirmed at Right Angle in its first Vertical plane, if it is considered on the line C.D. as a measure, described a circle so that it is perpendicular to the Horizon, in the middle of the two combatants, as represented by the figure, and perpendicular to the first vertical plane, it will be of great use to regulate the movement of the Swords of both combatants; because if the Sword of the Fencer moves from the center D. to any of the eight marked courses, it will form not only the three Right, Obtuse, and Acute Angles, but also those called movements of the Sword, both simple and mixed, and the simple and mixed straightnesses, all in this way.

Demonstration of How Angles are Considered in This Figure, Through a Pyramid Formed with the Arm and Sword

The angles are considered in the common section of the first vertical plane, and of the surface and axis of a Pyramid, which is formed with the lines N.E. and N.C. whose base is the circle, and the vertex the point N.

Because being the Fencer affirmed on a right angle, and with his arm and sword on the axis of this circle and Pyramid N.D., we will say that he is affirmed in a right angle, which is caused in the confluence of D.N. with the vertical N.A.

Being affirmed with his arm and sword in the upper part N.E., it will cause the obtuse angle A.N.E greater than the right angle.

Being affirmed in the lower part N.C., it will cause the acute angle A.N.C. less than the right angle, as seen in the figure. And all these three angles are in the first vertical plane C.D.E.

How Simple Movements are Considered in This Circle and Greater Pyramid

Through the lines, or parts in which the circle was divided, and from the angles that have been mentioned, one comes to understand the types of simple and mixed movements that can be made. Because if from the axis D. the arm and sword rise through the primary vertical plane, which is represented with D.E., the movement that is made is called violent; and if it descends from the axis and center D. through the same primary vertical plane along the line D.C., the movement will be natural.

The strange movement is made by retracting the sword through the axis N.D., and the accidental movement is made by going forward through the same axis.

The movement made along the line D.G. will be parallel to the Horizon, towards the right hand, and is called remiss from D. to G., and the movement made from the circumference and point G. through the same upper horizontal plane, until converging in the center and axis D., is called reduction.

The movement that the Fencer makes to his left hand through the line D.K. is also called remiss from the center to the circumference, and the one made from the circumference and point K. to the center D. is called reduction.

With this explanation, it will be understood how in this figure the six types of simple movements are found, and now it remains to be heard how it also comprehends mixed movements.

How the Four Main Types of Mixed Movements are Found in This Figure, for Each of the Oblique Planes

In the division of this circle, we also imagine two oblique planes through the four intermediate directions of the four simple movements: violent, natural, remiss, and reduction. It is through these that the mixed movements are regulated.

The first one on the right side has its beginning on the surface from line F. to line I.

On the left side, it begins on the surface, and point L. to point H.

Thus, when the Fencer moves his arm and sword from the axis N.D., where the right angle is considered, to line F., this movement will be called a mixed movement of remiss and violent to his right side; and if through the same plane he moves the sword from the circumference and point F. to the axis D. and right angle, this movement will be a mixed movement of natural and reduction.

If from the axis N.D. he makes a movement with his sword through the same plane and line D.I., this movement will be a mixed movement of remiss and natural to his left side.

If from point I., the Fencer moves his sword through the same plane to the axis and center D., this movement will be a mixed movement of violent and reduction.

If from the axis N.D. he moves his sword through the oblique side on the left through line D.L., this movement will be a mixed movement of violent and remiss on his left side.

If from the axis N.D. he makes a movement through the same plane along line D.H. from the center to the circumference, this movement will be called a mixed movement of remiss and natural to his right side.

If through the same line and plane he moves the sword from the circumference and point H. to the axis and center D., this movement will be a mixed movement of violent and reduction.

With this, the types of mixed movements are also explained, and with the same doctrine, the Fencer can regulate the many movements he can make of the same types from the axis to the surface of each of the four quadrants we have considered, and from the same surfaces of them to the axis; all of this is very important for the Fencer to have knowledge of the tricks he performs, and those of his opponent, which are formed by these oblique planes: noting that those formed from the upper plane, and obtuse angle, should not pass the sword from the axis of the Fencer, and from that of his opponent, to the lower plane, and acute angle, for greater perfection and safety.

The movements made from the axis of this pyramid to its surface are preparatory; and those made from the surface to the axis are executive: with one difference, that those made from the upper surface, and obtuse angle to the axis, will be more secure, and the executions stronger.

The movements made from the lower part, and jurisdiction of the acute angle, from the surface of this figure to the axis, to attack the arm, will be of little effect; and the tricks less secure than those executed from the upper part.

Cautions regarding these mixed movements, generalizing them further

Firstly, it is noted that although we have considered movements from the right angle, as has been done so far, for the universality of this science and its true understanding, it should be imagined that these movements take their beginning through the first vertical plane, which passes through the right angle and axis of this pyramid, and not only from the axis of it, because there are situations in which one can strike without depending on the right angle, as will be said in its place; thus, whenever the tip of the Fencer’s sword moves away from this plane to one side or another, and moves through any plane parallel to the horizon, it will make a remiss movement; and if it is reduced by the same plane to the primary vertical, it will be a reduction movement.

Every time the tip of the sword moves away from this primary vertical plane to any upper side, to one side or the other through an oblique plane, the movement made will be a mixed movement of remiss and violent.

Every time the sword is reduced on one side or another through an oblique plane from any upper part to this vertical plane, the movement made will be a mixed movement of natural and reduction.

If from any upper part of the primary vertical plane the sword descends on one side or another through an oblique plane to the lower part, this movement will be a mixed movement of natural and remiss.

If from any lower part, outside the primary plane, the sword also moves on one side or another through an oblique plane, to any upper part to this primary vertical plane, this movement will be a mixed movement of violent and reduction.

How the six simple straightnesses are considered in this figure, in which a man can assert himself, as has been imagined so far.

By placing his sword on the line N.E, the Fencer will be in the high straightness, and by placing it on the line N.C, he will be in the low straightness, and by placing it on the line G, he will be in the straightness of the right side, and being on the line K, he will be in the straightness of the left side, and being on the line D, he will be in the straightness of the front, and by retracting the arm and sword, he will be in the straightness of the back.

However, considering that these six simple straightnesses do not encompass the universality of the Art, nor all the possibilities of a man in asserting himself, we imagine four other species of mixed straightnesses.

How mixed straightnesses are considered in this figure.

If the Fencer is affirmed with his arm and sword on the line F, he will be in the mixed straightness of high and remiss, on his right side.

If he is affirmed on the line I, he will be in the mixed straightness of low and remiss, on his left side.

If he is affirmed on the line L, he will be in the mixed straightness of high and remiss, on his left side.

If he is affirmed on the line H, he will be in the mixed straightness of low and remiss, on his right side.

How these mixed straightnesses are considered more universally

Every time the Fencer moves his sword away from the primary vertical plane on both sides, to the upper part and jurisdiction of the obtuse angle, through any oblique plane, these will be mixed straightnesses of high and remiss.

Every time he moves his sword away from the same primary vertical plane on both sides, to the lower part and jurisdiction of the acute angle, also through any oblique plane, these will be mixed straightnesses of low and remiss.

Lamina Octava del libro ſegundo.

 

Plate Eight of the second book.

 

CHAPTER FIFTEEN

How the Circular Movements that the Sword Can Make in the Air are Considered.

Now that we have explained the movements that are made through planes, we will now deal with the circular movements that the Sword can make. The first is the one it makes around its own center, in imitation of the one made by the body around its own, forming a circle with both quillons of the Sword, which we will also divide into eight equal parts, in conformity with how we have divided the others.

Another circular movement is the one that can be made with the length of the Sword, caused or described by its tip, with the wrist center being the vertex.

Another circular movement can be described with half of the arm, with the elbow or vein being the vertex.

Another circular movement can be described with the guard of the Sword, when the opponent with the left hand grasps the tip of the Fencer’s Sword, or when the latter strikes a thrust from the remote end at the center of the opponent’s right arm, and in order not to come out to the middle of proportion, the opponent attempts to strike him, and the Fencer defends himself by applying his guard, considering for this two vertices, one at the tip of the Sword, whose axis is the straight line to the guard; the other, the center of the arm, and the axis, its length up to the same center of the guard, which is with which the base of this circular movement is described.

Also, as the guard moves through its circle, each division of the Sword makes its own, and all are understood to be divided into the referred parts, to regulate the movements of both the arm and the Sword, and the guard.

Another circular movement, and the largest that the Sword can make, is through the circumference of this large circle, which we consider between the two combatants, causing the Sword with the arm to form a conical pyramid, according to the definition of Apollonius of Perga, with its base being this circle, and the vertex the center of the arm, noting that at the time it is revolving, the Sword will pass through each of the divisions of the circle, and dividing the surface of the Pyramid into eight equal parts, causing with these divisions lines that take the name of the divisions, such as 2, 3, 4, etc., up to 8, 9.

This same circle can be imagined as placed on some plane of those considered in the opponent perpendicular to the first vertical plane, as shown in the second figure of this ninth plate; and in this case, with the arm at a right angle, the Sword can incline through the lower part until, if it were longer, it could touch the lower circumference, which is at point A. And being in this inclination, it will form its movement, or Pyramid, with the center of the wrist being the vertex: but as the tip of the Sword only reaches up to the wrist of its opponent, it will form there a smaller circle, as seen in the figure, and indicated by the letters L.K.M, and the middle division of the Sword will form another, as seen by the letters R.S. This second Pyramid, which is made with the defensive strength of the Castle, which we have to consider defending the Fencer, can be seen by the same demonstration of these Pyramids, that if there were a shield placed between the two combatants, of the size that is the circle R.S., with both combatants standing at a right angle, it is recognized that it would cover the whole body, if the Sword were of the length of T.A. And when this Pyramid is not sufficient to defend ourselves, as the vertex of this Pyramid can move to various parts, and not always have to maintain the posture of a right angle, I show that the Fencer with a portion of this Pyramid, can force the opponent to have his Sword out of two or three planes of defense, which are the ones that constitute the bastion that always guards this Fortress, if the Fencer is not careless in the opposition of the part of the Pyramid that is appropriate.

This Pyramid of defense, and the one that can be formed with the arm, with the base being the guard, are of such importance in the Skill, that without them, it could not be said that there was defense, on which its essence is based.

Within this Pyramid, two others can be considered: so, the inner, and smaller one we will call the first, and it has about two and a half feet in diameter its base, considered in the body of the opponent; but at the tip of the Sword a little more than one foot, and in the defense, which is made with the middle division of the Sword about half a foot, and will pass through the head, and the waist of the opponent: the second passes through the knees, and the third corresponds to the feet, as everything is demonstrated by the figures, both by the upper one, which is in perspective, and the lower one, which is in plain view.

The three planes of defense, which we have mentioned, that serve as a bastion to the Fencer, are two of them vertical, or perpendicular to the Horizon, touching the cylinder of the Fencer, converging at the guard of the opponent, and the third is an oblique plane that passes through the guard, and touches the head of the Fencer: these three planes are of great use in the Skill, because the defense of the Fencer consists of nothing else but in keeping the Sword of the opponent out of these three planes, as I have already noted elsewhere, and will demonstrate when I manifest the way the Fencer will have in forming the Angles of the bastions of the idea of the Fortress.

And for more amplitude, and ease in the understanding of the circular movements, that the Sword can make in the Air, I will make myself understood through the explanation of each of the Pyramids, which I will demonstrate to our Fencer.

Lamina nona del Libro ſegundo.

 

Plate nine of the Second Book.

 

CHAPTER SIXTEEN

Wherein a more specific explanation is given of the Pyramids considered for the use of Skill in Arms.

First Pyramid, Orb, or Revolution, that can be described with the main center of the arm, which is the shoulder.

In this first Pyramid of Figure 10, we consider the Fencer affirmed on the right angle A.G., and at a right angle with his arm, and Sword D.B.A., with the vertex of this Pyramid at the main center B.

It is formed with the interval of the arm and Sword, with its length, which is 6 geometric feet, giving a revolution, and causing it, with the tip of it describes the base C.D.E.F., and all of it B.E.D.C.F. graduated each quarter of Pyramid in 90 degrees, both in its elevation or inclination of the Sword; and by the pitipie N.L. the measurements of the body, arm, and Sword, and the lower plane six feet in length of the body, and six feet of the arm and Sword will be adjusted.

pitipie from the french petit pied or small foot, the scale of a map or plan

 

Parts into which this Pyramid is divided, whose divisions must be understood in each of the others

Having explained the largest Pyramid, necessary for the practice of Skill in Arms, imagining it formed, with its axis on the upper plane of the right angle, so that with this knowledge it can be considered in any other part where it is necessary to form it, or portions of it: it is now important that for its use we explain in how many parts one is divided, and for this we put an example in this one which is the largest, whose vertex is in the center of the arm, and is formed with it and the Sword, holding it from the Fencer in the hand affirmed at an angle, and upon a right angle.

Let us suppose again the Swordsman affirmed on the right angle A.G. and at a right angle D.B.A. The first thing we consider in the common section of the primary vertical plane, and of this Pyramid, which is made by the axis B.D. causes the triangle 2. B. 6. by the axis, whose sides B.2, and B.6. are the first two lines that we imagine on the surface of this Pyramid; to the upper B.2. we give the name of the second, and to the lower B.6. of the sixth.

Then we consider another common section of the upper horizontal plane and this Pyramid, which results in the triangle by the axis 4.B.8. whose base is the line 4.8. and since this whole triangle is parallel to the Horizon; the one on the right hand B.4. we will call the fourth line; and the one on the left hand B.8. the eighth line: and as the primary vertical plane and the plane of the base of the Pyramid are perpendicular to the horizontal plane, it follows that their common sections at the base 2.6.4.8. will also be cut at right angles by the 19th of the eleventh of Euclid, and will divide the circle of the base into four equal parts, or quadrants.

Imagining each of these quadrants divided into two equal parts by two oblique planes, the first starting from the right side, no. 3. to number 7. and from the left side from number 9. to number 5. which also cut at the axis, will cause on the surface of this Pyramid four more lines, caused by the common section of the oblique plane of the upper right side, no. 3. and ends on the lower left, no. 7. and so we call the upper line B.3 the third line, and the lower line B.7 the seventh line.

The other two, which are caused by the common section of the oblique plane that begins on the upper part of the left side, number 9. and ends on the lower part of the right side, number 5. the upper line B.9. we call it the ninth line, and the lower line B.5. the fifth line.

The axis of this Pyramid, which is the right angle, is the first line.

So, the common sections of these four planes, the primary vertical and the upper horizontal, and the other two oblique planes, cause on the surface of this Pyramid eight lines, and their intersection with each other causes another line, which is as has been said in the axis of this Pyramid, and the first line.

The usefulness of this and the other Pyramids will be recognized when the maneuvers, such as the five which are the cut, reverse, thrust, half-cut, and half-reverse, as well as in the formation of the general rules, are explained.

The line in Cross will never be performed with the perfection demanded by the Art if this greater Pyramid does not intervene in its formation.

Also, through it, one comes to understand what has been said and demonstrated in the explanation of the movements, by finding in it encrypted the majority of the things that pertain to the Sword, because by dividing its base into the lines it shows, it will be recognized with evidence that if from its axis the Sword is moved to any part of the circumference, or from the circumference to the axis and center of the Pyramid, it will form not only the simple and mixed movements but also the right, obtuse, and acute angles, and the six straightnesses or general postures of up and down, to one and the other side, forward and backward, and the intermediate or mixed ones considered among the simple.

Explanation of the second Pyramid, Sphere, or revolution, which can be described, with the center of the wrist as its vertex.

In this second Pyramid, we also imagine the Fencer positioned at a right angle A.K. and in a right angle with his arm and sword E.B.A., with the vertex of it at the center of the wrist C.

It is formed with an interval of four geometric feet, which is the length from the hilt and pommel of the sword to the tip, and by revolving it, it describes the base D.E.F.G. and the entire pyramid C.F.E.D.G.

The usefulness of this Pyramid will be seen in the formation of the three general rules: closing in, weakness, below and above the strength, as in all these the arm should not move from the right angle; rather, all the movements that these rules consist of (except the line in cross) until executed, will be done by the hand, which nature has disposed to enjoy the four straightnesses: C.D. is the straightness above, C.F. the straightness below, C.4. the straightness to the right side, and C.8. the straightness to the left side.

The distance between one straightness and another can also be subdivided, placing the sword in the intermediates, and in as many quarters as it is divided, they will be of the jurisdiction of the straightness that the sword participates in; and the same is preached of the movements and angles.

In these two Pyramids that have been explained, the greater and the lesser, whose vertices are in the center of the arm and wrist, as they can be formed in front of the body of the adversary, the tactics are disposed and executed, sometimes by the same axis occupied by the arm and sword for the thrust wounds, and other times to strike through any of the vertical, horizontal, or oblique planes, because the circular movements that converge in them are only dispositional to reach to strike these planes.

It is also noted that these two greater and lesser Pyramids can be formed in all the simple and mixed straightnesses, although not always will it be necessary to form the greater one, as will be seen in the explanation of the combined and more universal Pyramids, and in the jurisdiction of each one, according to the demands of the battle circumstances; and wherever they are made, the same divisions will always have to be considered in each one, and everything else that has been explained and preached about the greater Pyramid; and it will be at the will of the Fencer to form the larger or smaller ones, or the portion of them that is necessary, according to what the nature of the tactics requires, or the movements of the adversary oblige. Through these two Pyramids, the Fencer achieves not only offense when it suits, but also defense, because through them he places the sword of his adversary in the three vertical planes of his defense, sides of the angles of each one of them, according to the intentions he has in the battle: with which it is recognized how necessary and universal these two greater and lesser Pyramids are, and their use, because the one that has its vertex in the wrist always forms in front of the chest of the Fencer, and is only dispositional for the execution of it, which follows as such.

Explanation of the third Pyramid, which can be described with the forearm, being the elbow the vertex of it.

In this third Pyramid, we also imagine the Fencer positioned at a right angle A.L. and in a right angle with his arm and sword N.B.A., and the vertex of this Pyramid at the center M. of the elbow of the arm.

This Pyramid is formed in front of the chest and face with an interval of a foot and a half, which is the distance from the elbow M. to the exterior of the guard C., and on the exterior of it, it describes the base C.F.G.

In this Pyramid, which is formed with the forearm from the elbow forward, only two straightnesses belong to it, which are the one above, and the one to the left side, in this way: if the line M. is the joint of the elbow and N. the tip of the Sword: to make the straightness of the left hand, carry the arm and Sword from where the tip N. is, bending the joint of the arm until it is brought close to the chest, and the tangent line, which is imagined from one shoulder to the other until it occupies the line M.H.

The straightness above is done by carrying the Sword from point N. to the obtuse angle, passing through the intermediates, or half divisions of this straightness.

Warning

Note that this Pyramid, whose vertex is in the elbow, can never have its axis at a right angle, because for its formation, it is necessary that, making the center and angle at the same elbow, it deviates from it; and although it can be formed around its axis, like the other two, there is a difference, the base of it will not include the opponent, because the Right-hander forms it obliquely in front of his chest, and on his left side. Therefore, the guard that causes the defense describes its base on a plane parallel to the left collateral plane, oblique to the Horizon, and the axis will be the line that is considered from its vertex to the center of the base of this Pyramid, and will be parallel to the left collateral plane. This leads to the conclusion that this Pyramid, as its axis is not directly facing the opponent, is dispositional and only serves to carry the Sword to the left side until placing it in the primary vertical plane, for the moves of vertical cuts, horizontal cuts, thrusts, and diagonal cuts, and for the cuts to the arm, known as elbow strikes; although for the precise formation of these moves, the movement of the wrist and shoulder helps, though not as much as it does. And for the rigorous precision of the moves, the jurisdiction of this Pyramid does not extend to the formation of reverse vertical or diagonal cuts, because on the right side where they are formed, no portion of it can be made according to the organization of the arm, as anyone can experience for themselves. And if the Diagonal reverses, and the half cuts, and half reverses, are formed perfectly, this Pyramid also has no jurisdiction over them, because the half cuts and half reverses are formed by oblique or horizontal planes, and the Diagonal reverses by these same planes: in the end, this Pyramid is a means that serves as a link between the two extremes of the shoulder and the wrist, and for all the moves of the Skill it is necessary the movement, or motion of some of the three Pyramids explained, except for the thrust, which will consist only of the accidental movement.

Knowledge of three other Pyramids, no less necessary than the preceding three for the practical part of the Art of Fencing.

Notice has been given of three Pyramids: the largest, whose vertex is at the center of the arm, and its axis we imagine occupies the length of the arm and sword. Another, whose vertex is at the center of the wrist, and whose axis occupies the length of the sword.

The third and last one, whose vertex is at the center of the elbow joint, whose axis is the line considered to emerge from the center of its base; and this axis is occupied by the part of the arm from the same center of the elbow joint to the line of the hilt, and the guard of the sword of the Fencer, describes the base in front of his chest: so that the vertices of these last two are in the arm and wrist of the Fencer, and are parts of the length occupied by the axis of the larger Pyramid, and all three have been universally explained, and their admirable use.

Now it is appropriate to give reason for three other Pyramids, which are also considered in the same length of the arm and sword, as the previous three referred to, with a difference, that two are imagined to be formed independently of the opponent, and the other is necessary that the vertex be considered at the tip of the sword of the Fencer, while striking with it the same opponent.

Explanation of the fourth Pyramid, the first of these three.

For a good understanding of the fourth Pyramid, and first in the explanation of these three, the Fencer is also imagined to be affirmed over the right angle A.G., and in right angle with his arm, and Sword A.B.D., with the center of this Pyramid at the center of the arm B.

It is formed by giving a revolution with an interval of two and a half feet, which is the length of the arm up to the exterior of the guard, and with the exterior of it describes the base C.D.E.F.

Since this Pyramid has its vertex at the main center of the arm, and its axis in a straight line, which we imagine to emerge from the same vertex to the exterior part of the guard of the Fencer’s sword that occupies the arm, and the same guard, which is two and a half feet long, forming this rectangular Pyramid, its base will be two feet minus a quarter distance from his body, and will have a diameter of three and a half feet, as verified by the figure, and becomes evident by demonstrating it as such.

Being affirmed the Fencer in right angle A.B.D., imagine that he raises the arm to the obtuse angle B.C. in such a way that it causes a semi-right angle with the line B.D. and drawing the perpendicular line C.H.E. over B.D., the triangle C.H.B. will be right-angled isosceles, and the line C.H. will be equal to the line H.B. as the two angles in C.B. are semi-right and equal to each other by the sixth proposition of the first of Euclid’s Elements.

Imagine that this triangle, or the arm that represents the C.B., gives a revolution around the side B.H., and the rectangular Pyramid C.D.E.B. will be formed at B.

Now, it is necessary to examine what will be the diameter of its base C.E. and its axis B.H., which is easy to know and explain: because the triangle C.H.B. has its right angle at H., and it will be by the 47th of the first of Euclid’s Elements: the square of B.C. equal to the squares of B.H. and H.C. and being isosceles, each one of the squares C.H. and H.B. will be half of the square of the hypotenuse B.C. Thus, with B.C. being known as the length of the arm and guard of two and a half geometric feet, which makes 40 fingers, each of the other two sides C.H. and H.B. will also be known to be 28 fingers, which are two feet minus a quarter, and the whole C.E., which is the diameter of this Pyramid, will be 56 fingers, which are three and a half feet. This operation is done in this way.

Square the number 40, which corresponds to B.C., the length of the arm and guard, and the product, or square, will be 1600. Dividing it by half, each will be 800, which will be the square of C.H. and H.B., whose nearest square root is 28 fingers, corresponding to the line C.H. and likewise to the line H.B. for being equal. And since the triangle B.H.E. is equal to the triangle B.H.C., H.E. will be equal to H.C. Thus, the diameter of the base of this Pyramid is 56 fingers, which are, as said, three and a half feet, which is the largest circle that can be described as the base of this Pyramid, and will be separated from the body of the Fencer by two feet minus a quarter, represented by the line B.H.

Since this base is described with the guard, it serves as if it were a shield with a steel handle, having the same thickness as it, because as the opponent cannot place his Sword at one time, except in one part; and the movement or movements that he makes with it will always be much larger than those that the Fencer has to make to oppose this Pyramid and guard of his, which describes it, it is very conform to reason the comparison, that it will serve the Fencer, following its precepts, as if it were a steel shield.

However, it should be noted that the base of this Pyramid should never be as large, nor its portions as in the past, because it will be enough that they are of the necessary size for the Fencer to place with his guard the Sword of the opponent in the plane parallel to the Horizon, passing through the vertex of his head; and with his Sword the opposite in the two vertical planes of his defense, sides of the angles of the bastions of our Fort: and the smaller the base that is made, it will be further away from the body of the Fencer; thus, the use of it is at his discretion, to regulate this Pyramid and its portions that he has to make, according to the intentions he carries or the movements that the opponent makes with his Sword.

It is very important to note that, even though the Fencer has his arm and guard at a right angle, with a small amount of movement made through the primary vertical plane towards the upper part of the obtuse angle, and to his right and left side, he cannot be offended by his opponent with the use of this Pyramid.

The lower part of the acute angle will be defended, on both sides, by the Pyramid made with the Sword, whose vertex is in the center of the wrist: and because these cases are particularly demonstrated in the idea of our Fort, and it is explained how the use of this Pyramid of the arm and guard is the main wall of it, we refer to what is explained about all of it: and having extended ourselves in mathematically demonstrating this Pyramid has been because it is so essential, and also so that by the method used in the demonstration of this, anyone can demonstrate the other five if they wish; and not having done so is to avoid prolixity, and having said enough about them for their understanding and use: and so now we will explain the second Pyramid, which turns out to be the second wall of our Fort, more external and further away from the Fencer than the one caused by the arm and guard, and we consider it in this way.

Explanation of the Fifth Pyramid, and Second of These Three

In this fifth Pyramid, which is the second of the three, we also imagine the Fencer standing firm on a right angle A.H. and at a right angle with his arm and Sword I.B.A., with the vertex of this Pyramid being considered at the center of the wrist, and along the receptive line G.

This Pyramid is formed by revolving with an interval of two Geometric feet, which is the length from the center C. of the wrist and the hilt of the Sword to the midpoint of it marked by point E., and with it, it describes its base D.E.F.G. and the entire Pyramid C.F.E.D.G.

We imagine this second Pyramid at the midpoint of the Sword’s length from the hilt to the tip, in the amount of Sword from this division to the exterior of the guard of the same Sword of the Fencer, and this is where the axis is, and it is the strongest part of the Sword; and it is evident in the reason that whenever the entire Sword is used to form any larger or smaller Pyramid, at any degrees and point of it, we can imagine that it forms with each a base, and that the entire line for the same reason we have given for the guard, describing the Pyramid of the arm, will cause the same effect; and compared to the opponent’s power with that of the Fencer, the latter will be as if forming an entire Pyramid of steel; thus, using it as a Fencer, it will serve for his defense as if it were one: and with this understanding well established, we can very well consider this second Pyramid that the Fencer can form, or portions of it, whenever he moves his Sword to any part; and because this smaller Pyramid is formed with the greatest degrees of force of the Fencer’s Sword, whenever the opponent’s enters its jurisdiction with lesser degrees of force, the Fencer will have greater power to place it with the portions that are necessary to make of it on both sides in the two vertical planes of his defense: and most commonly, this second Pyramid is used when it is formed from the entire Sword, whose vertex is in the wrist, and the Fencer’s movements are very brief in respect to this second Pyramid, and he has a great advantage over those of the opponent, who makes them with the entire arm and Sword, or at least with the entire Sword, as we will demonstrate and explain in our Fort, and in its cases, to which we also refer.

Explanation of the Sixth Pyramid, and the Last of These Three

We consider the third and last of these three Pyramids when the Fencer strikes a thrust from the remote end at his opponent in the center of the right arm or slightly away from it, and because he does not immediately move to the middle of proportion, the opponent also attempts to strike him. In this case, the Fencer must imagine that the tip of his Sword with which he strikes is the vertex of this Pyramid, and its axis is the straight line from it to the center of the base, which can be described with the guard of his Sword. With it, he can defend himself in any part where the opponent attempts to strike him, from the right angle to the upper part of the obtuse angle, and in the lower part of the acute angle, up to the middle plane, moving his Sword in the two vertical planes of his defense, up to the horizontal plane, which we imagine passes through the vertex of the opponent’s head. This base is common to this Pyramid and the one of the arm, whose vertex is considered at the main center of it; thus, they come to be two opposing Pyramids, and although they are opposing, the Sword’s Pyramid cannot cause defense without the arm’s Pyramid coinciding with it, accompanying it to any part where it is formed, or portions of it. However, the arm’s Pyramid, which is responsible for the main defenses (as already noted), can do so without depending on it; and if in the referred case the opponent lowers his Sword from the middle plane to strike, then the Fencer will have to rely on the smaller Pyramid, whose vertex is imagined at the center of the wrist and is formed with the length of the Sword to be defended. To give the Fencer more individual knowledge of what is explained in this third Pyramid, I will demonstrate it in the following manner.

In this Pyramid, we also imagine the Fencer standing firm on a right angle A.G. and at a right angle with his arm and Sword K.B.A., assuming he moved from the middle of proportion to the proportioned, striking the opponent with a thrust, who also waited, standing firm on a right angle I.H. and in order to attack the Fencer, remained at a right angle only with the arm L.K.H. because at the time the Fencer struck him directly in the right collateral, represented by point K., he raised the Sword to the obtuse angle L.M. to strike him with a cut on the head; and the Fencer causes his defense with the portion he makes of his Pyramid of the arm and guard, also raising it to the obtuse angle from D. to C. And although with much less portion of this Pyramid he could have been defended, as seen in the figure, by the distance from the opponent’s tip M. to the Fencer’s head; still, for clarity, it has been arranged in the form shown in the figure.

Also for the sake of clarity, we assume that the opponent lowered his Sword to the acute angle, and the Fencer followed with his own to the same angle, making another portion of his Pyramid from point C. to point E. to keep the opponent’s Sword on the surface of his own so that it had no direction to his body: and in this position, the opponent’s Sword has not been placed in the figure, to avoid causing confusion, and the Fencer in any other position that the opponent attempts to strike him, can use this Pyramid to cause the same defense.

This Pyramid differs from the previous two because they focus solely on defense; however, this third one pertains to both defense and offense, and the Fencer achieves both effects because it is opposed to the Pyramid of the arm and shares the same base, which is described with the guard. Because the arm’s Pyramid (which, as we have already said) accompanies it, is primarily responsible for defense, and for this reason, it can safely use the Sword’s Pyramid to attack the opponent.

One who knows how to use these two Pyramids with the perfection required will have mastered one of the greatest skills in the practical aspect of Fencing, and it could not truly be said that there is science in this art without the use of these Pyramids. Through them, one can unite defense with offense, as will be clearly recognized in the course of this work, and particularly in the Treatise on Techniques.

With this, we have explained the six most essential and necessary Pyramids for all operations in Fencing, whose use is more clearly seen in the explanation of our Fortress’s concept and its cases.

Lamina dezima del Libro ſegundo.

 

Plate ten of the Second Book.

 

CHAPTER SEVENTEEN

Proposition I. Theorem I.

It is demonstrated that whenever the Fencer is positioned at a right angle, and at a right angle in his vertical right plane, and his opponent attacks him to strike with a thrust through the same plane, he can defend the depth of his body with a guard of two fingers in semi-diameter; however, it is necessary that the centers of the guards are in the common section of this vertical plane and the superior plane.

Let the circle A.M.T. be the common section of the Fencer’s cylinder and the superior plane, and the circle B.N.K. be that of the opponent’s cylinder with the same plane, and the line A.B. be the common section of the Fencer’s vertical right plane and the same superior plane, and let this distance A.B. be that of the middle of proportion of eight Geometric feet.

A.E. of two feet is the length of the Fencer’s arm from its center to the wrist, and A.F. of two feet and a quarter is the length from the center of the arm to the center of the guard, and the same is considered in B.L. and B.H. for the opponent: thus, the center of his guard will be six feet less a quarter distant from the surface of the Fencer’s cylinder, and the tip E. will reach two feet distance from the body of the Fencer; and from this position to be able to offend, it is imagined that the opponent takes a step of two and a half feet: thus, if the guard of the Fencer did not prevent it, the opponent would reach with the tip to strike him with a thrust through the same line at point D. which represents the axis of the cylinder, and the center of the guard of his Sword will be at point P.

I say that in this position, having the Fencer the center of his guard at point F, whose Semi-diameter F.G. is of two fingers and two fifteenths, he will defend the depth of his body, even though it has a diameter of one foot, which is more than what a well-proportioned man should have.

Determination that settles the question.

 

Draw from point P, the center of the guard, the line P.I. that touches the circle of the Fencer at point I, and the line D.I. from the center D to the contact point I. Draw the line F.G. from the center F of the Fencer’s guard parallel to D.I by the 31st of the first book of Euclid’s Elements.

Construction

 

Since in the triangle B.P.D.I. the line F.G. is drawn parallel to the base D.I., it will divide the sides P.D. and P.I. in the same proportion by the second proposition of the sixth book of Euclid’s Elements, and will form the two similar triangles I.P.D. and G.P.F. for having the angles P.G.F. and P.F.G. equal to the angles P.I.D. and P.D.I., external to internal by the 29th of the first book, and the angle at P common, thus the three angles of one are equal to the angles of the other, each to each.

Demonstration

 

Therefore, by the fourth proposition of the sixth book, the homologous sides will be proportional, and as P.D. to D.I. so P.F. to F.G. and of these four proportional quantities, three are known, the P.D. of 60 fingers, the D.I. of 8, and the P.F. of 16. And forming with these numbers the rule of three, the result will be a quotient of two fingers and two fifteenths of another finger, which is the proportion. Therefore, &c. which is what was to be demonstrated in figure 1.

Note

Because it is difficult for the centers of the guards of the two opponents to be on the line A.B. or common section of the two vertical and superior planes, not only has the semi-diameter of the guards been doubled in Spain, as it is very close to four fingers, but it is also necessary to make use of our Pyramids, as we demonstrate in the idea of our Fortress; and to know the defense that is provided by the guards in Spain, we will show what they cover of the body in the three most principal planes, which are the vertical right, right collateral, and vertical plane that passes through the chest vertical.

Proposition II. Theorem II.

Given the same as in the previous figure, except for the semi-diameter of the opponent’s guard, which in that was a question, and in this is given as four fingers, as is common for guards in Spain, the question is to know how much it will cover in the length and width of the body?

From P, the center of the Fencer’s guard, draw the tangent P.G. and extend it as necessary; from point F, the center of the opponent’s guard, draw F.G. to the contact point, and from point D, draw D.I. parallel to F.G. meeting P.G. at point I. I claim that D.I. will be fifteen fingers, which is demonstrated in this way.

In the triangle P.D.I., since the line D.I. is parallel to F.G., the sides P.D. and P.I. of the triangle P.D.I. will be divided in the same proportion, and since the angles in F.G. are equal to the angles D.I., and the angle at P is common, the triangles P.I.D. and P.G.F. will be similar by the first definition of the sixth book; and by the fourth proposition of the same book, the homologous sides will be proportional, and as P.F. to F.G. so P.D. to D.I. But P.F. is 16 fingers, F.G. is four, and P.D. is sixty; forming the rule of three, the D.I. of fifteen fingers will be found, which is about one foot: therefore, the guard of the Sword, which has a semi-diameter of four fingers, can cover thirty fingers of breadth and length of the body, which are two feet less two fingers, which is what was to be demonstrated in figure two.

Proposition III. Theorem III.

With the Fencer in the same distance from his opponent with the center of his guard at point P, as in the past two propositions, and both centers of the guards P.F. occupying the common section of the opponent’s right collateral plane with the superior plane, in which position his guard is three fingers closer to his body than in the previous ones, will cover a space in circumference of 25 fingers and one-third in diameter of the breadth and length of his body.

Let A.B. be the common section of the opponent’s right collateral plane with the superior plane, with the same distances as in the previous ones between the two fighters, except that the center F of the opponent’s guard, in this position, is three fingers closer to his body. I say that it will only cover a space in circumference of 25 fingers and one-third in diameter of the breadth and length of his body, whose semi-diameter D.I. will be twelve fingers and two-thirds.

From point P, the center of the Fencer’s guard, draw the tangent P.G. extended to I. From point F, the center of the opponent’s guard, draw F.G. to the contact point G, and from point D, draw D.I. parallel to F.G.

In the triangle P.D.I., since the line D.I. is parallel to F.G., the sides P.D. and P.I. of the triangle P.D.I. will be divided in the same proportion; and since the angles in F.G. are equal to the angles D.I., and the angle at P is common, the triangles P.I.D. and P.G.F. will be similar by the first definition of the sixth book; and by the fourth proposition of the same book, the homologous sides will be proportional, and as P.F. to F.G. so P.D. to D.I. But P.F. is 19 fingers, F.G. is four, and P.D. is 60. Forming the rule of three, the D.I. of 12 fingers and two-thirds will be found: therefore, the guard of the Sword, with a semi-diameter of four fingers, placed in the right collateral plane as described, will cover 25 fingers and one-third in diameter of the breadth and length of the body, which is what was to be demonstrated, as shown in figure three.

Proposition IV. Theorem IV.

With the Fencer at the same distance from his opponent with the center of his guard at point P, as in the previous three propositions, and both centers of the guards P. and F. occupying the common section of the opponent’s vertical chest plane with the superior plane, in which position his guard is eight fingers closer to his body than in the first two figures, will cover a space in circumference of twenty fingers in diameter of his breadth and length.

Let the line B.A. be the common section of the opponent’s vertical chest plane with the superior plane, with the same distances as in the previous figures between the two fighters, except that the center F of the opponent’s guard is closer to his body than in the first two figures by eight fingers: I claim that it will only cover a space in circumference of twenty fingers in diameter of his breadth and length, whose semi-diameter D.I. in this position will be ten fingers.

From point P, the center of the Fencer’s guard, draw the tangent P.G. extended to I. From point F, the center of the opponent’s guard, draw F.G. to the contact point G, and from point D, draw D.I. parallel to F.G.

In the triangle P.D.I., since the line D.I. is parallel to F.G., the sides P.D. and P.I. of the triangle P.D.I. will be divided in the same proportion; and since the angles in F.G. are equal to the angles D.I., and the angle at P is common, the triangles P.I.D. and P.G.F. will be similar by the first definition of the sixth book; and by the fourth proposition of the same book, the homologous sides will be proportional, and as P.F. to F.G. so P.D. to D.I. But P.F. is 24 fingers, F.G. is four, and P.D. is 60. Forming the rule of three, the D.I. of 10 fingers will be found: therefore, the guard of the Sword, with a semi-diameter of four fingers, placed as described, will cover a space of 20 fingers in diameter of the breadth and length of the body, which is what was to be demonstrated, as shown in figure four.

Lamina once del Libro ſegundo.

 

Plate eleven of Book Two

 

CHAPTER EIGHTEEN

Symmetry of the Arm and Sword, and of the Divisions Considered in Both, from Whose Revolution Result the Six Necessary Orbs to Regulate the Movements of the Body on the Lower Plane, to Understand and Determine the Perfect Selection of Proportional Means.

Both in the Book of Science and in this one on the Art of Managing and Governing the Armed Instrument, the Sword, we have shown that the Skill of Arms is a science subordinated to Mathematics, particularly to Geometry, as it is founded on the consideration of all four types of quantity, etc. And that, following the example of ancient Philosophers and Cosmographers, who, in order to find the movements of the Stars in the Sky and to regulate the movement of Ships on Water, necessarily relied on Mathematical sciences, as it was impossible by other means; and that we too have been forced to rely on them to regulate the movement of the Sword in the Air, and of the body on the Earth. Moreover, those dealing with Military Art, to know not only the movement or path of the bullet through the Air, the movement to be made by the Artillery and Squadrons through the Approaches to get closer to the Fortress, but also the movement to be made to direct mines beneath the earth to the part convenient for the intended effect, give rules based on Mathematics: all of which I mention so that we can begin the construction of a figure, through which the foundation of this science becomes clearer and more understandable, assuming what all those who have dealt with Mathematics have assumed: namely, that every point moves in a straight or curved line; every line moves in a line or forms a surface; every surface moves in a surface or causes a body, according to Euclid Book 11, Definitions 12 and 18. Every body, when it moves, if its movement is local, causes a body of another kind; but if it moves about its axis, some describe different bodies, and others do not. With this in mind, I move on to the construction or explanation of the figure.

Explaining the Symmetry of the Arm and Sword.

This explanation can be made in two ways, the first taking on the lower plane the quantity A.B. of six Geometric feet, divided into six parts, as indicated by the numbers from B to A.1.2.3.4.5.6., and with the center A, if a revolution is given from each of these divisions, the circle B.D.F.H. will be formed, representing the orb of the Sword, and each point will have described one of the other five orbs, as seen in the figure.

The second method is to suppose the Fencer affirmed on a right angle at A.N. and at a right angle with his arm and Sword M.L.A., with the same divisions in the arm and Sword, on the upper plane 1.2.3.4.5.6., and from the extremity of the tip of the Sword and from each one of the divisions, draw a perpendicular to the lower plane B.D.F.H. that ends on the line B.A. at the same numbers 1.2.3.4.5.6. corresponding to those of the lower plane, as seen in the figure that is in elevation.

Imagine that the Fencer makes a revolution around the center of his right foot, maintaining the same posture of body, arm, and Sword, with each of the extremities of the six perpendiculars causing its circle on the lower plane, and six concentric circles will be formed, whose intermediate spaces we call Orbs of one Geometric foot each, indicated by the same numbers 1.2.3.4.5.6. In these Orbs, we have placed the projection of the Sword in the divisions of the eight directions that we imagine as traces left by the revolution in the Air when it passes through the eight main planes, which we also imagine to be of so much use and foundation in Skill that we have deemed it appropriate to mark them with the Swords, leaving their explanation for later in their place; and these eight planes have their common section in the center A. of the figure, and are the most essential paths through which the Fencer must regulate his operations: and because the figures in elevation are not intelligible to all, we have put the one that follows it, with the same projections in plan, which is the first one explained, as it is easier to perceive. And in both, we have avoided multiplying letters, because for their understanding it is enough with those that have been placed, to avoid confusion.

Having explained the idea of our Fortress and the size or dimensions that the shield must have for its defense, the most immediate thing is to provide knowledge, according to the order that has been established, so that the Fencer can achieve both ends, defense and offense if appropriate; and so to make evident what they consist of, and how the inner and outer bulwarks of our Fortress can be formed, we will use statics, to demonstrate through it how easy its possibility is.

Lamina doze del Libro ſegundo

 

Plate twelve of Book Two.

 

CHAPTER NINETEEN

Demonstrating through Statics How to Understand the Degrees of Strength and Weakness of the Arm and Sword, as Managed by Its Wielder, in Relation to Its Power.

Explanation of the First Figure

It is a well-established concept among Mathematicians that the property of the scales (one of the five powers of statics) is to proportion weights to the distances at which they are placed in relation to the fulcrum (commonly called the Balance), as seen in the first figure of Plate F.G. In this figure, we suppose that the line A.D. represents the arm and sword extended straight, as it comes from the shoulder parallel to the Horizon, whose length is six Geometric feet, two from the center of the arm A. to the wrist line, or wrist O., and the other four from the wrist O. to the tip of the sword D., which is the length from the pommel to the tip, divided into six equal parts, two pertaining to the arm and the other four to the sword.

For this demonstration, it is supposed that at point B., four feet away from the center of the arm A., a weight of six pounds is hanging at F., and that the line A.B. is extended to C., so that A.C. is equal to A.B., and from point C., another weight of six pounds is hanging at E. It is evident that they will be in equilibrium, as they are equally distanced from the fulcrum A., where the center of gravity of these two weights is, through which passes the line of direction H.I., as demonstrated by Guido Baldo, proposition one of the Lever.

From this, it follows that if the Fencer is affirmed at a right angle with his arm and sword and sustains a weight of six pounds hanging from point B., he will have the same power as the weight of six pounds hanging from point C.

To regulate this power with another weight hanging from the tip of the sword D., a rule of three is formed, taking as the first term six, which is the length of the arm and sword D.A., as the second term A.C., which is four feet, and as the third term the weight hanging from point C. of six pounds; and performing the operation, the result is the weight G. of four pounds, hanging from the tip of the sword. These two weights will also be in equilibrium, by the aforementioned first proposition of Guido Baldo, where he shows that the proportion that the length D.A. has to A.C., which here is sesquialtera, is reciprocally the same that the weight E., hanging from C. of six pounds, has to the weight G., hanging from D. of four pounds.

Corollary

From this, it follows that since A.B. is equal to A.C. and weight F. is equal to weight E., the same proportion that D.A. has with A.C., D.A. has with A.B., according to Euclid’s ninth proposition of the fifth book: then as D.A. is to A.B., so is weight E. to weight G. But since weight E. is equal to weight F., according to proposition seven, also of the fifth book, the line D.A. to the line A.B. will have the same proportion, reciprocally sesquialtera, as weight F. to weight G., which is what was required to be demonstrated, and is demonstrated by the first figure of Plate F.G.

Explanation of the Second Figure

In this second figure, the same length as in the previous one is given to the arm and sword A.D. of six feet, and A.C. of three feet, and weight G. of four pounds hanging from the tip of the sword D., and it is desired to examine, in respect to this power, the weight that can be sustained at point N., three feet away from the center of the arm A.

By rule of three, the proportion that the length A.N. of three feet has to the length A.D. of six feet is the same as the weight G. of four pounds, hanging from point D., to another; and performing the operation, the result is, in double proportion, the weight F. of eight pounds, hanging from point N., which is what can be sustained according to this power, represented by the weight E. of eight pounds, hanging from point C., which is what was required to be demonstrated in the second figure.

Explanation of the Third Figure

In this third figure, the same length as in the previous ones of six feet is given to the arm and sword A.D., and A.C. of two feet, and weight G. of four pounds, hanging from the point of the sword D., and, in respect to this power, it is desired to examine the weight that can be sustained at point P. on the wrist, two feet away from the center of the arm A.

By rule of three, the proportion that the length P.A. of two feet has to the length A.D. of six feet is the same as the weight of four pounds G. hanging from point D. to another; and performing the operation, the result is weight F. of twelve pounds, hanging from the wrist point F., and it will be in triple proportion to the weight G. hanging from the tip of the sword D., which is what was required to be demonstrated.

Corollary

From these three demonstrations, it follows that in the divisions and degrees of the sword that are closer to the guard and arm, there will be greater strength than in the divisions and degrees that are more remote; and to examine the power that will be had in each one, proportioning the greater and lesser lengths in the order that has been maintained in these demonstrations, anyone can examine the strength and weakness that will be had, according to their power, in any degree of their sword.

Lamina treze del Libro ſegundo.

 

Plate thirteen of Book Two.

 

CHAPTER TWENTIETH

Explanation on How We Imagine the Eight Vertical Planes Considered in Each of the Two Combatants for the Use of Fencing.

Let the line A.K. be half a foot, which is half the width that, according to the rules of Symmetry, we have found to be the figure of a well-proportioned man, and the line K.H. be two feet, corresponding to the length of the arm, from the center K to the wrist.

Imagine that the entire line A.H. makes a revolution around point A. Point K will cause the circle K.L.M.N.O.P.Q.R. and point H will cause the circle H.B.I.C.

Divide these circles into eight equal parts, with the diameters D.C.H.I.D.E.F.G.

Consider that the Right-hander is inside the smaller circle so that his direction line corresponds to the center A, and the diametral of the chest corresponds to A.B. and that being in this position, the smaller and larger circle, with all their diameters, rise parallel to the Horizon up to the vertex of the head.

In these considerations, we will first find that the inner circle with this movement will have caused a cylinder, in which we imagine the Right-hander is contained, and the eight points K.L.M.N.O.P.Q.R. will have caused with this movement 8 lines on the surface of this cylinder: and the one described by point M, because by supposition corresponds to the chest, will be called Vertical, or Diametral of the chest. And the one described by point Q will be called Vertical of the back. And the one described by point L will be called Right Collateral. And the one described by point P, opposite, will be Left Collateral of the back. And the one described by point N will be Collateral of the left side. And the one caused by point R, opposite, will be Right Collateral of the back. And the one described by point K will be the Right Vertical. And the one described by point O, opposite, will be the Left Vertical.

With the same consideration, not only is the cylinder formed, with its eight surface lines that have been explained; but also outside of it, four vertical planes are formed, with the same movement, that divide the cylinder into eight equal parts; and all are divided in the middle in the axis of this cylinder, which corresponds to the direction line, whose imagination in Fencing is of great use and utility; and although in rigor there are no more than four planes, for more intelligence we divide them into eight, and give each one the denomination of the line by which it passes, in this way.

The one caused by the line A.B., for passing through the vertical of the chest, we call it Vertical Plane of the chest. And the one caused by the line A.C., opposite, because it passes through the vertical line of the back, we call it Vertical of the back. And the one caused by the line A.D., for passing through the right collateral line, we call it Right Collateral Plane. And the one caused by the line A.E., opposite, for passing through the left collateral line of the back, we call it Left Collateral Plane of the Back. And the one that causes the line A.F., for passing through the left collateral, we call it Left Collateral Plane. And the one that causes the line A.G., opposite, for passing through the right collateral of the back, we call it Right Collateral Plane of the Back, we call it Right Vertical Plane. And the one that causes the line A.I., for passing through the left vertical, we call it Left Vertical Plane.

Notice

These circles with their lines of Diameter, divisions of the planes, and letters, we could have imagined them in the plane that passes through the vertex of the head of the Right-hander, parallel to the lower plane, and that from this plane it was going down parallel to the Horizon, until the same lower plane, causing with its movement the same cylinders, lines, and planes that we have explained, whose common section in the lower plane will cause the same semidiameters corresponding to the upper ones, for the consideration of the planes; but as this would be difficult, for those who are not used to these imaginations, to consider first these circles, and their divisions in the Air, it has seemed to us, to facilitate their intelligence, to imagine them first in the lower plane, where they can be described, to satisfy more the understanding; although it is necessary, that for the intelligence of this harmony, and of what is preached about it, and of the organization of man, that these imaginations be considered in the plane that passes through the vertex of the head, and that the two circles, and lines go down, as has been said, parallel to the Horizon, until the lower plane, so that the common section of the four Vertical planes, with it, cause the eight semidiameters in the same lower plane, which serve as compasses in navigation, so that the Right-hander gives by them his straight, transversal, strange of trepidation, and mixed of trepidation and strange compasses; whose knowledge is very important, and its use, for the practical of Fencing, as will be seen in the figures in which the Right-hander will have to exercise, and in particular in the one we call Universal, which includes all the exercises that can be done, and the propositions that must be worked in Fencing, to which we refer ourselves for not being of this place.

With this, the great importance of these imaginations will be recognized, and the fruit that is drawn from them, since they are the foundation of all Fencing, as will be pointed out at the end of this discourse.

The imagination of these planes has been in order so that the operations of the arm and Sword of the Right-hander in the Air, and of the body in the lower plane, can be regulated, in imitation of the Mathematicians, who to regulate the movements of the Stars in the Heavens, and of the rays of the Sun, and of the sight in the Air, and of the Ships in the Waters, make use of the imagination of straight and circular lines, planes, and bodies of different species, from which they have drawn, and draw admirable utilities, as is notorious to the World; and so that the Right-hander can achieve them in Fencing with accuracy, it is convenient to explain the fruit that will be drawn from each one of the imaginations that we have made.

Being, then, the Right-hander affirmed in such a way, that his arm, and Sword is in his right vertical plane, which is represented in this figure with the line A.H. will be in his greatest reach; but for having it totally disjointed from his whole, he will have in it his greatest weakness.

If it were possible to put his arm, and Sword in the left vertical plane, which corresponds to A.I. he would find himself in his greatest strength, because he would have the arm united to his whole; but he would have two feet less reach, which is the length he has from his arm from its center to the wrist, or straight line; because in this consideration he will be embedded in the width of the body, as anyone can experience by putting the arm to the chest, and putting his Sword in the least reach, so that the tip is in this plane.

In the other three planes, which are the two collaterals, and the diametral, he will participate in the weakness, or strength, and reach, according to how far away his arm, and Sword are from these two extremes.

Because the diametral plane, which represents the line A.B. for being equally distant from the two vertical right and left planes, it will be found that in it participates in the properties of both, that is, of the strength of the vertical plane A.I. and of the reach of the vertical plane A.H. and for this reason, it will have less reach, than in the first plane A.H., the excess that there is from V. to X. orb of the Sword, and less strength, than in the fifth plane A.I.

In the right collateral plane A.D. second, it will participate in the greater reach of the plane A.H. first, and less strength, than in the third plane A.B., for the same reason that has been said.

Being the arm in the left collateral plane A.F. fourth, it will participate in the strength of the vertical plane A.I. fifth, and will have less reach, than in the first diametral plane A.B.

With these foundations settled, it will be found that whenever the Sword, being in some plane, moves to any of the others, it will lose the nature of that plane, and will acquire that of the other plane to which it is approaching.

Like if being in the right collateral plane A.D. as it approaches the right vertical plane A.H. it will acquire more reach, and will lose the strength, which participated the plane A.D.

If being in the same collateral plane A.D. as it approaches the diametral plane of the chest A.B. it will lose the reach, and will acquire more strength.

If you have the Sword in the left collateral plane A.F. as it approaches the vertical plane of the same side A.I. it will be found with more strength, and less reach.

If being with his Sword in the same left collateral plane A.F. as it approaches the diametral plane of the chest A.B. it will lose its strength, and will acquire more reach.

With this knowledge not only will the nature of these planes be known, but also that of all their intermediates.

The other three planes, corresponding to the back, which are the right and left collaterals A.G. and A.E., and the diametral A.C., are not used for the arm because it cannot reach them with the required perfection. Thus, they serve only in the lower plane as a guide for the three compasses: the one given by the line A.C. is called Compass of Trepidation; the one given by the lines A.G. is Transversal to the right side; and the one given by A.E. is a mix of Trepidation and Strange, along with their intermediates. More detailed reasoning on these and other compasses will be provided in their respective sections.

The explanations of the first five planes are understood without difference with the opponent opposite the Right-hander, as they are predicated on the organization and composure of man, which is common to all. For the same reason, the other three planes at the back, which serve in the lower plane for the aforementioned effects, are also understood in the opponent.

Notice

It is noted that wherever either of the two combatants moves, they will carry with them the consideration of their planes, as they all intersect at the axis of their cylinder, passing each one through its determined line on the surface of it. Thus, it is evident that with any movement the cylinder makes, all will move, each maintaining the position in which it was considered in its origin. For example, in the vertical plane passing through the Diametral of the chest, which was caused by the line A.B., there are two parts: the one caused by A.M. remains inside the body of the same cylinder, in a determined and fixed place, and the M.B. outside of it; but these two parts can never be separated. Therefore, as the part A.M. moves, it is necessary that M.B. also moves, and this with any type of movement that is made. This same consideration applies to all other planes, as the same reason converges in each one of them; thus, moving any of these planes, at the same time, all will move.

In what we have said, knowledge of the nature of each of these planes, considered in each of the two combatants, and their properties, has been given, recognizing there is inequality among them in terms of greater and lesser strength, and greater and lesser reach, and how they accompany the body in each of its movements. Because all Fencing, in its practice, consists in the Right-hander having inequality with his opponent, to perform his proportions, remaining defended at the time he offends, we want to show how through the use of these planes he can achieve this inequality. To do this more accurately and clearly, we rely on the imagination of a plane, called primary and common among the two combatants, which must serve as a guide for all operations of Fencing; and as such an important foundation, it is appropriate that before entering to treat its use, we give knowledge of it.

Lamina catorce del Libro ſegundo.

 

Plate fourteen of the Second Book.

 

CHAPTER TWENTY ONE

On the Consideration of the Primary Vertical Plane Universally in Relation to Defense and Offense in All Operations of Fencing, as the Principal Guide by Which to Govern and Regulate.

In Astronomy, to regulate the movements of the Stars, Mathematicians have imagined various circles, among them a principal one, called the Primary, whose nature is through the Zenith, the Pole of the Horizon, and by the true East, and as long as this point or Zenith does not change, this circle does not move; but as it moves away from the equinox, or approaches it, this circle also changes its place in the heavens: so much so, that if it were possible, that the Zenith reached the Poles of the World, there would be no point in the entire globe through which this primary vertical circle had not passed.

In the Art of Arms, we imagine a circle, which being vertical, bears much resemblance to this primary, because we consider it to pass through the Zenith of the two combatants; and more precisely through the two axes of the two cylinders, in which we consider the two combatants perpendicular to the Horizon, and if neither of them moves, this circle remains fixed; but moving circularly over its own center, or by the circumference of the circle of its opponent, there will be no point on the entire surface of the combatants through which this circle or primary vertical plane has not passed, according to the movement it has made, relative to itself or its opponent: that is, if the Fencer moves over his own center, this primary vertical plane will pass through all his planes and body surface; and if he makes a movement from place to place, by the circumference of the circle of his opponent, then he will make this primary vertical plane pass through all the particular planes of the same opponent; and for this reason, and resemblance, we rightly name it the primary vertical.

Thus, to consider the universality of this primary vertical plane, it is necessary to imagine that the two combatants are each contained in a cylinder, which is constituted in the form mentioned in Chapter XIV, where the eight particular planes that are imagined in man for the use of Fencing are explained.

This primary vertical plane, or common, as we have already defined it, is the one that is considered to pass through the two axes of the two cylinders in which the two combatants are considered to be affirmed, perpendicular to the Horizon, from whatever distance they are found, and whatever their aspects may be.

The property found in this primary plane is to be the shortest distance between the two opponents, and it is of such importance to pay attention to this plane, to execute or defend tricks, that not having it as a guide, it could be said that Fencing had no true foundation of science, because it is a universal principle, to regulate with knowledge and accuracy the particular planes of the Fencer, and those of his opponent; and for this reason, we imagine in this plane the Angles of the bastions in the idea of our Fort.

Through the compasses, or motions, over the center of his particular circle, and the Pyramid of the arm and guard, in which the main defense lies, one strikes through this primary vertical plane, or common, and it is achieved with security, with the inequality that is caused; and with this Pyramid of defense, the placing at the time of execution the Sword of the opponent in the two vertical planes of the defense, which are the sides of the Angle of these bastions.

For the teaching of the use of this primary plane, we first suppose two figures, which correspond to the bases of the cylinders of the two combatants with their Diameters, and common sections, which they cause in the lower plane, and are the first that follow.

Note that the figure in which the Fencer is supposed to be affirmed is marked with capital letters, and that of the opponent with the same letters, but small, to differentiate between them.

Explanation of the Two Figures in the Plate

Given are two figures, or plans of the two cylinders at any distance, provided it is not less than a foot and a half, which is the width we have found to be of a man’s body from shoulder to shoulder, and we mark them with the letters M.K.Q.O. as the base of the cylinders in which we consider the Fencers; although for the use of Fencing, and for clearer understanding, we consider that between the two cylinders from point A to point A there are eight feet of distance, which is the half of proportion, where the combatants are affirmed, facing each other squarely, as shown both by the cylinders that are in the plan, and by the figures that are in elevation.

From the center A draw the line A, which represents the common section of the primary vertical plane, and common in the lower plane, whose primary plane must always be considered between the two opponents with the universality that will be said later, and now according to our construction, corresponds to their vertical chest planes, particular to each one of the two, the Fencer marked with A.B. and that of the opponent with the letters a. and b. small, in whose position, being both planes of one nature, and property, will be in equal potency.

Given, then, that the opponent does not move, and that the Fencer gives a revolution around the center A. and direction line of his cylinder, in which we consider him, he will be applying his particular planes: in the primary A.a. as for example can be seen thus: If the Fencer moves to his left hand, he will apply his right collateral plane, represented by the line A.D. in the primary plane A.a.

Continuing the revolution, he will apply the plane A.H. on the same primary plane, and successively the planes that represent the lines A.G.-A.C.-A.E. and A.I. so that, when the revolution is finished, he will have applied all his particular planes in this primary plane.

Although we have said that the three planes, which correspond to the backs are of little use, as here we deal with the universality of them, we include them all; and also with the attention that there is a trick in the common Fencing, called the Turnaround, with which the application of all these planes is made in the primary vertical.

Note that in the same revolution that the Fencer gives, moving on the center, putting his particular planes in the primary, the immediate one to the one he applies in this primary, occupies the place of the plane he left; and successively, in this same order, the planes are occupying the places of their predecessors; and applying one in the primary, all of them change at the same time, as it is clearly recognized by reflecting on this figure.

As in the example we have put, in which the two combatants are affirmed squarely, and the primary plane passes through the Zenith of their heads, and the vertical planes through their diametrical chest, and made their position that the Fencer makes the revolution around his direction line.

We note that the Fencer may pass his direction line to the center of his right foot, or to the center of the left, and cause the primary plane in any of his vertical planes, and make the same revolution, or portion of it that is necessary, according to the purposes he carries in his operations.

Lamina quince del Libro ſegundo.

 

Plate fifteen of the Second Book.

 

CHAPTER TWENTY TWO

Demonstration of How the Right-Hander Applies the Primary or Common Vertical Plane to Any of the Particular Planes of His Opponent, Who is Assumed to be Waiting, for a Clearer Explanation of the Following Figure.

We have already shown how the Right-hander will apply all his particular planes to the primary and common plane by revolving around the center of his cylinder.

Now it is necessary to show that by giving his compasses around the circumference of the maximum Orb of the means of proportion, how the Right-hander can apply the primary and common vertical plane to the particulars of his opponent. We explain this through the following figure.

Let the maximum Orb AAAA be given, described with an interval at A of eight feet, which is the distance between the two centers or axes of the two cylinders when the two combatants are affirmed in the middle of proportion, facing each other squarely. Let the circle M.K.Q.O. be described with an interval of three-quarters of a foot (which is the base of the cylinder) in which the opponent is considered, and the outer circle B.H.C.I. be described with an interval of two feet, which is the distance from point A, center of the figure, and line of direction, to the extremity of the arm or straight line, placed at a right angle.

Divide all these circles into eight equal parts, using the four Diameters of the maximum Orb AAAA. &c., all intersecting at the center of the opponent’s cylinder at A.

Making centers at the extremities of these Diameters AAAA. &c., eight figures equal in every way to the central one will be described on the circumference of the maximum Orb: the inner circle of each of them Q.O.M.K. represents the base of the Right-hander’s cylinder, in which we imagine he has, as said, a diameter of a foot and a half, and the outer circle C.I.B.H with a diameter of four feet, whose Semidiameter A.B. of two feet represents the distance from the line of direction, and center of the cylinder where the centers of the feet are in lines, to the straight line or extremity of the arm.

Divide these eight circles into eight equal parts, each with another four Diameters C.B.I.K.E.D.G.F. intersecting at the center A. of each figure, where they will be divided into eight Semidiameters, representing the eight vertical planes we have imagined in the Right-hander, explained in the following way.

The line A.B. represents the vertical plane of the chest, for passing through it and the Diametral or vertical of the same chest.

The line A.C. opposite to A.B. represents the vertical plane that passes through the back, because it passes through it and the vertical of the same back.

The line A.D. represents the right collateral plane, for passing through this line and the right collateral.

The line A.E. opposite to A.D. represents the left collateral plane of the back, for passing through this line and the collateral of the same side.

The line A.F. represents the left collateral plane of the side, for passing through this line and the same collateral.

The line A.G. represents the right vertical plane of the back, for passing through this line and the same side.

The line A.H. represents the right vertical plane, for passing through this line and the vertical of the same side.

The A.I. represents the left vertical plane, for passing through this line and the vertical line of the same side.

These eight vertical planes, which we have explained, have their common section with the lower plane at the center of the figure and the line of direction of the Right-hander’s cylinder, which is perpendicular to point A.

The other seven figures, which are also on the circumference of the maximum orb, were described with the same intervals, divisions, and letters as the first one, which we have explained and is on the circumference of the same orb. This is to understand that as the Right-hander gives his compasses to his right or left side, he will carry with him this first figure, with its particular planes and the considerations that have been made of them.

Now it is appropriate to show how the Right-hander will apply the primary and common plane, through his compasses, to the particular planes of his opponent.

Imagine then, with the opponent affirmed squarely, his line of direction corresponding to the center of the maximum orb and of his cylinder a., and the Right-hander is also affirmed in the same way squarely in his particular first figure on the circumference of the same maximum orb, his line of direction corresponding to the center of it, and of his cylinder A. In such a way, that the Right-hander’s vertical chest plane A.B., and the opponent’s vertical chest plane a.b., both passing through their diametrals, are opposed, and through them passes the primary or common vertical plane A.a. that we imagine between the two, as is shown both by the figure in plan and by the bodies that have been placed in elevation.

Being thus affirmed, we consider that this primary vertical plane A.a. passes, as has been said, through both of their particular chest planes, applied by the Right-hander in the particular vertical of his opponent, also caused in his own particular chest, which being of the same nature both particular planes will have equal potency; and to see the universality, and manner, as the Right-hander will apply this primary plane around the circumference of the same maximum orb, it is necessary for its understanding, we suppose for example, that the opponent waits in the same square position, and that the Right-hander passes giving compass to his left side, from the first figure, in which we affirmed him, to the second, preserving the same position of his particular planes with respect to the primary one he had in the first, to preserve in it his particular vertical chest plane A.B., with which he will have changed its place with respect to his opponent, to whom he will have it opposed in this second figure by the same primary A.a. and it is found that he has applied it to his right collateral plane, which represents the line a.d., and as this plane of the opponent is of a weaker nature than the vertical chest A.B. of the Right-hander, he will have dominion over the Sword of his opponent to divert or include it, in order to offend and remain defended.

What we have noted in this second figure, as to the position of the Right-hander’s planes with respect to his opponent, the same must be observed as he passes to the other six figures, which are on the circumference of the same maximum orb, through his compasses, with which in each one he will oppose his particular vertical chest plane A.B. to the particular planes of his opponent, which being stronger, he will have an advantage in them by the same primary A.a.

From this second figure, the Right-hander will pass to the third, keeping the same position as in the previous two, will have applied the primary plane A.a. to the right vertical plane of his opponent, corresponding to the line a.h., and simultaneously will have opposed it, by the same primary, his vertical chest plane A.B.

If from this third figure the Right-hander passes to the fourth, maintaining the same position as in the others, he will have applied the primary plane A.a. to the right collateral plane of the opponent’s back, which represents the line a.g., and opposed it, by the same primary, his vertical chest plane A.B.

If from this fourth figure the Right-hander passes to the fifth, he will have applied the primary plane A.a. to the opponent’s vertical back plane A.C. that represents it, and opposed it, by the same primary, his vertical chest plane A.B.

If from this fifth figure the Right-hander passes to the sixth, he will have opposed the primary plane A.a. to the left collateral plane of the opponent’s back, which represents the line A.E., and opposed to it, by the same primary, his vertical chest plane A.B.

If from the sixth figure the Right-hander passes to the seventh, he will have applied the primary plane A.a. to the opponent’s left vertical plane, which represents the line A.I., and opposed it, by the same primary, his vertical chest plane A.B.

If from this seventh figure the Right-hander passes to the eighth, he will have opposed the primary plane A.a. to the opponent’s left collateral plane, which represents the line A.F., and opposed it, by the same primary, his vertical chest plane A.B.

Thus, the Right-hander will have made a revolution of the primary plane, with respect to his opponent, and the line of direction of his cylinder in which he is considered affirmed, applying it to each one of his eight particular planes, which is what we intended to demonstrate.

With the light of this doctrine, the Right-hander, in this revolution, can make the same consideration of this primary plane A.a. and of his vertical chest plane A.B. in which he causes to apply it to the intermediate planes that are between the eight particular planes of the same opponent, noting that the more he approaches these planes with this revolution, the more inequality the Right-hander will acquire with him, except when he is further away from each one of these planes.

In the preceding sections, we have explained how the Right-hander can apply the primary plane to his particular planes and also how, through his compasses, he will apply the primary plane to any of the particular planes of his opponent. The universality of the application of this primary plane is understood not only as the Right-hander can apply it through his vertical chest plane, as exemplified, but also through all his other particular planes that are more used in Fencing, and through his intermediate vertical planes, as we will explain later.

It is now important to note that although there are eight particular planes, the five most used in Fencing are the right vertical plane A.H. (which we call the first), the right collateral plane A.D. (second), the vertical chest plane passing through the diametral A.B. (third), the left collateral plane of the side A.F. (fourth), and the left vertical plane A.I. (fifth). The other three planes A.E.-A.C. and A.G. correspond to the back and are the least used, as mentioned.

These five planes, and any of their intermediates, can be opposed by the Right-hander to his opponent’s particular planes, through the primary plane, and by the two aforementioned methods. To always maintain the necessary inequality when starting his propositions from the posture of the Sword, the Right-hander should oppose his stronger planes to counter his opponent’s greater reach advantageously; and by the profile of the body, he will oppose the planes of his greater reach to overcome, according to the teachings given later, his opponent’s planes of greater strength. By keeping these precepts, the Right-hander will begin and end his tricks with advantages and will be in immediate disposition to choose the proportionate means of the wounds, and to exit to the maximum orb of the means of proportion, where the precepts given in the explanations of the exercises that the Right-hander must perform are also to be kept, to which we refer.

These foundations and precepts are essential for the practical aspect of Fencing, as they guide how to offend without being offended, as will also be seen in the Chapter on proportionate means and in the Treatise on Tricks, where it is evident that the means of each one is reduced to the consideration of the inequality of these particular planes and the primary or common plane, which is the guide by which they are governed, and the shortest distance between the two combatants, as is explained and seen in the main figure and the others in it. The understanding and teaching of all this will always be common to both opponents; and whoever makes use of these precepts more perfectly and quickly will be the victor.

Because in different parts, we have not only called this primary plane the guide by which the other particular planes are governed, but we have also called it common, which implies equality between the two combatants. To satisfy this objection that may be raised, we say that this name common refers to the fact that either of the opponents can cause it in any of their particular planes, and apply it to the particular planes of the opponent, as has been explained. However, whoever anticipates doing so with more perfection and speed, as mentioned, will overcome his opponent. And in this rule lies the whole operative aspect of Fencing, as far as the choice of tricks and the ability to execute them securely are concerned.

By keeping these scientific and necessary precepts, one will always come to strike through the shortest distance, which is the line of Diameter, which until now has only been considered in the common circle between the two combatants, with the universality mentioned. Paying attention to the primary plane and the opposition of inequality that must exist between the particular planes of the two adversaries, the Right-hander will find himself in the battle with the required knowledge and great ease and promptitude to regulate his operations, without attending to the lower plane, as it is very difficult in the rigor of the battle, due to either of the two opponents, or both together, moving from place to place, erasing those first species that were imagined in the lower plane and common circle, and much more with the speed at which the two combatants move from one part to another, resulting in greater confusion, and the inability to keep the precepts produced by this science. This has led us to speculate on how to avoid this and to ensure that the Right-hander has a universal guide and easy foundation in his exercises with his opponent, and in real situations, so that neither acceleration nor anger have jurisdiction to remove him from the scientific knowledge to govern his actions; in such a way, that in them he has defense and offense against his opponent, if appropriate.

In terms of this defense and offense, the Right-hander must always seek to cause this primary vertical plane in one of his particular planes, with motion over the center of his particular circle, or through one of his compasses, and for the same purpose, apply this primary plane to one of his opponent’s particular planes, which is inferior to his particular plane in which he caused the primary, through which he will strike, because in this lies the achievement of both defense and offense without risk.

Having affirmed the opponent on the right angle to explain the universality of this primary plane and the other particular planes has been so that they can be more easily understood, imitating those who have written about fortification, who first explain regular places so that irregular ones can be better understood. In Fencing, there is regularity in how one combatant affirms himself with another, and the Right-hander, according to our precepts, must observe to affirm himself perpendicular to the Horizon. Many nations do the opposite, affirming themselves by disproportionately spreading their feet, creating extremes, placing the Sword out of term. To be able to judge these irregularities, it was convenient to affirm the Right-hander perpendicular to the Horizon at a right angle, as it is the most perfect and regular posture, so that with the knowledge of the considerations and precepts we have given, no matter how much the opponent disproportionates his body in them, he can never fail to give his planes to the Right-hander, so that he can regulate his propositions; especially since the most perfect wounds are executed from the waist up, and this part of the body can never be hidden by the opponent from the Right-hander, nor prevent him from considering him constituted in a cylinder. Moreover, no matter how disproportionated the opponent is affirmed, to attempt to wound the Right-hander, it is necessary that he reduce himself, even if he does not understand it, to causing his primary plane in one of his particular planes, and that he apply it to a particular plane of the Right-hander, or in the intermediate of them; and as this cannot be hidden from the Right-hander, he can easily make a judgment, according to the posture in which his adversary is affirmed, on which plane he can try to wound him, and have prepared the plane that he must oppose, which is superior to his. And while the case of offense does not arise, he can, with only our posture of the acute angle, prevent any inferior or superior plane in which he is affirmed, whatever it may be; so that his Sword does not have direction to his body, and that it is in one of the vertical planes of his defense, or that it passes the parallel plane to the Horizon, which we imagine passing through the vertex of the head; and no matter how much the opponent brings his Sword restless, the Right-hander’s movements to achieve these effects of his defense, with respect to his own, will be so brief that he can easily continue to prevent the plane in any part from which he wants to attack. And since it is not of this place to explain how these planes are to be opposed to the postures that the opponent makes, so that through the practice of Tricks, where individual knowledge of everything necessary will be given.

Laminda diez y ſeis del Libro ſegundo.

 

Plate sixteen of the Second Book.

 

CHAPTER TWENTY-THREE

Explanation of the Other Planes Parallel and Oblique to the Horizon, of Which the Fencer Must Be Aware, to Direct Straight, Circular, and Semicircular Techniques to Their Proper Targets on the Opponent’s Body; This Also Includes Knowledge of the Three Lower, Upper, and Middle Planes, All Very Necessary for the Practice of Skill in Arms.

To explain these planes with the necessary clarity, we do so through the following figure, in which they are delineated clearly and distinctly.

Given a right-handed fencer positioned in a perfect right angle and with his arm and sword also in a right angle in his right vertical plane, we imagine his body, which represents the cylinder (as we have previously explained), divided into eight parts through four parallelograms and their two diagonal lines each.

The first parallelogram C.D.F.E. encompasses the head and face, with its diagonals C.F. and D.E. extending to reach the centers of the arms G.H.

The second G.H.L.M. extends from the centers of the arms G.H. down to the waist L.M. with its diagonals H.L. and G.M. covering the chest and everything down to the waist L.M. In this section, we imagine a circle G.L.M.H. that touches the two vertical lines.

The third L.M. and N.O. is imagined from the waist L.M. down to the knees N.O. and includes the belly and thighs, with its diagonals L.O. and M.N.

The fourth N.O.P.Q. we imagine from the knees down to the feet and the lower plane, also with its diagonals N.Q. and O.P., which includes the knees, legs, and feet.

All diagonals of these four parallelograms intersect on their line of direction A.B. as they are perpendicularly affirmed to the Horizon.

The horizontal planes are three: the lower T.P.Q.V., the upper I.G.H.K., and the middle plane R.L.M.S. The eight diagonals of the four parallelograms mentioned above we consider to represent as many oblique planes in this manner:

The first oblique plane is represented by the line D.E., which we imagine passing from the left side of the head D. to the right arm’s center G., and on this plane, diagonal cuts and half cuts are executed.

The second oblique plane, represented by the line C.F., is imagined to pass from the right side of the head C. to the left arm’s center H., and on this plane, diagonal reverses and half reverses are executed.

The third oblique plane, represented by the line H.L. in the chest, is imagined to pass from the left arm’s center H. to the right side of the waist L. It shows the movement of the sword in the formation of the diagonal thrust and also corresponds to this plane the formation of cuts to the arm from the inside.

The fourth oblique plane, represented by the line G.M., corresponds to the obliquity with which the sword moves when attacking from the inside, executing cuts to the outside part of the arm, known as elbow cuts; it should be noted that the safest and strongest cuts will be those executed perpendicularly to the elbow and wrist.

The fifth oblique plane, represented by the line M.N., though it doesn’t serve to execute strikes on, is very important as it prevents the opponent’s sword from immediately delivering a blow from the upper or lower part by placing the sword on the outside corresponding to this plane.

The sixth oblique plane, represented by the line L.O., also doesn’t serve for striking but is as important as the previous one because it prevents the opponent from delivering immediate strikes from the upper or lower part, with the right-handed fencer placing his sword on the inside corresponding to this plane.

The seventh oblique plane, represented by the line O.P., serves to direct cuts to the legs.

The eighth and last of the oblique planes, represented by the line N.Q., also serves to direct reverse cuts to the legs.

Upper Plane

The upper plane I.G.H.K., passing through the centers of the arms G.H., is where the right angles are formed, determined at the common section of this plane with the primary vertical plane, which is the shortest distance between the two combatants.

In the common section of these two planes, all types of movement begin, and in it are made the remissive movements and reductions on both sides, and the straightness forward with the arm and sword, which also serves as the axis of the main pyramid. In it, the vertical, oblique, and horizontal planes intersect, from whose common sections result the perpendicular, horizontal, and oblique lines. These same lines are used for considering the straightness imagined for the use of Skill, both from this upper plane upward, as in the part below it, and in the same plane.

Note that the right angle is formed on this upper plane, sometimes with the arm and sword, other times with the lines of the sword and not the arm, and others with the arm and not the sword, whose differences are important, as will be recognized in the use of postures and maneuvers.

The wounds that can be executed on the opponent in this upper plane are thrusts on the upper tangent line of the circle imagined on the chest, as detailed explanations of everything referred are given in their proper places, to which we refer.

Middle Plane

The middle plane R.L.M.S., passing through the waist, is where the guard and the sword must be placed to have a Atajo in place on both the inside and outside from the far end: so that they do not pass from this plane, unlike when these Atajos are made from the near end because then it is necessary that the guard and the sword be placed below this middle plane, and also for the Atajo that is put on the inside to execute the thrust of the fourth circle, as will be explained in its place. And through these Atajos, which are assumed from the far end on both sides, one enters to strike if the opponent gives an opening, and if not, approaches are made to be able to offend with the types of maneuvers that the same approaches dispose of.

The Atajos made from the near end on both jurisdictions are usually for making finishing movements. And with these Atajos from the far and near end, on both sides, not only is what has been said achieved, but the opponent’s ability to immediately offend is removed, and he is forced to make more movements than the Diestro to attempt to offend if he does not change posture after being blocked.

Lower Plane

The plane T.P.Q.V. represents the horizontal lower plane (which is the ground), and thus, this plane is not imagined like the others but is real. However, it is of great importance for the use of Skill, as it is considered for this purpose. Just like cosmographers, hydrographers, and navigators use the imagination of rhumbs and other lines representing the circles of latitude or parallels to the equatorial circle to guide ships at sea and determine the location and place they are in, we too imagine straight lines representing the rhumbs by which the Diestro is to guide himself to execute his maneuvers and circles. Similar to latitude circles, these determine the place and site where the Diestro is to choose his proportionate means and measures, through the use of straight, transverse, curved, trepidation, and mixed trepidation and extraneous compasses. To regulate these compasses, we use the eight lines caused by the common section of this lower plane with the four vertical planes, which we call Rhumbs, a common circle imagined between the two combatants, a Maximal Orb for each one, considered the means of proportion, and another particular circle also for each one, with its tangents and two isosceles triangles, the other on the body’s profile, whose vertices are in the inner orb of one of the two Maximal Orbs, and their bases on the tangent of the common circle. The perpendiculars and the two of these two triangles serve for the most refined aspects that have been discovered in terms of compasses, to pass with very natural disposition and great security to the places that are mathematically determined for the proportionate means of maneuvers in both jurisdictions within the common circle and Maximal Orb of the means of proportion. Also, the place and means of the block made by the sword’s posture and the distance to pass to the middle of this block without risk and with ease are determined.

Also described is the Diestro standing on a right angle and in a right angle with his arm and sword on his right collateral plane and upper plane, occupying with the center of his right foot the center of his Maximal Orb in it, six other concentric Orbs, each one having one geometric foot of thickness, which correspond to the six divisions considered on the arm and sword, which are also one geometric foot apart from one another.

The first from the arm’s center to the elbow, from the elbow to the wrist, and the other four from the wrist and pommel of the sword to its tip, describing the sixth Orb we call the Sword Orb, in which its greatest reach lies.

Of these six Orbs, one foot each in thickness, we imagine their projections on this horizontal lower plane, which are determined in it by perpendicular lines coming from the upper plane and the same divisions considered on the arm and sword. The first two Orbs from the arm’s center to the wrist and pommel of the sword determine the means of proportion when the Diestro stands on it with his opponent, as it’s an inviolable precept that the tips of their swords should not pass the pommels and recta lines of their wrists.

The third Orb corresponds to the guard, which the most proportionate ones have from the pommel to the outside of them, two-thirds of a foot; so, what remains uncovered from the sword’s line are three feet and a third.

The fourth, fifth, and sixth Orbs are places and sites determined where the proportionate means are chosen from the far and near ends, by the sword’s posture and body profile, to execute the species of maneuvers and wounds that each of these means pertains to, in this manner.

The fourth Orb is the place occupied by the left foot for the movement of conclusion, and the fifth Orb is the place for the block from the near end, and the vertical and diagonal cuts, and half cuts, and half reverses; and the sixth and last Orb is the place for first intention wounds and fourth circle, and the four general maneuvers in both jurisdictions.

In this lower plane, we describe the idea of our Fort, with its Arms Plaza, foundations, with its bastions, and circumvallation, whose construction is founded on these Orbs, and the divisions we’ve considered on the arm and sword in the upper plane, and its projection, as mentioned on this lower plane. We give necessary rules and precepts on how to storm and defend this Fort, as will be explained in its place.

This Fort, and all other considerations and things we’ve imagined in the Diestro, we also consider in the opponent, with no difference whatsoever, assuming they are affirmed in the means of proportion, as will be seen in our universal figure and its explanation, and the remarkable harmony it has among itself for the operational use of Skill, and all else that we explain through figures in their proper places, with much distinction and clarity.

Lamina dieze y ſiete del Libro ſegundo.

 

Plate seventeen of the second book.

I’ve split this from Plate 17 in the proceeding chapter for clarity

 

CHAPTER TWENTY-FOUR

How the Diestro can apply the primary vertical plane in a way that gains an advantage over their opponent, creating the necessary inequality for their security in all propositions and operations of Skill.

The first thing we assume for a better understanding of what is intended to be explained is that the most universal discovery for the practical use of Skill are four movements; two that belong to the body and the other two to the arm and Sword; to which correspond another four terms, which are to impede the plane, to apply the plane, to oppose the plane, and to strike through the plane.

The first of these terms concerns the arm and Sword of the Diestro, to impede the plane through which their opponent must move to attack, ensuring safety to move to the second term, which pertains to the body, making a movement from one place to another through some of the compasses that must precede the proposition intended to be executed. Thus, in the newly acquired position, they can apply the primary or common plane to their opponent’s particular plane corresponding to it, simultaneously opposing it with their own particular plane on which they have an advantage, which pertains to the third term; and with this, they can proceed to the fourth, which will be to strike their opponent through the same primary plane in which it was applied.

The Diestro will achieve the aforementioned safely due to the inequality they have with their adversary and the advantage of their particular plane over their opponent’s plane in which they have applied the primary one. By adhering to these precepts, the Diestro will execute all tricks with complete perfection and safety, as none are excluded from this universality.

The Diestro must always create the primary plane in their particular plane, which is more advantageous than their opponent’s particular plane, to which they will have to give opposition through the same primary plane when applied. This means if it is weak, for example, if the Diestro has applied the primary or diametrical plane, which is strong, on the right vertical of the opponent, which although having greater reach is weak, the Diestro will overcome it with the opposition of their diametrical plane, which is stronger. And if the opponent has their diametrical plane of the chest forward, although it is stronger there, it also has less reach. Thus, in this case, the Diestro will oppose their right vertical plane of greater reach, trying to act from the farthest end so that the opponent cannot counter with their greater strength. In any proposition, the Diestro must govern themselves in a way that they always have a known advantage over the opponent, benefiting from the aforementioned precepts.

If the opponent deviates from these precepts during the battle, the Diestro will often find themselves in a position to act as if they had completed the first three terms and only had the fourth left to execute, which is the execution.

The aforementioned explanation boils down to how to apply the primary or common plane to the particular planes of the opponent and which ones the Diestro will put of their own, or the same primary plane, so that they can achieve, through scientific knowledge and use of these planes, the necessary inequality with their opponent.

Now it’s necessary to know the principal and most universal ways in which the Diestro, assuming they are affirmed on the right angle and in the right angle, can communicate their Sword with their opponent’s for more clarity, so that they can achieve the inequality and use of these planes discussed in the previous chapters. The first methods are reduced to four.

The first is making a block with their Sword on their opponent’s, from the inside, with the requirements taught in its explanation.

The second is making a block on the outside, adhering to the precepts given in its explanation.

The third is that having the Diestro’s Pyramid of the arm and guard in its place as the principal wall of their defense, they will lower their Sword to the acute angle, making contact with the opposing one from the inside and carrying it to their left side as necessary, observing the teachings given in its place.

The fourth method is that by stepping with the right foot to the same side, making first contact on the outside of the opponent’s Sword, through the same posture of the acute angle, they will carry it as far as necessary, also adhering to the precepts given in its explanation.

These four methods are the most universal for the Diestro to safely communicate their Sword with the opponent’s and apply the primary vertical plane to one of the opponent’s particular planes. Simultaneously, with the same safety, they can oppose one of their particular planes through the same primary plane, which has an advantage over the opponent’s.

It should be noted that when the Diestro finds contact on the opponent’s Sword at the time they communicate with theirs, they will act according to the disposition it provides, and through the assaults they can make from the side they find themselves on to strike, using diversions or through the same Sword if it’s not in its place.

But when the opponent only makes contact with their Sword on theirs, in this case, the Diestro can form the four general tricks on the side of the body or through the posture of the Sword because they will be capable of including it in one of their Pyramids or carrying it with pressure from them into one of the two vertical planes of their defense, according to the quality of the trick they intend to perform.

Through the blocks and other dispositions that will be mentioned in their place, the Diestro can proceed to make a concluding movement, and having done so, the opponent’s Sword will be in the vertical plane of their defense on their left side, more securely than in any other part. In all this, the Diestro will act according to the dispositions they have, following the precepts of the Art.

Other methods exist through which the Diestro can achieve the same effects in both jurisdictions, even if the opponent has their arm and Sword in a good place. These methods are as follows.

The Diestro can step with the left foot to the same side and with the right foot to the right side without communicating with the opponent’s Sword, impeding it with theirs from the plane through which it could immediately reduce to strike. This will be done through the posture of the acute angle. While they can impede it from the upper part, it won’t be as secure. Having caused this inequality, they can strike if the opponent doesn’t move, or make their assaults to achieve it through them. If the opponent does move, which will be necessary, they can also maintain their advantage to strike without risk by observing the individual precepts given for each case.

The other method is that when the opponent does not proceed as a Diestro in either jurisdiction, moving their arm and Sword away from the place where they have the defense, the Diestro will find themselves in a position to act with them as if they had completed the first three universal terms, only leaving the fourth term to be executed, which is the execution. The knowledge of this generality is considered sufficient for the Diestro to form their concepts from it. Thus, the individual explanation of it is left for the Treatise on Tricks to which we refer.

Lamina dieze y ſiete del Libro ſegundo.

 

Plate seventeen of the second book.

 

CHAPTER TWENTY-FIVE

On the knowledge of defense Pyramids that the Diestro can and must create with their Sword, arm, and guard, both in the middle of proportion and in proportioned positions, to place or contain their opponent’s Sword outside the two imaginary planes of their defense.

This proposition has various cases, and the most essential ones will be explained in order, starting with the three that belong to the profile posture or primary vertical plane. They are presented in one Plate, followed by the cases that pertain to the other two postures or planes.

First Case

Given that both combatants are affirmed in A.B. on the right angle D.C. and F.E. in the middle of proportion, with their Swords in the primary vertical plane passing through their right vertical planes, we want to examine the amount of movement or portion of the Pyramid the Diestro must make to the right and left to place or contain the opponent’s Sword outside the two imaginary defense planes, ensuring that the tip doesn’t have a direction toward their body and the cylinder in which we consider them.

Draw the line A.B. of nine feet, in which we imagine the primary vertical plane. Take the lines A.C. and B.E., each one of half a foot, and the remaining C.E. will be eight feet, the distance we have demonstrated must be the middle of proportion, and centers A. and B. The interval A.C. and B.E. describe the circles C.D. and E.F., which will be the bases of the cylinders in which we consider the two opponents. Take the C.G. from the center C. of the opponent’s arm to G. the center of the guard of their Sword, measuring two feet and a quarter, and the same measurement from the center of the Diestro’s arm E. to H. the center of the guard of their Sword. Draw from the center G. of the opponent’s guard the two tangents G.K.G.L., through which we imagine pass the two vertical defense planes that touch the cylinder containing the Diestro in the posture they are affirmed in.

Divide H.G. in the middle at point T. Take T.O. of four fingers and draw O.P. perpendicular to G.K. O.P. will be the smallest movement the Diestro must make to place the opponent’s Sword on their left side in the defense plane G.K. and on their right side in G.L. from this intersection O. of the Swords in the primary vertical plane A.B., and it’s examined in this manner.

Draw the line B.K., which, by proposition 18 of the third book of Euclid’s Elements, will be perpendicular to G.K. And as O.P. is also perpendicular to the same by construction, they will be parallel to each other. Consequently, by proposition two of the sixth book of Euclid’s Elements, the sides of the triangle G.B.K. will be divided in the same proportion, and the triangles G.B.K. and G.O.P. will be similar. So, as G.B. is six feet and a quarter, or 100 fingers, to B.K. of half a foot, or eight fingers, so will G.O. of two feet, or 32 fingers, to another fourth proportional, which comes out as 256/100, which is two fingers and a little more than half. This is the amount of O.P. and the movement the Diestro must make to place their Sword, from the primary vertical plane A.B., into the two defense planes G.K. and G.L., on either side, as demonstrated in the first figure.

Case Two

Given the same conditions as in the previous case, except that in this one, we assume that both opponents are at the distance of the proportionate medium for thrusts that are on the circumference of the sixth orb of the Diestro, having moved two feet from the proportionate medium, from point C to point M. Consequently, the center of his sword guard has moved to point I to strike with a thrust.

Draw the two tangents I.K.I.L. to the cylinder, draw B.L. to the point of contact, and it will be perpendicular to I.L. Draw H.N. perpendicular to I.B., and two similar triangles will be formed, placed subcontrarily, because both are right-angled and have the common angle at I. Thus, the corresponding sides will be proportional, and it will be as I.L. to L.B. is to I.H. to H.N. But since there is so little difference between I.L. and I.B., instead of I.L., we take I.B., saying as I.B. to B.L. is to I.H. to H.N. But of these four proportionals, three are known: I.B. is four feet and a quarter, which is 68 fingers, B.L. is half a foot, which is eight fingers, and I.H. is one and a half feet, which is 24 fingers; and performing the rule of three, the result for H.N. is slightly less than three fingers. Thus, it becomes evident that with the semi-diameter of the Diestro’s guard being four fingers on each side, with the aforementioned three fingers, without the Diestro making a move, he achieves defense with his guard, as verified by the second figure.

Case Three

Given the same conditions as in the previous two cases, except that in this one the opponent took a three-foot step from the medium of proportion to step on the fifth orb, which is the medium for cuts, intending to execute them. Consequently, the center of his sword guard comes to be three feet less a quarter away from the Diestro.

Draw the two tangents I.K.I.L. to the Diestro’s cylinder, and B.L. to the point of contact, and at the Diestro’s sword guard, draw N.H. perpendicular to I.B. This will form the similar triangles I.L.B. and I.N.H. By the same reasoning given in the previous case, it will be as I.B. is to B.L. is to I.H. to H.N. However, I.B. is three feet and a quarter, which is fifty-two fingers, B.L. is half a foot, which is eight fingers, I.H. is another eight fingers, and H.N. will be a quarter; and forming the rule of three, the result is one finger and three quarters of another finger. Since the semi-diameter of the Diestro’s guard is four fingers, this exceeds the necessary amount for his defense in the guard on both sides by two fingers and a quarter, as demonstrated in the third figure.

Para el Plano Vertical derecho

 

For the Right Vertical Plane

 

In the previous diagram, the three cases pertaining to the right vertical plane were explained. In this following diagram, we will demonstrate another three cases pertaining to the right collateral plane.

Case Four

Given that both opponents are affirmed in the medium of proportion C.E. as in the previous cases, the opponent is in his right vertical plane at a right angle and above the right angle on the base of his cylinder, which has a diameter of one foot at D.C., and the Diestro in his right collateral plane, also at a right angle and above the right angle at F.E. Since more width is exposed in this plane, the base of his cylinder K.L. is given a diameter of one and a quarter feet. We want to examine how much movement or portion of a pyramid the Diestro must make with his sword to the left or right to place it or contain it outside the two vertical planes of his defense.

Draw the tangents G.K. and G.L. Draw the B.K. to the point of contact. Divide the G.H. which is between the two centers of the quillons in half at T. Take a quarter of a foot from T. to O. Draw O.P. parallel to B.K., which will be perpendicular to G.K., forming two similar triangles G.B.K. and G.O.P, and their corresponding sides will be proportional. It will be as G.B. is to B.K. as G.O. is to O.P. However, of these four proportional values, three are known: G.B. is six feet, which is thirty-two fingers; forming the rule of three in this order, it is found that O.P. is three fingers and one ninth, which is the amount of movement that the Diestro must make at this intersection of the swords with his defensive Pyramid P.H.Q. to place with a portion of it the opponent’s sword, from the primary vertical plane, on both sides, outside the planes of his defense G.K. and G.L., as seen in the figure.

Case Five

Given the same conditions as in the previous case, except that in this instance, the opponent steps forward two feet from point C to point G to strike a thrust at the Diestro, moving the center of his quillon guard from point G to point I. This results in point I being four feet less a quarter away from Diestro’s cylinder F.E. The query is to determine how much movement, or what portion of a pyramid, the Diestro must perform from the primary vertical plane A.B. to his left side to place or contain his opponent’s sword on the surface of his cylinder.

Draw the two tangents I.K.I.L. and B.K. to the point of contact, and H.N. perpendicular to I.B. This results in the formation of two similar triangles I.B.K. and I.H.N., placed subcontrarily, with their corresponding sides proportional; but for the reason given in the second case, of these four proportionals, three are known, as I.B. is four feet and a quarter, which is 68 fingers, B.K. is 10, and I.H. is one foot and three quarters, which is 28 fingers. Forming the rule of three, it is found that H.N. is four fingers; thus, the Diestro must move the center of his guard, and his quillons, four fingers to the left and right to place the opponent’s sword outside the two vertical planes of his defense I.K.I.L. to remain defended.

Case Six

Given the same conditions as in the previous case, except that it is assumed the opponent steps forward three feet from point C to point O to step on the Orb of cuts, vertical and diagonal reverses, and half cuts, and half reverses of the same species, and reaches with this step the center of his guard to point I. This point is three feet less a quarter away from the Diestro and allows striking with one foot of the sword; the query is to examine how much the Diestro must move the center of his guard and quillons from the primary vertical plane A.B. to both sides to remain defended.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. and B.K. to the point of contact, and H.N. parallel to it, or perpendicular to I.K. This forms two similar triangles I.B.K. and I.H.N., with their corresponding sides proportional, as I.B. is to B.K. so is I.H. to H.N. However, of these four proportionals, three are known, as I.B. is three feet and a quarter, which is 52 fingers, B.K. is 12, and I.H. is 20 fingers. Forming the rule of three, it is found that the fourth proportional H.N. is four fingers and three-fifths, which is the amount of movement the Diestro must make from the primary vertical plane A.B. to both sides, with the center of the guard and quillons of his sword, to place and contain his opponent’s sword outside the two vertical defense planes I.K. and I.L. to remain defended from any of the circular and semicircular tricks and species of them with which he may be attacked in the jurisdiction from the superior plane upwards, as verified by figure nine.

Para el plano colateral derecho

 

For the right colateral plane

 

In the two plates preceding this one, the three cases pertaining to the right vertical plane, as well as the three cases related to the right collateral plane, are declared. In this current plate, the three cases belonging to the Diametral plane of the chest or square posture will be presented.

Case Seven

Given the same conditions as in the first and fourth cases, except that in this case, the Diestro stands with his arm and sword in his vertical plane of the chest. In this position, he loses half a foot of reach and exposes all his width, which is half a foot more than what was given to the diameter of the cylinder in the first case, where he is supposed to stand in his right vertical plane. To remain defended in this square posture, including the shoulders, the diameter of his cylinder F.E. is given as one and a half feet. The query is to determine how much movement or what portion of a pyramid the Diestro must perform with the center of his guard, from the primary vertical plane to his left and right, to place or contain his opponent’s sword in the two vertical defense planes.

Draw the tangents G.K. and G.L. to Diestro’s cylinder F.E. Draw B.K. to the point of contact, divide G.K. in the middle at T. Take T.O. as four fingers, draw O.P. parallel to B.K. or perpendicular to G.K. This results in the formation of two similar triangles G.B.K. and G.O.P., with their corresponding sides proportional, as G.B. to B.K. so is G.O. to O.P. However, of these four proportionals, three are known, as G.B. is six feet and a quarter, which is 100 fingers, B.K. is 12, and G.O. is two feet and a quarter, which is 36 fingers. Forming the rule of three, it is found that the fourth proportional O.P. is four fingers and a third. This is the amount of movement the Diestro must make from the primary vertical plane A.B. at this intersection, to both sides, with the defense pyramid H.P.Q. to place and contain his opponent’s sword outside the two vertical defense planes G.K. and G.L. tangent to his cylinder F.E. with the center of his guard, to remain defended.

Case Eight

Given the same conditions as in the previous case, except that it is assumed the opponent takes a step of two feet from point C to point G to reach the first Orb of thrusts, and in this position, the center of the guard and quillons of his sword reach point I to strike a thrust at the Diestro, whose point is four feet less a quarter away. The query is to examine how much movement the Diestro must perform with the center of his guard and quillons to place and contain his opponent’s sword outside the two vertical defense planes I.K.I.L. tangent to his cylinder F.E.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. and B.K. to the point of contact, and H.N. parallel to B.K. or perpendicular to I.K. This results in the formation of two similar triangles I.B.K. and I.H.N., and their corresponding sides are proportional, as I.B. to B.K. so is I.H. to H.N. Of these four proportionals, three are known, as I.B. is four feet and a quarter, which is 68 fingers, B.K. is 12, and I.H. is two feet, which is 32 fingers. Forming the rule of three, it is found that H.N. is five fingers and two-thirds. This is the amount of movement the Diestro must make from the primary vertical plane A.B. with the center of his guard and quillons to both sides to place and contain his opponent’s sword in the two vertical defense planes I.K. and I.L. tangent to his cylinder F.E. to remain defended, as shown in the figure.

Case Nine

Given the same conditions as in the two previous cases, except that it is assumed the opponent takes a step of three feet from point C to point O to step on the second Orb of proportionate means for circular and semicircular wounds; and in this position, the center of his guard reaches point I, which is three feet less a quarter away from the Diestro, to execute with one foot of his sword his tricks on the Diestro. The query is to examine how much movement the Diestro must make to his left and right sides, from the primary vertical plane A.B. to place and contain his opponent’s sword outside the two vertical defense planes.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. Draw B.K. to the point of contact, and H.N. parallel to it, or perpendicular to I.K. This results in the formation of two similar triangles I.B.K. and I.H.N., with their corresponding sides proportional, as I.B. to B.K. so is I.H. to H.N. However, of these four proportionals, three are known, as I.B. is three feet and a quarter, which is 52 fingers, B.K. is 12, and I.H. is 20 fingers. Forming the rule of three, it is found that the fourth proportional H.N. is four fingers and three-fifths. This is the amount of movement the Diestro must make from the primary vertical plane A.B. to both sides, with the center of the guard and quillons of his sword, to place and contain his opponent’s sword outside the two vertical defense planes I.K. and I.L. to remain defended from any circular and semicircular tricks and their species aimed at him in the jurisdiction, as verified by figure nine.

Para el plano diametral del pecho

 

For the diametral plane of the chest

 

CHAPTER TWENTY-SIX

Demonstration in which the method by which the Fencer will have the Angles of the bastions of the idea of our Fort is manifested, which consists of containing the sword of his opponent in two vertical planes, touching on both sides of the cylinder in which we imagine the Fencer, or others with a larger diameter than the base requires; and the intersection of these planes is considered along a perpendicular line that falls from the center of the quillons of the guard of the opponent’s sword to the lower plane, wherever it may be located; and this perpendicular line we imagine produced up to the horizontal plane, which passes through the verticals of the two combatants: and because this demonstration has some cases, they will be explained in their order with their figures.

First, in dealing with the demonstration of this proposition, it is necessary for the Fencer to understand that his opponent cannot attempt to offend him, except through one of the three Angles - straight, obtuse, and acute - and through the jurisdiction of each one of them, which we have defined; in whose jurisdictions are included all the postures and operations that a man can perform with the sword in hand.

Exposition of the first proposition

We suppose that the two combatants, the Fencer in A.T. and the opponent in B.Z., are standing on a right angle, and on a right angle in the medium of proportion (as we have explained) when there are eight Geometric feet of distance between the two centers of the arms and the right feet.

We also suppose that the opponent from his right-angle posture lowers his Sword to the acute angle, with the motion over the center D. of the hilt, describing with the tip of the Sword the arc of the circle C.F. of 45 degrees in the primary vertical plane.

Determination

It is necessary to ascertain what the Fencer must do to place his opponent’s Sword on the surface of his imaginary bastion, whose plan is represented by the Angle M.L.N., in such a way that it acts as a defense as if it were made of steel or other dense material.

The Fencer places his Sword with the motion of the center C. of his hilt in an acute angle, describing the arc D.E. with the tip of the Sword, causing a semirect angle with the line C.D. part of the common section of the primary vertical plane with the superior plane, cutting the line of the opponent’s Sword D.F. at point G. in equal degrees, resulting in having equal power; in this position, it is recognized that the tip of the opponent’s Sword does not have direction to the body of the Fencer.

I say that from this position the opponent will not be able to make an immediate movement to hurt, without the Fencer being able to make another, or others at the same time for his defense, even though he makes it with at least ten times the speed, as will be demonstrated; although there may be many, due to the possibility of the opponent directing his Sword in the jurisdiction of the acute angle to different points of contact on the Fencer’s body, for clarity, we will reduce them to three, because once these are understood, the others will be understood as well.

For this, we imagine the length from point G. to the hilt of the Fencer, divided into three equal parts 1.2.3., and through them, his Sword will have to pass to be reduced to the right angle, to have greater reach.

First Case

Given, then, that the opponent raises his Sword from point G. to point 1. to hurt, in which action it is necessary that he puts degrees of lesser force into others of greater force than those of the Fencer; it is necessary to ascertain, what amount of movement does the Fencer make to place his opponent’s Sword in either of the two vertical planes that constitute the imaginary bastion of his Fortress?

Construction

Draw from point D, the center of the hilt of the opponent’s sword, the perpendicular line D.L. to the lower plane, intersecting the common diameter Z.T. of the two combatants at point L. From this point L, draw lines L.M. and L.N., tangent to the base of the Fencer’s cylinder N.O.M.

From point 1, draw another perpendicular to the lower horizontal plane, intersecting the two tangents at points P.Q. and the common diameter at Y, bisecting angle L.

We say that the equal distances Y.P. and Y.Q. determine the movement that the Fencer, positioned at the first section point, must make with the opponent’s sword to move it from the primary vertical plane to his right or left side, so that his sword passes over the surface of the bastion M.L.N., ensuring his defense, as clearly seen in the figure, without further demonstration.

However, for clearer understanding, we will examine it in this way: Draw from point T, the center of the Fencer’s cylinder, the line T.M. to the point of contact, which will be perpendicular to it by proposition eighteen of book three of Euclid’s Elements, forming the triangle L.T.M., similar to the triangle L.Y.Q., as they are subcontrary sections and both equiangular, since angle T.M.L. (right) is equal to angle L.Y.Q., and angle L is common, and the remaining angle T is equal to angle Q. Thus, their corresponding sides are proportional, and as L.T. is to T.M., so is L.Y. to Y.Q. Given the negligible difference between L.Q. and L.Y., to avoid fractions, we take L.Y. instead of L.Q. Thus, of these four quantities or sides, being three known, the fourth Y.Q. will also be known, though it can be verified with a compass, which is the diameter line divided as said, for clarity we do it by numbers, using the rule of three, saying: If six feet and a quarter of another, which are 100 fingers, give us half a foot, T.M., which are eight fingers, what will L.Q. give us, two feet and a quarter, which make 36 fingers? It will be found that the line Y.Q. will be two fingers and 88 hundredths of another, which are about 3 fingers; and this is the amount of movement the Fencer must make with his sword to place the opponent’s sword tangent to his cylinder M.O.N.

Corollary

From this demonstration follows the understanding of the great advantage the Fencer has over his opponent by utilizing the principle of movement, since to initiate an attack from the medium of proportion, the opponent needs to make a movement with the whole body, at least two feet and a quarter, which are 36 fingers, whereas the Fencer, in the position shown in the figure, with just a three-finger movement of the center of his wrist, causes the opponent’s sword to be unable to offend, producing the same effect as if he were actually behind the bastion, in which we imagine him, represented in its base L.P.q. In this case, not only does the Fencer have an advantage of at least ten to one, but even twelve to one, in terms of swiftness.

We say that the two lines L.M. and L.N., initially imagined as tangents to the base of the Fencer’s cylinder N.O.M. in the lower plane, which are the two sides of the larger triangle M.L.N. with vertex L. also common to the smaller triangle, whose sides are L.P. and L.Q. and its base P.Q., determines the plan of the Fencer’s bastion in its exterior polygon; and the line P.Q. and F.Q. determine the distance the Fencer must move his sword away from the primary vertical plane, on either side, to keep it on the surface of his cylinder.

We imagine that all this moves from the lower plane, and that the two sides of the larger triangle L.M. and L.N., without departing from the surface of the Fencer’s cylinder, and the vertex of angle L., rise equally, creating two vertical planes from the top of the Fencer’s head, always parallel to the horizon.

From this construction and this imaginary bastion, follows a true consequence: if the Fencer’s body is encompassed by the two vertical planes forming the angle of this bastion, and the opponent’s sword is outside them, no one can doubt that the Fencer will be defended; and having demonstrated in this first case the ease with which the Fencer can place the opponent’s sword in either of these two vertical planes, with swiftness and advantage in the short movements he makes, the purpose and great utility that results from the imagination of our Fort’s idea are proven, which in effects serves the Fencer any bastion of it, as if it were of dense material, as each one can experience, making use of what has been demonstrated and will be demonstrated in other cases.

Notice

Although in this and other propositions and figures related to the formation of the angles of the bastions of our Fort’s idea, we suppose that from the posture of the right angle, the swords descend to the acute angle with the movement of the wrist, to the extent that it seems they fall from the hand, since they cause a semi-right angle with the line of the upper right angle; the Fencer is advised that this has been done to calculate more accurately and ascertain the amounts of movements; thus, understand that in the operations of the battle, it is not necessary for the swords to descend so much into the acute angle, but only as much as necessary, as will be demonstrated in the parries and tricks of the third book.

Lamina veinte y vna del Libro ſegundo

 

Plate twenty-one of the Second Book

 

Case Two

Given the same as in the previous case, it is assumed that the opponent raises his sword from the first point to offend the Fencer, in a right angle, and when reaching the second point, the Fencer, making use of the greater degrees of strength of his sword, in the weaker degrees of the opponent’s, moves it to his left side with the movement of his wrist, so that it does not have direction towards his body; and to know how much movement he will have to make from this position to achieve it, avoiding the Geometric demonstration that we made to demonstrate the previous case, to avoid prolixity, given that it turns out to be the same demonstration, due to the similarity of the triangles.

We say by the rule of three, if the line L.T. of six feet and a quarter, which are one hundred fingers, gives me T.M. which is half a foot, which are eight fingers, what will L.5. of forty-four fingers give me? And it is found that the movement that the Fencer will have to make to place his sword against the opponent’s on the surface of his cylinder, will be three fingers and fifty-two hundredths, which are just over three and a half fingers: and if at the same time the opponent gives his step of two feet and a quarter, which are thirty-six fingers, to offend him, still the Fencer will have an advantage in swiftness, as of ten and two-sevenths to one.

Lamina veinte y dos del Libro ſegundo.

 

Plate twenty-two of the Second Book.

 

Case Three

For this third case, it is assumed that the opponent, from the second point, raises his sword to the guard of the Fencer’s sword at the third point, while simultaneously taking a step of two feet and a quarter to reach a contact point on the Fencer. When the opponent’s sword reaches the third point, the Fencer attempts to defend and move it in such a way that he cannot be struck; it is necessary to examine the amount of movement he must make from this position to his left. As in the previous two cases, we rely solely on the rule of three.

We say, if L.T. are six feet and a quarter, or one hundred fingers, and it gives me T.M. of half a foot, which are eight fingers, what will L.8. give me, which are three feet and a quarter, or fifty-two fingers? Performing the operation, it indicates the amounts marked 8. and 9., and it will be found that the movement the Fencer must make with his sword to place the opponent’s from this position on the surface of his cylinder will be four fingers and 16 hundredths, which are just under four and an eighth, at the time when the opponent takes his step of two feet and a quarter, which are thirty-six fingers, giving the Fencer an advantage of eight and three-fifths of a finger to one; and this advantage that the Fencer has over his opponent is greater than what is usually given by the Military to any of those defending the Royal Fortresses against the besiegers, which is about six to one, although some authors give it as ten to one. This means that one of those in the Fortress is worth six of those outside attacking.

The same calculations made in the three cases mentioned also apply if the Fencer places his sword on the outside of the opponent’s, to carry it with his own to his right side, moving it away from the vertical plane. In this same order, all other positions can be calculated, whether on the inside or outside, in which it will always be verified that the Fencer has a significant advantage over his opponent, and that at least, as said, he will have an advantage of eight to one, enjoying only the beginnings of the movements, in the way that has been noted.

Lamina viente y tres del Libro ſegundo

 

Plate twenty-three of Book Two

 

Preamble to Demonstrate Greater Advantages that the Fencer Has in the Referred Cases

In the three preceding cases, it has been demonstrated that, when the opponent attacks the Fencer intending to strike with a thrust, and the swords are in the acute angle on the left side, and on the right, the amount of movement that the Fencer must make for his defense is established. This is done by placing his sword on the opponent’s, within the two vertical planes formed by his bulwark, thereby ensuring his defense.

To recognize the defense that the Fencer also has in any other situation, I assume the same three cases in the obtuse angle. Since the same rules apply to their examination as in the previous three cases, without any difference, and our intention is to avoid repeating what can be understood from what has already been said, we refer to them. However, to satisfy, we will explain them in the following manner.

Fourth Case, Including Others Pertaining to the Obtuse Angle

Given the same conditions as in the previous cases, except that in those, the swords are in an acute angle, and in these, it is assumed to be an obtuse angle, with the same divisions from point G. to 1.2.3. &c., as shown in the following plate. Thus, the demonstrations we made in the previous cases also apply without difference to the cases of the obtuse angle, because the Fencer will make the same amounts of movements on both sides, at the time the opponent moves his body or the cylinder we imagine it in, as demonstrated. Therefore, we avoid the demonstrations of the other cases to not repeat them, since drawing their perpendiculars from the points of the divisions on the lower plane will cut the plant of the bulwark, imagined for the Fencer’s defense, causing the same similar triangles, with their corresponding sides, in the same way they were caused, and the plant of this bulwark, from the divisions, in the types of figures passed, with both opponents affirmed with them in the jurisdiction of the acute angle. It concludes that there is no essential reason for difference from the cases of the acute angle to those of the obtuse angle, and that the defenses the Fencer has in the former are of the same quality in all respects as the defenses he has in the latter.

Lamia viente y quatro del Libro ſegundo.

 

Plate twenty-four of Book Two.

 

Warning

In what we have demonstrated about the concept of our Fort, it has been mentioned how with short amounts of movements the Fencer will defend himself with his sword at the time his opponent wishes to offend him with a thrust in any of the jurisdictions of the 3 angles, assuming a compass movement of two feet and a quarter, and the advantages he will gain, regulated by the amount of his opponent’s compass and by the movements of his sword, so that the opponent’s sword does not have a direction towards his body. Now, it is appropriate to demonstrate how the Fencer gains many greater advantages in any of these cases. For this purpose, we assume as a constant that at the time the opponent gives the referred compass movement to strike, the Fencer can simultaneously make a revolution or Pyramid with the center of the wrist; in such a way that the actions of both end at the same time, considering that it is even easier and quicker for a part to move than its whole, as anyone can experience, and we have asked this to be acknowledged by petition. Given the possibility of this equality between the two opponents, we will prove this greater advantage in the fifth case, whose understanding will serve for the others that remain explained.

Case Five

Given the same proposition as in the first case of the concept of our Fort and what we demonstrated in it, and the assumption of the aforementioned equality, we examine the greater advantage in this manner.

We imagine that having moved the opponent’s sword from point G to I, it has entered the jurisdiction of the Fencer’s defensive Pyramid, in which it has greater degrees of strength and power, to place the opponent’s sword in its vertical plane of defense (side of its bulwark) and the surface of its cylinder, by simply making point I of the intersection of the swords move to its left side by an amount of three fingers; and to know the proportion these three fingers have with the amount of movement that can be made in the entire revolution of this point I, or defensive Pyramid with the semidiameter I.K, we will describe the circle X.Q.I.P. and it will be the base of this Pyramid C.I.X., with I.X. as its diameter; take I.P.I.Q. on both sides of the diameter I.X. equal to I.P.I.Q. that are on the plan of the bulwark P.L.Q., each one of them, as we have said, is three fingers; and by the same figure mechanically, it can be found, more or less, how many times this smaller portion of I.P. enters the entire circumference of the circle, or base X.Q.I.P., which will be about 42 times, an advantage that the Fencer will have over its opponent; and the same is found by numbers, examining by the amount of the diameter I.X. which is two and a half feet, or 40 fingers, the circumference of the circle by Archimedes’ rule, saying: If seven give me 22, what will 40 give me? and the quotient will be 126 fingers, which will be the circumference of this circle: and dividing it by the three fingers, that the Fencer needs to make, so that the opponent’s sword does not have a direction to its body, and passes by the surface of its cylinder, it comes to 42, which proves that the advantage that the Fencer will have over its opponent, enjoying the beginning of the movement, when it gives its compass to strike it with a thrust of first intention, is like 42 to one.

But because it is in the opponent’s will to attack on one side, to strike on the other, assuming that it intends so, it is necessary to ascertain in the precise movements that must concur, what advantage the Fencer will still have over its opponent.

Given, then, that it attacks the Fencer, as in the previous case, from the inside, to strike from the outside, in two ways the Fencer can make its defense; one will be, at the time it is attacked from the inside, to make from the primary vertical plane, where its sword has the amount of the three fingers of movement to its left side, as has been demonstrated, to remain defended; and attacking immediately to strike it from the outside, it will have to make from the same position an amount of six fingers of movement to its right side, to also remain defended: so that the Fencer will have made in these two actions an amount of nine fingers of movement, and having made the account in the referred order, it will be found that in the circumference of the circle, or base of the said Pyramid of 126 fingers, the advantage will be like 14 to 1.

Because the opponent can carry the intention of making three attacks, the first two being to dispose, and the third to return to execute from the inside: in this case, the Fencer to remain defended will have to make another amount of six fingers of movement to its left side, with which there will be fifteen fingers that the Fencer will have made in the three actions; and having made the account in the same order, it will still be found that it enters the circumference of the circle, or base of 126 fingers, eight times.

Since these calculations are adjusted strictly to the precise movements of the defense, and it is so that the acceleration of the attacks will often oblige the opponent many times to make the Fencer do more movement, on one side and the other, we advise the Fencer, for greater security, not to allow its opponent to attack it by the primary vertical plane of first intention, but when it lowers its sword to the acute angle, to gain the advantage of the first three fingers, immediately impeding the plane, on any side in which the opponent’s sword has direction to its body, to remain, without further diligence, defended, trying to have contact with the sword, to have knowledge of its movements; with which, not only will it have the aforementioned advantages, but also in these three actions of attack more advantage of three fingers, which it will not have to make of movement, from which the Fencer will follow another advantage, because by impeding its opponent’s planes immediately, it will oblige it to make a greater portion of Pyramid to offend, and the one it makes will be much smaller, and with more composure, because as these actions are repeated to the attacks, it causes some kind of more alteration, and in the greater portion of Pyramid that the opponent will make, the Fencer will have a supplement, when it makes by mistake, or by another accident, more than the six fingers of movement, on one side and the other, respecting what has been said: and they will always be, however this is examined, its greater advantages; and the Fencer immediately impeding the planes to its opponent, will be by means of our four universal modes, which are reduced to real or virtual blockages, as explained in their place.

The second mode with which the Fencer can make the same defenses, which we have explained, will be to immediately impede the planes of its opponent, also giving compass for defense, or offense, or both things together, as will be specified in the Treatise of the Tricks, and this way of working will be safer, and more immediate to offend.

With which we have explained the defenses that the Fencer has in the three angles, right, obtuse, and acute, when its opponent wants to offend it with a thrust; but as our intention is that the Fencer can perform its defenses and offenses universally, not only against thrusts, but also against vertical, diagonal cuts, and reverses of both species, and against cuts, and horizontal reverses, and half cuts, and half reverses of the species that can be formed, which are all the tricks of the possibility of man; and the one and the other necessarily have to be executed with natural, accidental, and reduction movements, and their mixtures.

Because in what has been demonstrated in the previous figures, only the accidental and natural movement has been dealt with, it is necessary, for this to have generality, that the Fencer is also given defense for the offensive movement. We say that the opponent, according to its possibility, can assert itself in one of two ways, and that each one of them is capable of different postures.

The first, can be asserted in different ways, so that its sword has direction to the body of the Fencer, both in the primary vertical plane and in other planes, and postures; and in all of them, keeping the Fencer to the precepts that have been demonstrated in said figures, it will be able to place the opponent’s sword in any of the two vertical planes of its defense, by means of its imaginary bulwark.

To ensure adherence to the aforementioned principles in fencing, a general rule is provided: whenever the opponent’s sword is directed towards one’s body, a vertical plane should be considered as the primary reference. This plane should pass through the opponent’s sword and the center of its cross-guard, as well as along the fencer’s directional line. Whether this plane passes through the fencer’s right side, aligns with the diametral line of the chest, or is positioned in any other affirmed manner, the fencer should always occupy this plane with their own sword and guard. This occupation should be similar to when both fencers are positioned at a right angle on the primary vertical plane, which is assumed to be a shared point of reference for both combatants. Just as the opponent places their sword on one of the vertical planes of defense, the fencer should do the same in any other plane where the opponent’s sword is directed towards their body. Even when the fencer’s sword positions the opponent’s within the vertical planes of defense, this specific plane should remain occupied by their guard, passing through the center of their cross-guard and that of the opponent’s, or by employing other precepts in all instances, as when they are positioned on the primary vertical plane.

Warning

 

Thus, the fencer will have two forms of defense: one by positioning the opponent’s sword within one of their vertical planes of defense, and another by occupying the aforementioned plane with their guard, preventing the opponent from attacking without passing through the jurisdiction of one of the pyramids demonstrated in previous cases. This approach requires the opponent to make significantly more movements than the fencer does to remain defended, often positioning them to attack the opponent.

The second method involves the opponent assuming any posture they wish, without their sword being directed at the fencer’s body. Whenever this happens, the fencer creates the necessary bulwark for their defense. By positioning their sword and body, the fencer can immediately block entry into their imaginary bulwark, striving to block other indirect and distant approaches the opponent might use to attack. This is achieved by positioning the fencer’s arm, guard, sword, and body in accordance with the principles of this science, which will be further clarified when discussing how the fencer can break down this Fort using various strategies: sometimes by making contact with the opponent’s sword, and other times without, depending on the posture and plane in which the opponent’s sword and arm are positioned.

For added security, the fencer can, through either contact or without, ensure that the opponent’s sword is kept further away from their own cylindrical space. Although the figures given have a diameter of one foot, which is necessary for defense, the fencer can choose to have the opponent’s sword further away to attack them in a different cylinder, possibly two feet in diameter or more, as best suits the situation. This can be easily achieved by considering, in any of the aforementioned postures, that the vertex of their outer bulwark corresponds to the center of the opponent’s cross-guard, and ensuring that the angle of the bulwark is greater than necessary, since the vertical planes of defense will be on either side of this angle, regardless of its formation.

Since this universality will be specified when discussing the formation of strategies, allowing the fencer to perfectly use this doctrine to form them, it is unnecessary to elaborate further here. With the information provided, the ease with which the fencer can form their defensive Fort and combine it with offense should be clear, as well as how they should conduct themselves in any situation, whether moving around the center or taking steps. In any case, they will always carry the concept of their Fort, considering the positions and postures of their body, arm, and sword in relation to the opponent’s, whether they are both in a proportionate middle ground, or if the opponent attempts to break the distance to attack. In this case, it is advised that if the fencer wishes to maintain a proportionate middle ground to use the bulwark of their external polygon, they can achieve this only by moving through the pyramid we consider in the strongest degrees of the sword, and the pyramid of the arm and guard. These two are especially useful when the opponent breaks the distance to attack; the two main ones are the arm and guard, and the entire sword, which includes the imagined pyramid in the strongest degrees. With these three pyramids, using them as required according to the precepts of this science, the fencer will find themselves in continuous defense during combat, ready to exploit immediate opportunities provided by the opponent, and those acquired for attacking.

However, it seems appropriate here to also discuss the advantages the fencer has with their sword for defending against their opponent when they attempt to strike, as demonstrated in previous cases and figures. We will also mention the advantages of moving the body around the center of the right foot within their particular circle, in opposition to the steps the opponent may take around the circumference of the circle of proportionate means, and also when the opponent attempts to enter.

Lamina veinte y cinco del Libro ſegundo.

 

Plate twenty-five of Book Two.

 

Proposition Theorem

Every time the opponent, being affirmed with the Fencer in the middle of proportion, wants to give compass through the circumference of the Fencer’s maximum orb, he can oppose him with the motion on the center of his particular circle, and will always have an advantage, at least as 8 to 1.

Exposition

It is assumed that the line of circumvallation A.E.B.D. is the plan of a Castle, Fortress, or jurisdiction of the means of proportion, whose center is C, and the small circle is the plan of the Fencer’s body, where he is affirmed on right angle, and in right angle with his Sword, and the center of his right foot at point C. It is also assumed that his opponent is also affirmed on right angle, and in right angle at point A, at a distance of eight feet from center to center of the right feet, and that being impeded the passage by the line A.C, he wants to attempt his assault through any of the sides A.F.A.H. Assuming that he gives a compass through the circumference of the means of proportion from point A to point F, draw the line F.C. to the center of the Fencer’s particular circle.

Determination

I say that moving the Fencer on his center C, from point O to point P, in opposition to the compass of his opponent at point F, will have an advantage, at least as 8 to 1.

Demonstration

Because according to what was demonstrated by Archimedes, proposition three, all circumferences of circles have the same proportion as their Diameters; and so in this figure, the proportion that the semidiameter C.O. has to the circumference A.F.B. and permuting, will be like the semidiameter C.O. to the semidiameter C.A. the same has O.P.S. to A.F.B. and the part O.P. included in Angle A.C.F. to the part A.F. But by the same assumption, the semidiameter C.O. is one-eighth of the semidiameter C.A. then also the O.P. is one-eighth of the A.F. with which it is proven, that the advantage that the Fencer makes to his opponent, is as eight to one; this is understood by giving the semidiameter of the Fencer’s particular circle a Geometric foot.

But if it is given what Alberto says in his Symmetry, which is one-tenth of the height of the man, supposed to be six feet long, the advantage will be as nine and a half to one; and the same reason in proportion follows in everything if the opponent wants to give compass to hurt the Fencer from point A to point L, stepping on the orb of his Sword, if he gives compass to the middle of proportion at point H, or to the proportionate at point M, orb of the Fencer’s Sword.

From this, it results that if the opponent continues to give his compasses through the circle of the means of proportion, or wants to enter to hurt, giving compass from the distance of point A to point L, by moving the Fencer on the center of his particular circle, through the entire circumference of it, he will oblige his opponent with his compasses, in whatever part he will make the same advantage, opposing his bulwark; and according to these considerations, the Fencer will be found within his Fort, guarded by the bulwarks of his defense, as he will be in his possibility to place them in all the parts that are necessary in opposition to his opponent.

All the aforementioned includes the larger or smaller compasses that the opponent gives, provided that the Fencer will move on the center of his particular circle in the same proportion, and the advantages will always be the same.

Lamina veinte y ſeis del Libro ſegundo.

 

Plate twenty-six of Book Two.

 

CHAPTER TWENTY-SEVEN

The universal advantages that the Fencer will have, both for defense and offense, if they scientifically use the concept of our Fortress.

Although with the universality with which we have exemplified the idea of our Fortress, it seems we could avoid discussing it further, referring, as we have said, to the individual tactics; but as our aim is to facilitate the understanding and use of this science, and that of our Fortress, and to provide knowledge of all the advantages that the Fencer can have in its use, we have not wanted to avoid explaining what we have outlined, that the Fencer will not only be able to form their cylinder with a geometric foot in diameter, which is necessary for their defense; but it can be given two feet more or less, as best suited, a common possibility to both combatants, and to be able to affirm themselves in profile, and half profile, and squarely, and that from the obtuse angle plane, from the primary vertical plane, and from other planes and angles, the opponent, on one side or the other, can not only form their thrusting tactics, which is what has been exemplified in the previous cases; but also all the other circular and semicircular tactics of their possibility, and it is convenient for the Fencer to know in generality how to defend against them with safety; and so we suppose for a more extensive exposition of this doctrine that the Fencer be affirmed squarely, in which posture they will give the greatest disposition to be offended by their opponent, now that they are affirmed in profile, or in any other manner.

In this supposition, we give that the Fencer be affirmed squarely, and the opponent in profile, which is a posture chosen against the square to form tactics.

For the Fencer to have a defense in any event, and in the greatest disposition possible to be attacked, we give that their cylinder be two feet in diameter, so that with their Sword they can place their opponent’s in the vertical planes of their defense, tangent to their cylinder of two feet in diameter, which is double the diameter we have given in the preceding cases. This way, with their Sword, they can place their opponent’s in the vertical planes of their defense, tangent to their cylinder, on both the right and left sides, and to avoid multiplying calculations by the rules we have used.

We say, assuming that the diameter of the cylinder is double what we said in the cases that have been demonstrated; it follows that the amounts of movements that the Fencer will have to make with their Sword to put the opponent’s on one side and the other in the two vertical planes of their defense, will be double; and so in the first case, three divisions were considered in the Fencer’s Sword at point 1. 2. and 3. and it was supposed that the opponent wanted to give their compass of two feet and a quarter, to offend the Fencer with a thrust through each of these three divisions, the amount of movement that in each of them the Fencer had to make with their Sword in the opponent’s, to put it on one side and the other in the surface of their cylinder, and in the two vertical planes of their defense; and it was calculated that at point 1, a movement of about three fingers was to be made; and at number 2, three fingers and a half; and at number 3, four fingers and an eighth: and so if found squarely, the movements that are made at point 1 will be about six fingers less, and at number 2, seven fingers, and at number 3, eight and a third.

With this light, and that which has already been given in the other cases, it will be possible, in whichever one is wanted to be supposed, to examine the advantages that the Fencer will have, because it would be very cumbersome if we stopped to do it in each proposition; assuming that to offend can only be done by a straight or curved line, as will be seen in the course of this work.

Because our intention is for the Fencer to act with as much perfection as possible, and it is not doubtful that the smaller the dispositions given with their movements, and the smaller the amount they make, the more perfectly they will act, and that being affirmed in an obtuse angle with the common section of their Swords at point G, as was supposed in the aforementioned, not only can they try to hit the Fencer with a thrust; but they can form a vertical or diagonal cut, and reverse of both species.

We say that they can defend themselves from all these species of wounds, by putting the center of the guard of their Sword four fingers and a third away from the primary vertical plane to their left side, which with another four that has the semidiameter of the guard on the same side, will be eight fingers and a third, which is the necessary amount to be defended by that side, and for the opponent’s Sword to be placed in the vertical plane of their defense on the same side.

At the same time that this movement is made with the guard, they will necessarily make another with their Sword on their right side, with the attention that the Fencer must have, that the quillons of their guard are in an oblique plane, and that they virtually occupy the diagonal line of the square, which is considered in the opponent’s face from the extremity of the left eye’s eyebrow to their right side of the beard, and being in this position their guard, and Sword, they will be defended from all species of wounds that the opponent wants to execute on the face, and head of vertical, and diagonal cut.

To defend themselves from the same species of wounds, the Fencer can put their Sword in such a way, that it corresponds to the other diagonal line of the said square from the extremity of the right eyebrow of the opponent to their left side of the beard, moving to their right side four fingers and a third the center of the quillons of their guard, in the way that has been advised for the cuts because with both positions they will cut the planes that their opponent will have to occupy, to enter their fortress, and offend them.

It is given as a general rule, that from whichever plane, and Angle, that wants to form these species of circular wounds to execute them on the face, and head, the Fencer will be defended in the same way by making the same defenses.

The advantages that the Fencer will have over their opponent are so evident and considerable, that they excuse us from the embarrassment of calculating them, assuming that with four fingers and a third of another, that they make a movement, from the primary vertical plane to their right or left side, they will defend themselves from the circles that their opponent forms to execute their cuts, and reverses vertical, and diagonal of free or subject cause, sometimes with the whole arm, and Sword, and others with the center of the elbow, or wrist; and as the movements of these circles are irregular, because it is in the will of the opponent to make them larger or smaller, it cannot be adjusted, the Fencer will always have very known advantages, considering that the opponent, for their formation, will have to make the entire Pyramids, or most of them, and the Fencer by making a small portion of theirs of four fingers and a third, will be defended.

Objection

It might be said that while the Fencer is defending against vertical and diagonal cuts and reverses in the manner described, the opponent could abandon executing these on the head and face, due to a lack of opportunity, and instead lower their sword to thrust. In this case, the guidelines we have provided may not be beneficial.

Response

In presenting a science, it is appropriate to discuss its possibilities and extent, ensuring that the principles are validated in the propositions, as seen in the preceding examples. This approach better informs the understanding of its universality.

Even in the aforementioned cases, the Fencer would have the possibility to prevent what the objection covers by swiftly lowering their Sword to an acute angle and moving it from one side to the other, thus blocking the planes that the opponent intends to occupy with their sword to attack.

However, to ensure that our Fencer does not act hastily or create an opportunity for the opponent to believe they can successfully attack, we want to provide a universal method for the Fencer to defend against vertical and diagonal cuts and reverses, as well as half-cuts and half-reverses that the opponent may attempt to execute on their head and face, both from the right and left sides. This method also applies to defending against cuts and reverses, half-cuts and half-reverses typically aimed at the arm; and against horizontal cuts and reverses, and half-cuts and half-reverses of the same types, which encompass all the wounds that can possibly be inflicted by a person.

The Fencer will achieve this universal defense even if they are in a squared stance, as mentioned in the previous proposition, which offers the greatest opportunity for the opponent to attack. They should position their arm so that the guard of their sword at the top corresponds to the base of the nose, which is where the vertical plane intersects, creating a diametrical line passing through the forehead, nose, and chest. The tip of the upper quillon should vertically align with the start of the hairline, and the sword, without changing this arm and guard position, should be lowered to an acute angle, creating a semi-right angle with the upper horizontal plane, which we imagine when the Fencer is in a right angle stance, both vertically and horizontally. Even in this square stance, the arm and sword of the Fencer will create the same semi-right angle with their sword, because in all upper and lower planes, which are parallel to it, they will invariably be in a semi-right angle position.

With the Fencer thus affirmed with their arm and guard, which constitutes the principal Pyramid they can form for their defense, they will defend themselves against all vertical and diagonal cuts, reverses, half-cuts, and half-reverses that the opponent might execute on the face and head from both the right and left sides.

The Pyramid formed by their Sword, centered at their wrist, and particularly the Pyramid imagined within it at its greatest degrees of force, will defend them from the cuts, reverses, half-cuts, and half-reverses aimed at the arm.

They will also be defended from horizontal cuts and reverses, as well as thrusts aimed at them from any of the three Angles: with the Pyramids of the Sword, those thrown from the right angle downwards; and with the guard, those directed from the right angle upwards.

When the opponent attempts to lower their sword to strike with circular or semicircular wounds, or thrusts at the legs or feet, from either side, the Fencer can, for greater safety, lower their arm and guard as necessary. This will also lower the sword more towards the acute angle, enabling it with greater degrees of force to position the opponent’s sword within any of the two vertical planes of their defense, tangential on either side to their cylinder. In this figure, we give the cylinder a diameter of two feet, although one foot is sufficient for defense, as has been demonstrated.

The method the Fencer should use to avoid all these straight, circular, and semicircular wounds will be without disrupting the posture of the Pyramid of their defense formed by the arm and guard. With this Pyramid, they will impede the execution of vertical and diagonal cuts, half-cuts, and half-reverses directed at the face and head.

With their sword in the same position at the acute angle, if these types of wounds are aimed at the Pyramid, which we imagine at the highest degrees of the sword’s strength, the Fencer can position their opponent’s sword within either of the two defense planes with this Pyramid. And if the strikes are aimed, as mentioned, at the guard, the Fencer can, for greater defense, make a small movement, to either side, of a finger and a half or two, to achieve greater defense.

To further detail this understanding, the Fencer can make this small movement on their right side to defend against vertical and diagonal reverses and half-reverses, maintaining on this side the same precepts that have been given for the left side against vertical and diagonal cuts, half-cuts, and half-reverses.

They will also remain defended, exercising the same diligence, on both sides, in the Pyramid at the highest degrees of their strength, from cuts, reverses, half-cuts, and half-reverses that are typically aimed at the arm, without altering their Pyramid or guard.

The Fencer will also defend against thrusts from both sides, those coming from below the right angle, because if they end up above the guard or its sides, it will be sufficient to defend against them.

Moreover, as previously noted, if the opponent lowers their sword significantly, intending to strike with a thrust or circular or semicircular wounds on the legs or feet, the Fencer should lower their arm and guard towards the acute angle, to more closely align with the posture of their sword, enabling them to more forcefully position the opponent’s sword on both sides within the vertical planes of their defense.

Since the opponent can lower their sword to a greater or lesser extent towards the acute angle, and this cannot be precisely regulated, it is up to the Fencer to lower their arm and sword only as much as necessary, as required by the positions chosen by their opponent.

Because all this doctrine boils down to the demonstrations we have made in the previous cases and figures, simply with regard to positioning the opponent’s sword on the sides of the Fencer’s defense bastion, both in the external polygon and the internal one, where the vertical planes of the Fencer’s defense will always be. By following the same principles, the Fencer will be defended as if the sides of the bastion and the vertical planes they create were made of steel or some other dense material. This is because the Fencer, through the use of their arm, guard, and sword (which are dense materials), can achieve this easily and with minimal movement, as has been demonstrated. Since this has been done, it is not necessary to repeat it, nor to examine again the advantages the Fencer has over their opponent, as they remain the same in these cases as in the previous ones, without any difference. For greater clarity, we have chosen to exemplify this universality across all types of wounds, to fully illustrate the concept of our Fortress.

Thus, we have shown how universal this Fortress is, assuming that the Fencer waits for their opponent, ready to counter any and all possible attacks, and the great advantages this provides. However, these and even greater advantages will be more individually and clearly recognized in the tactics through the use of their compasses, maintaining the four universal principles in the formation and execution of these tactics, principles that underlie all operations of this science.

In these operations, it will be recognized that in the same ways we have mentioned that the Fencer will have for defending themselves in their Fortress, most often they will be in a position to immediately offend their opponent, if they attempt to strike without recognizing the Fencer’s defense. Indeed, some attacks will necessarily encounter the guard of their Sword, and others will meet the Pyramid we have imagined in its strongest degrees of force. In this case, the Fencer will not only be positioned to offend their opponent after having placed the opponent’s sword in one of the two vertical planes of their defense, but will also have control over it to include it within their Pyramid, to strike the opponent in the nearest part, according to the disposition given to them.

If the opponent lowers their Sword to an acute angle to attack the Fencer’s legs or feet, the Fencer, for greater security, after having followed the principle of placing it along with their own in one of the two vertical planes of their defense, can return to the right angle, either by giving a compass or without it. This will force the opponent to raise their Sword to the same plane, and then the Fencer can form the tactics that are most immediate.

To demonstrate that the concept of our Fortress, however it is considered, has solid foundations that support its reality in its effects, although in what we have demonstrated, and particularly in the chapter that deals with the force distribution, which we used to examine the strong and weak points of the Sword, in order to provide knowledge of the advantages and disadvantages in its degrees of lesser and greater force; it is verified that the Fencer has advantages in the brevity of their actions, arising from the perfection of their body postures, arm, guard, and Sword. This necessarily requires the opponent, if they wish to attack, to make longer movements than what the Fencer needs to do for their defense.

We say, for the greater satisfaction of the Fencer, and the credibility of the idea of our Fortress, that when we assume that the Fencer moves in their actions at the same times as their opponent does, and that the movements in terms of amounts are equal; still, the Fencer, due to the perfection of their postures, will always compel their opponent, if they wish to attack with circular and semicircular tactics, or with thrusts, to always pass the weaker part of their Sword through the stronger degrees of force of the Fencer’s, or over the guard, or its sides, as has been demonstrated. This means that not only will the Fencer have the advantage of placing their Sword in one of the vertical planes of their defense, but also to immediately attack, making use of the greater degrees of their force, occupying the plane that corresponds to their posture, excluding the opponent’s Sword from being able to attack; and if appropriate, they can include it in one of their Pyramids, or a portion of them, by virtue of their greater power, as the occasions demand, to attack and remain defended.

These advantages of such consideration, as is the ability of the Fencer to scientifically position themselves, becoming master of their opponent’s sword every time the opponent attempts to attack, either by excluding or including it according to their goals, due to their greater power, are among the greatest excellences and advantages that this science can produce, being little or not at all subject to chance, due to the very brief movements with which the Fencer can achieve their defense and offense against their opponent.

These warnings are understood if the opponent forms their tactics without paying attention to the perfection of the Fencer’s positions and their defense; but if the opponent is also knowledgeable and uses the idea of our Fortress with the requirements that are needed at the time of forming them, then it will come down to a contest between the two combatants, and only the one who becomes careless among the two will be defeated, because this science is common to all, and its effects, when following its rules and precepts, are universal.

CHAPTER TWENTY-EIGHT

On the Different Ways Commonly Used by Men to Place Their Feet When Standing and Walking: An Examination of the Most Perfect and Secure Method for the Use of Skill.

Many things are done by people without giving them much thought, as they are seen as natural dispositions inherent in their organization. For example: Although people have the use of their senses, most do not speculate on the causes of their operations, leaving them as matters that belong to philosophers.

It is also very natural for humans to place their feet firmly on the ground and to walk, moving the body from place to place through steps. There will be few who ponder the reason for this, nor the differences observed in walking, as each person walks according to their organization, or by habit usually acquired in childhood. Some walk with their feet in parallel lines, others form an acute angle with the convergence of lines imagined passing through the tips and extended lengths of the feet; others form with these same lines a right angle, and others an obtuse angle. Undoubtedly, the most natural and refined way of walking is when these lines form a right angle between each other, as will be explained later.

Although some authors have said that walking consists of rest and effort, they do not explain the basis of this natural operation, nor anything related to it. Therefore, it is necessary to do so to better understand the positions of the body with the feet in terms of the use of Skill, and its artificial movements from place to place through compass steps. Although I have seen most of what has been written on this subject in Spain, and other parts of Europe and America, I have not found anyone who explains these compass steps, other than that they are accepted as precepts that deviate from natural walking. Considering that the closer they are to being natural, the easier they will be, and the less force will be needed, I have been compelled to this speculation, and others, which are explained later in this book. This is because it is one of the two universal foundations to which the practical part of skill is reduced, as it involves nothing more than movements of the body on the ground and the lower horizontal plane, and of the arm and sword in the air.

Since philosophers and mathematicians have not taken it upon themselves to write expressly on this subject to provide the necessary insights, I have deemed it appropriate, for the common benefit, to try to explain it through simple means that anyone can experience for themselves if they wish. For greater clarity, this will be done using figures.

Let the first figure, A.B., represent the base of one foot. The question is asked: Why can’t the human body be as stable standing on it, as when it is firmly planted on both feet together in parallel lines, C.D. and E.F., as seen in the second figure?

To answer this question, it is necessary to recall what we have said about the nature of the center of gravity and the line of direction, which is imagined in every heavy body. For the human body to be supported, it must not extend beyond the base formed by its feet. The larger this base, according to our definition, the better the human body, which is similar to a column, will be supported. The wider the base, the stronger it will be; and if narrower, weaker. As the width of one foot is not a sufficient base for the body to remain stable on it, due to its limited size relative to the body’s weight, it will be very close to moving outside of the line of direction and falling. From this, it follows that the body will be more firmly supported on two feet, as in the second figure, because its width and base will be greater than when supported on just one foot, as in the first.

From this conclusion, it also follows that the body will be more firmly supported as in the third figure G.H.L.I than in the second C.D.E.F., where the feet are together.

In the third figure, the left foot is placed near the vertical plane of the chest T.V. at G.H., and the right foot is on the other side of this plane, occupying L.I., which forms an angle with the same plane. Thus, the line of direction extends across the entire area of the triangle G.H.I, the base of the body, which is larger than the area in the second figure.

It also follows from the explanation that the body will be in the third position, or any other, with the right foot at P.O. and the left foot at N.M., with the tips of both equally distanced from the vertical plane of the chest T.V., such that with it, each foot forms a right angle, and together, they form a right angle. In this position, the line of direction will extend over the entire area of the right-angled triangle M.N.O., the base of the body. And because this seems to require evidence to make it clear, I will demonstrate it.

Of the triangles that have the diameter of the circle as their base and their vertex on the circumference, the largest of all is the Isosceles triangle.

Let any semicircle be given, and let’s consider the one in the fifth figure A.B.C., with its diameter A.C. On this diameter, construct the isosceles triangle A.B.C.

I claim that any other right-angled triangle A.E.C. inscribed in this semicircle will be smaller.

Draw the line B.F. parallel to the base A.C. Extend A.E. until it intersects with B.F. at point F. Because the triangles A.B.C. and A.F.C. have the same base A.C. and are between the same parallels A.C. and B.F., they will be equal to each other according to Proposition 37 of Book One of Euclid’s Elements. However, the triangle A.F.C. is larger than the triangle A.E.C. Therefore, the triangle A.B.C. will also be larger than the same triangle A.E.C.

The same can be demonstrated for any other scalene right-angled triangle in the semicircle.

First Corollary

From this demonstration, it follows that by drawing the lines D.B. and D.E., the isosceles triangle A.B.C. will be divided into two equal right-angled triangles, A.B.D. and D.B.C.

The scalene triangle A.E.C. will be divided into two other isosceles triangles, one obtuse-angled A.D.E. and the other acute-angled D.E.C. And given that the entire isosceles triangle A.B.C. was larger than the other scalene triangle A.E.C., their halves will also be larger than their respective halves.

Second Corollary

From this, it follows that of the two triangles having their base on the circumference of the circle and the vertex at the center, as in the triangle A.D.B. with the base A.B., in the triangle A.D.E. with the base A.E., and in the triangle E.D.C. with the base E.C., the largest and most capacious is the right-angled triangle A.D.B. Therefore, the right-angled triangle M.N.O. in our fourth figure will be more capacious than any other acute-angled or obtuse-angled triangle; consequently, the body will be stronger when affirmed in this position with the feet on this right angle, as it has a greater extension of the line of direction in it than in the other two.

The explanation of the four preceding figures aims at the purposes referred to in each of them; and since the positioning of the feet is so important for the use of Skill, and the movements of the body are one of its principal foundations; it is necessary to investigate the differences that can exist in the positioning of the feet, their conveniences or inconveniences, what is not possible in the organization of the human body, and which of all the positions is the most perfect: for better and clearer understanding, we will be explaining them through figures, first describing two quadrants, where the various modes of affirming the body will be placed, to more easily examine their positions.

Describe two quadrants of a circle E.G.D.F. on each side of the line S.R. which we imagine to be the common section of the vertical plane of the chest with the lower horizontal plane, and in both quadrants draw the lines E.G., E.D. and E.F. in such a way that the line E.D. divides the two quadrants into two equal parts, and in them form the squares E.I.D.H. In each of these quadrants, let the right foot occupy the E.F, E.D. and E.G. on the right side of the line S.R., and let the left foot occupy the E.F. and E.D. and E.G. on the left side of the same line S.R., as seen in each of these quadrants.

First Quadrants, First Position

With the left foot occupying the E.F. in its quadrant, and the right foot the E.F. in its quadrant, the body will be affirmed with the feet in parallel lines, relative to itself, and to the vertical plane of the chest S.R., separated by one foot from center to center of the heels.

This position is flawed and unnatural because the line of direction needs to resist the two impulses of the body forward, and the two, to have at the same time extension on both sides in a way that can comfortably stand; and in this case, although the line of direction has the space between the two feet and their widths, it does not have it for the sides more than in the width of each foot, and it is not a sufficient amount for the body to subsist much, and to walk in this position with the necessary security to not fall, as explained in the first and second figures of the first four: moreover, this way of walking is not very natural, nor of good air, and for Fencing it only serves to dispose in this position in such a way that the points of contact are removed from the opponent, and to have more reach on him.

Second Position

If the left foot remains affirmed in the same line E.F. in its quadrant parallel to the vertical plane of the chest S.R., and moves over the center of the right heel, passing it to occupy the E.D., the body will be affirmed at a right angle, which is formed by the line imagined to pass through the tip and length of the right foot, produced with the line imagined to pass through the tip and length of the left foot, also produced at point Q, parallel to S.R. This increases the base and the extension of the line of direction more than what was in the preceding position by the space of the triangle D.E.K. in the quadrant on its right side.

Nevertheless, this position lacks perfection, because in it the body will not have the integrity that is required; and consequently, it is not very natural and graceful for moving forward, and inappropriate for Fencing.

Third Position

If the left foot is in its quadrant, occupying the same line E.F., and moves over the center of the right heel from the line E.D. to occupy E.G., the body will be affirmed at a right angle. This is formed by the line imagined to pass through the tip G. of the right foot, and its length, produced in the line imagined to pass through the tip F. of the left foot, and its length parallel to the vertical plane of the chest S.R. at point E. This increases the base of the body more than what it had in the position before this, and the extension of the line of direction by the quantity I.G. in its right collateral plane; in such a way that the line of direction, in this position, extends in the length and width of the entire left foot E.F. and the distance from the center of this foot E. to point G., where the tip of the right foot ends.

Fourth Position

If the left foot occupies the line E.D. in its quadrant and the right foot the line E.F. in its own, the body will be affirmed only at a semirect angle. This angle is formed by the line imagined to pass through the tip D. of the left foot, and its length, produced in conjunction with the line imagined to pass through the tip F. of the right foot, and its length, also produced parallel to the vertical plane of the chest S.R.

This position is similar to the second one, with the only difference being that in this one, the semirect angle is caused on the left side of the same vertical plane, while in the second position, it is on the right side; therefore, what was explained about the second position should also be understood for this fourth position.

Fifth Position

If the right foot remains in its quadrant occupying E.F. as in the previous position, and if the left foot moves over its heel in its quadrant to occupy E.G., the body will be affirmed at a right angle with the left foot forward. This is caused by the line imagined to pass through the tip F. of the right foot, and its length parallel to the vertical plane of the chest S.R., and the line imagined to pass through the tip G. of the left foot, and its length, converging at point E. on the right side.

In this position, the body will be affirmed at a right angle with the left foot forward, and it can serve for a left-handed person to affirm themselves against their opponent, and for a right-handed person when making a concluding movement with the perfection taught by the Art.

Sixth Position

If the body is affirmed with the feet in parallel lines in each of its quadrants, occupying E.F. and E.F., and then moves over the center of the heel of each one to occupy E.D. and E.D., it will be affirmed at a right angle. This is caused by the line imagined to pass through the tip D. of the left foot, and its length, converging with the line imagined to pass through the tip D. of the right foot, and its length, with both converging at line S.R., the common section of the vertical plane of the chest with the horizontal plane below, at point P. This results in the centers and tips of the feet being equally distanced from this line S.R.

This posture and right angle is the most spacious of all other angles, as has been demonstrated in the fourth position of the first four positions explained before these, and it is the most perfect and natural, where the body is most robust, graceful, and strong, both when affirmed in it and when walking forward, if this right angle is maintained in its steps. It is the most appropriate for the use of Fencing, as explained in the first figure of the last three that follow these positions being explained.

Seventh Position

If the body is affirmed at a right angle, as assumed in the position before this, and one wishes, while keeping one foot firm, to move over the center of the heel of the other foot to occupy E.G., although this action is possible, the body will be strained, and the line of direction will have little space for the front part. The feet will form an obtuse angle of 135 degrees between them, a flawed posture, and little or not at all suitable for Fencing.

Eighth Position

If the body is affirmed at a right angle, as in the sixth position, and wishes to move over the center of its heels to its right and left sides, to occupy with each foot in its quadrants the line E.G., it will find no possibility in its organization to be able to do so.

Second Quadrants, Ninth Position

If each foot occupies in its right and left quadrant the line E.K., they will form with the lines that are imagined to pass through the points KK. and their lengths, produced by EE. in the line S.R. at point Q., an acute angle of 22.5 degrees on each side, and the body will be affirmed on the semirect angle of 45 degrees caused in it.

This position is suitable for walking forward, especially when going quickly, but not very appropriate for Fencing, because the body is not in it with the firmness and disposition necessary for the successive actions that arise in its practice.

Third Quadrants, Tenth Position

If each foot occupies the E.N. in its quadrant, the body will be affirmed on an obtuse angle of 135 degrees, formed at the meeting point of the lines that are imagined to pass through the tips of the feet NN. and their lengths, produced in EE. and converging at R. At this point, this angle intersects the line S.R. Although the line of direction extends to the sides at E.L. and forward at E.O., it is a short distance for maintaining this position and resisting the body’s forward impulses. Moreover, this position is hardly natural and is of no use in Fencing.

From the explanation of the aforementioned ten positions, it is inferred that the most important positions for Fencing are the three where the body is affirmed on a right angle, each for different purposes.

The first position is with the right foot forward, the second with the left foot forward, and the third is caused by the lines that are imagined to pass through the tips of the feet and their lengths, which, when produced, each will form a right angle with the vertical plane of the chest. This common intersection with the horizontal lower plane represents the line S.R., and the convergence of both forms a right angle on the same line at point P.

This posture, as has been said, is the most spacious, natural, and perfect, both for being affirmed in it and for moving forward with integrity and grace. This is because the vertical plane of the chest is equally between both feet, as has been demonstrated, and its capacity is greater than any other position, in which the line of direction extends further; and for moving forward, it equally forms a right angle with its steps, with the same line S.R. on both sides, a right angle with each one, and a right angle with both, as will be demonstrated shortly.

It is also established that the body can be affirmed on parallel lines, and although this is not a position that is useful in Fencing for moving forward, it can be advantageous for better removing the degrees of the profile from the opponent, giving them less disposition to offend, and for having more reach in them, using this position according to the precepts of the Art.

In another demonstration and diagram, the explanation of three other figures will follow now, to provide evidence that the most perfect of all is this right angle position that has been emphasized.

Lamina viente y ſiete del Libro ſegundo.

 

Plate Twenty-Seven of Book Two.

 

CHAPTER TWENTY-NINE

Demonstration of How to Walk More Naturally, Strongly, and Gracefully by Positioning the Feet So That the Imaginary Lines Extending From Their Tips and Lengths Form a Right Angle, Rather Than Other Shapes, or by Keeping the Feet in Parallel Lines.

First Figure

Let the line A.B. represent the common intersection of the vertical plane of the chest with the horizontal plane below, and let the line B.D. form a semirect angle with B.A., occupied by the left foot.

Let E.G. form another semirect angle on the other side of B.A., also with A.B., and be occupied by the right foot, such that B.E., from the center of the heels, measures two feet, one solid and one hollow, although for this demonstration precise regularity is not essential.

I claim that the extended line G.E., reaching point C, will form a right angle with B.D. at point C.

If, having moved the line of direction over the right foot, which occupies E.G., one takes a step with the left foot, occupying H.K., then K.F. will also form a right angle with E.G. at point F.

If the feet continue to be alternately positioned in the same way, as shown in this first figure, the lines imagined to pass through the tips and lengths of the feet, when extended, will form the same right angle.

Because in the first triangle B.C.E., the angle C.B.E. is a semirect angle by construction, and the angle C.E.B. is equal to the angle H.E.F. in the triangle E.F.H., which is also a semirect angle by construction, as opposed by the 15th proposition of the first book of Euclid’s Elements. Therefore, by the 32nd proposition of the same book, the exterior angle E.C.D. of the triangle B.C.E. is a right angle, formed by the intersection of the lines passing through the tips and lengths of the feet extended, G.E. at C. and B.C. at D., at point C.

If, with the line of direction on the right foot, which occupies E.G., one takes a step with the left foot to occupy H.K., it will also form a right angle.

Because in the second triangle E.H.F., the angle H.E.F. is a semirect angle by construction, and the angle F.H.E., opposite to the angle L.H.I. in the triangle H.I.L. (also a semirect angle by construction), is equal to it by the 15th proposition of the first book of Euclid’s Elements. Therefore, by the 32nd proposition of the same book, the exterior angle H.F.G. of the triangle E.F.H. will be a right angle, formed at the intersection of the lines passing through the tips and lengths of the feet extended, K.F. at E.G., at point F.

In this manner, all other right angles that are formed in the described manner in the walking method of this first figure can be demonstrated.

Second Figure

Let the line A.B. represent the common section of the vertical plane of the chest with the horizontal lower plane, and let B.C., occupied by the left foot, form an acute angle of 22.5 degrees with A.B. Similarly, let E.F., on the other side of A.B. and occupied by the right foot, make another acute angle of 22.5 degrees with A.B., such that the distance B.E., from the center of one heel to the center of the other, is two feet, one solid and one hollow.

I claim that the extended line F.E., reaching point C, will form a semirect angle with B.D. at point C.

In the first triangle B.C.E. of this second figure, the angle E.B.C. is constructed to be 22.5 degrees, and the angle C.E.B., opposite to the angle H.E.F. in the triangle E.F.H. (also constructed to be 22.5 degrees), is equal to it, as per the 15th proposition of the first book of Euclid.

Therefore, the exterior angle E.C.D. of the same triangle is a semirect angle, as per the 32nd proposition of the same book, and is formed by the intersection of the lines extending from the tips and lengths of the feet, F.C. at B.D., at point C.

If, with the line of direction on the right foot occupying E.F., one takes a step with the left foot to occupy H.I., then I.F. will also form a semirect angle with E.G. at point F.

In the second triangle E.F.A. of this second figure, the angle H.E.F. is constructed to be 22.5 degrees, and the angle F.H.E., opposite to the angle L.H.I. (also constructed to be 22.5 degrees), will be equal to it, as per the 15th proposition of the first book of Euclid. Therefore, the exterior angle H.F.G. of the triangle E.F.H. will be a semirect angle, formed at the intersection of the lines extending from the tips and lengths of the feet, I.F. at E.G., at point F.

In this manner, all other semirect angles that are formed in the walking method of this second figure can be demonstrated.

Third Figure

Let the line A.B. be the common section of the vertical plane of the chest with the horizontal lower plane, and let the line B.C., occupied by the left foot, form an obtuse angle of 67.5 degrees with A.B. Similarly, let E.F., which is occupied by the right foot, form another obtuse angle of 67.5 degrees on the other side of A.B., such that the distance B.E., from the center of one heel to the center of the other, is two feet, one solid and one hollow.

I claim that the extended line F.E., reaching point C, will form an obtuse angle of 135 degrees with the extended line B.C. at point C.

In the triangle B.C.E., the angle E.B.C. is constructed to be 67.5 degrees, and the angle C.E.B., opposite to the angle F.E.H. (also constructed to be 67.5 degrees), is equal to it, as per the 15th proposition of the first book of Euclid. Therefore, the exterior angle E.C.D. of the triangle E.B.C. is an obtuse angle of 135 degrees, formed by the intersection of the lines F.E. extended to C and B.C. extended to D, at point C.

If, with the line of direction on the right foot occupying E.F., one takes a step with the left foot to occupy H.I, then an obtuse angle of 135 degrees will also be formed by the intersection of the lines extending from the tips and lengths of the feet, I.H. extended to F and E.F. extended to G, at point F.

In the second triangle E.F.H. of this third figure, the angle H.E.F., constructed to be 67.5 degrees, and the angle F.H.E., opposite to the angle L.H.I. in the triangle I.H.L. (also constructed to be 67.5 degrees), will be equal to it, as per the 15th proposition of the first book of Euclid. Therefore, by the 32nd proposition of the same book, the exterior angle H.F.G. of the triangle E.F.H. will be an obtuse angle of 135 degrees, formed by the intersection of the lines I.H. extended to F and E.F. extended to G, at point F.

In this manner, all other steps taken in the order of this third figure, alternating, will cause this obtuse angle of 135 degrees.

From the explanation and demonstration of all these figures, it is established that for the body to be firmly positioned, and to move forward more naturally, with firmness, good posture, and strength, the best position is that of the right angle. Each foot should be positioned at a right angle with respect to the vertical plane of the chest, so that they are equally distant from it, and this right angle is formed by the intersection of the lines that pass through the tips and lengths of both feet, as seen in the first figure of these last three. When the body is affirmed upon this right angle, it is the most perfect and capable posture among all others. In this position, the line of direction extends further to resist the impulses of the body, both to its sides and to the front, as demonstrated in the fourth figure of the first four. This conclusion is drawn from the explanations made of the different positions in which the body can be affirmed, following them successively, and particularly from what has been demonstrated in the first figure of these last three.

Because if this right angle is compared with the acute angle caused by each foot in the same vertical plane of the chest, with the lines imagined passing through the tips and their extended lengths of twenty-two and a half degrees, and with the concurrence of both lines forming a forty-five-degree semirect angle; it is found that this way of walking is not at all suitable for the Art of Fencing, and that it is best used for walking forward more quickly, because as the feet step closer to this vertical plane of the chest, less time is spent, and steps are taken more easily in this manner; however, it is not as secure, because on the outer side of the feet on either side, the line of direction has less extension than in the posture where a semirect angle with the same plane and a right angle is formed, as referred, with the lines passing through the tips and extended lengths of the feet.

If this same posture of a right angle is compared with the way of walking in an obtuse angle as shown in this third and final figure, it is found to be unnatural and unsuitable for the Art of Fencing, and that the line of direction has very little extension towards the front; this results in a risk of the body’s impulses, besides the fact that steps will be taken with difficulty, because the body will be strained as each foot is so far from the vertical plane of the chest. Indeed, each foot, with the line imagined passing through its tips and extended lengths to the same plane, on both sides, forms an acute angle of 67.5 degrees, and with the concurrence of both extended lines, an obtuse angle of 135 degrees.

The same conclusion in favor of this right angle is derived from the other positions, as explained for each one, to which we refer to avoid repetition.

First Corollary

From what has been explained about the ways in which the body can be positioned, it is understood that although no other species is predicated of the right angle, when wanting to take advantage of it for the Art of Fencing and its use, it is found that it has its differences. For instance, the right angle that has been praised as the most natural and perfect, formed when each foot is equally distanced from the vertical plane of the chest, is different from the right angle on which the body is affirmed. For example: When occupying the right collateral plane with the length of the right foot and the center of the left foot, and if a straight compass step forward is given through the same plane, it is followed by the left foot without moving the center of the heel from this plane. In this posture and way of walking, the vertical plane of the chest is left to its left side, which shows the difference, and that this way of walking is not natural, and will not be so in any direction where this step is given with the right foot, followed by the left; although it will be with other differences in carrying the body more or less strongly, depending on the nature of the planes through which it is given.

The right angle on which the body is affirmed with the left foot in front, for the movement of conclusion, in its left collateral plane, also leaves the vertical plane of the chest on its right side; and this position is also not natural, although for this purpose it is necessary that it can be affirmed in this way.

Even if the Fencer is left-handed, they can also affirm themselves, forming a semirect angle with each foot in their vertical plane of the chest, and a right angle with the concurrence of both lines, imagined passing through the tips and lengths of the feet produced, as has been explained for the right-handed person. Although for the use of Fencing with the sword in hand, it will not be as favorable for the left-handed person, but here we are only discussing the possibility.

The left-handed individual can also affirm themselves in their left collateral plane, with the left foot forward and the center of the right foot in the same plane, on a right angle, as has been explained. In this position, the vertical plane of the chest will be left to their right side, which also recognizes the difference of this position with the others on a right angle; and this position will not be natural either, nor will it be so for any other plane through which this compass step is given with the left foot, followed by the right foot; although it will be with its differences of being more or less weak, depending on the planes through which it is given.

If the left-handed person proceeds to make a concluding movement against a right-handed person, they will be affirmed on a right angle with the right foot forward in their right vertical plane, and the center of the heel of the left foot in it, leaving the vertical plane of the chest to their left side. In this position, the differences it has with the other postures on a right angle are also recognized: and although this is not natural, it cannot be avoided in this movement of conclusion.

Thus, in the explanation of these right angles, the essential differences they have among themselves in the practical part of Fencing become evident.

The other right-angle positions are observed for the execution of tactics and for the block, due to the posture of the Sword in order to ensure the Fencer’s greater safety; nor will any of the other positions that deviate from that of the right angle, participating more or less in the extremes that are usually caused outside of it, be natural, and all are less perfect than the posture of our right angle, which enjoys primacy among them, as deduced from the explanation and demonstration.

Lamina viente y ocho del Libro ſegundo.

 

Plate twenty-eight of Book Two.

 

CHAPTER THIRTY

Differences of Right Angle, considered for the use of Fencing.

We cannot but marvel, considering that in the majority of activities performed in the world by humans, especially those subject to Mathematics, such as Geometry, Astronomy, Optics, Perspective, and Architecture, the right angle plays a crucial role. The Geometer, to measure lengths, widths, depths, surfaces, and bodies, does so through right triangles, or by means of lines intersecting at right angles, or by sines, tangents, and secants, which always form right triangles.

The Astronomer does the same with their instruments, such as Quadrants, Radii, and Astrolabes, etc., which cannot be made or used except through the use of the right angle, nor can the movements of the Stars be regulated without considering certain circles: such as the vertical circles with the Horizon (which intersect at right angles) to know the heights; and the meridians or circles of longitude with the Equator, to know the declination; and the circles of latitude with the Zodiac, for the latitudes, which also all intersect with their principal circles at right angles.

The Optician in Dioptrics considers the ray of incidence (to determine the amount of refraction), which always falls at right angles onto the diaphanous body causing the refraction produced, if necessary.

In Catoptrics, to find the point of reflection, it is necessary to make use of the right angle.

In Perspective, which is commonly employed and with which things are represented on planes perpendicular to the Horizon, the primary point (which is the point of view) is set where the optical ray falls at right angles on the board on which it is to be painted.

The Architect, for their structures to stand, must base and erect them on right angles; and the rooms and interior spaces of buildings, for beauty and convenience, are arranged at right angles, among countless other applications that would require an extensive digression to enumerate fully. From this knowledge, it is concluded that the greatest and most difficult tasks are achieved and performed through the right angle, and it is no less significant for the understanding of Fencing, as will be recognized in the course of this work.

Thus, for the construction of the most essential operations within it, we rely on the right angle, which is the mean between the extremes where the Fencer causes obtuse and acute angles; and because different considerations of the right angle are made, being very necessary for the use of tactics, such as the one caused with the body on the horizontal plane, and with the feet on the same plane, and with the arm, and Sword in the plane we call superior, we will explain them in order.

Demonstration of the Convergence of Some Physical and Imaginary Lines, Which Cause a Right Angle Among Themselves, So That the Fencer May Know How to Be Affirmed in It, With the Body, With the Feet, and With Their Arm and Sword.

This proposition has three parts. The first is to examine where the right angle occurs with the body. The second is to examine how it should be formed with the feet. And the third is how it occurs with the arm and sword in the superior plane.

Part One

To examine the first part, we use what Euclid says in proposition 19 of his Eleventh Book, that when two planes perpendicular to another intersect each other, their common section will also be perpendicular to the third plane.

According to the explanation we have made of the vertical planes, all converge and intersect in the line of direction of the Fencer’s body; and to exemplify the first part of this proposition, we present the first figure of the Plate that follows.

First Figure

Given the cylinder A.B.H.G. representing the cylinder we have considered as the Plaza de Armas, in the idea of our Fortress (which we will explain later) with its bases A.C.B.D. representing the lower plane, and G.E.H.F. representing the upper plane.

Another cylinder L.M.N.O. we consider to encompass the Fencer, with its bases L.K.M representing the lower plane, and the base N.I.O representing the upper plane, and the line of direction I.K. serving as the axis to both cylinders.

Imagine these cylinders intersected by the vertical plane G.H.B.A. and the vertical plane C.D.F.E. both perpendicular to the horizon, whose common section is the line I.K. axis, as mentioned, of this cylinder, representing the body of the Fencer, which by the cited proposition, will also be perpendicular to the horizontal lower plane, as will the cylinder L.M.O.N itself.

Thus, we will say that whenever either of the two combatants stands straight, without leaning towards any side, as represented in the cylinder, it will be said to be affirmed with the body in the horizontal plane at a right angle, which is what was to be demonstrated.

Second Part

Demonstration of the Right Angle that can and should be made between the feet, and the correspondence they must have with the planes so that they, and the body, are ready to immediately regulate what concerns them in the lower plane, which is the foundation for the success of everything that is done in the upper plane with the arm and sword.

Figure Second

Let there be given one of the cylinders that form the particular Orbs of the Fencer A.B.C.D., divided into eight equal parts with the four diameters A.B., C.D., E.F., G.H., which intersect at the center I. of the figure, whose lines will be the common sections of the four vertical planes with the lower plane.

The Diameter A.B. represents two planes, the first A.I. represents the right vertical plane; and I.B. represents the left vertical plane.

The Diameter C.D. represents another two planes, the first I.C. the vertical plane that passes through the chest’s diameter; and I.D. represents the vertical plane of the back.

The Diameter E.F. represents another two planes, the first I.E. which we call the right collateral; and the plane represented by I.F. the left collateral of the back.

The Diameter G.H. represents another two planes, the first I.G. the collateral on the left side; and the one represented by I.H. the right collateral of the back.

The correspondence among these planes is such that they maintain the name of verticals, which are represented with the Diameters A.B. and C.D. intersecting at right angles at the center I.

The Diameters E.F. and G.H. that represent the collateral planes I.E., I.F., I.G., I.H. also intersect at right angles at the center I.

To examine the correspondence that the right angle, which must be caused between the two feet with these planes, must have, we have thought it appropriate to first suppose that the Fencer is affirmed in the center of the second figure, with the feet on parallel lines; in such a way that the vertical plane, which passes through the chest’s diameter, represented by the line I.C., is between both, in which position he had in the body, and that the movements he wanted to make with it from place to place, cannot be as prompt and immediate as required, as experience will tell.

Figure Third

We also present the third figure exactly like the second, and it is supposed that the Fencer is affirmed at the center I. of it, with the centers of the heels of the feet on parallel lines, and moves the right foot until it occupies its collateral plane on the same side I.E., and the left until it occupies its collateral plane on the same side I.G.

In this position, the Fencer will recognize that he is more natural and stronger than in the previous one, and with immediate disposition to make movement with the body to whichever side he wishes; he will also experience that if he continues the motion over the center, bringing the feet closer to the vertical planes I.A. right, and I.B. left, he will find that the body is somewhat forced, and not in a natural posture, which is required for this exercise.

From this, it results that to be affirmed with the body on a right angle with the feet, it is convenient for the Fencer to occupy with them their two collateral planes I.E., I.G.

However, as in the position that the feet are in this third figure, they cannot serve but when entering to execute some trick on the opponent, in which there will always be about a foot more of reach, as will be explained in the third Book, in the exercises that the Fencer must have, it is appropriate to give knowledge of the distance that the centers of the heels must be, to be perfectly affirmed on them on a right angle, as it is a much more natural posture, in which the immediate positions will be held, to be able to make the movements that are necessary with the body from place to place.

For this to have more generality, we do not oblige our Fencer to always occupy with his feet their two collateral planes, right and left, but he can also occupy, sometimes with the right and other times with the left, a line parallel to each one of his two collateral planes, without altering the distance that must be made for them to be affirmed on a right angle, as for example.

Fourth Figure

Given this fourth figure with the same lines representing the same planes as in the two preceding ones, with the same letters, and with the Fencer affirmed with the center of the heel of his right foot, occupying the center I. of the figure, and the foot occupying the right collateral plane I.E., and the center of the heel of the left foot in the collateral plane I.F. of the back, occupying with it the line K.L. parallel to the collateral plane of his left side I.G., spaced the centers of both feet so that there is one foot from center to center, it will be said that the Fencer is affirmed on a right angle, with the same disposition in everything, as if he were affirmed occupying with the feet their two right and left collateral planes I.E., I.G., with the centers spaced at a distance of one foot, as stated.

In imitation of the Pilots, who steer the Ships, whenever they do it by some lines parallel to the courses of their nautical chart, they give them the name of the same courses, and consider them as such, without difference; and there being no difference, in terms of the Fencer being affirmed on a right angle in the referred form, we demonstrate it by proposition 28 of the first of Euclid’s Elements, which proves that the external angle is equal to the internal and opposite on the same side.

Because the two parallel lines (in this figure) K.L. and I.G. are cut by E.K. at right angles, the external angle E.I.G is equal to the internal and opposite angle E.K.L.; and being both right angles, we will say that the Fencer is affirmed on right angles, as seen in the figure, which is what needed to be demonstrated.

From this, it follows that, being the Fencer affirmed on a right angle, as supposed in this fourth figure, he will have the same disposition as if he were affirmed on a right angle, occupying his two collateral planes I.E. on the right, and I.G. on his left side.

From all mentioned, it results that not only will the Fencer be affirmed on a right angle with the feet; but he will be perfectly affirmed in a right angle with the body, because the centers of the feet correspond in this posture to the two centers of the arms, between which there is also a distance of one foot, as there is from center to center of the two heels of the feet, and it has been demonstrated by the first demonstration of these figures that whenever the Fencer is firmly upright with the body in the lower plane, he will be at a right angle, and on a right angle, with respect to himself, and he can be so with respect to his opponent with the perfection required.

Since there are different figures that we have to explain, of the various ways in which the Fencer can be affirmed with the body at a right angle, and with the feet on a right angle; having already demonstrated both in the two referred demonstrations, we will excuse the lengthiness of repeating the demonstrations of each one, assuming that they can be demonstrated with the understanding of the demonstration of the first figure, and of this fourth one, and with this note, we will go on explaining them.

Figure Five

In this fifth figure, we suppose the Fencer to be affirmed on a right angle with his feet, as in the previous one, with a difference, that as seen in it, occupies the center I. with the center of the heel of the right foot, and in this figure, the body’s line of direction corresponds to the center I. of it, in the middle of the distance of one foot, which we suppose between the centers of the heels of both; and so we will say that he is affirmed on a right angle, caused by the lines E.K. and the parallel K.L. to the left collateral plane I.G.

Figure Six

The posture of this sixth figure is different from the others, because it occupies with the center of the heel of the left foot the center I. of the figure, and the foot its left collateral plane I.G. and with the right its right collateral plane I.E. and in this position, both feet are on their two collateral planes, which by intersecting at right angles at the center I. of the figure, and occupying it with the center of his left foot, we will also say that he is affirmed on a right angle.

Figure Seven

In this seventh figure, the posture is also different from the others explained, because although with the center of the heel of the left foot it occupies the center I. of the figure, and with it its left collateral plane I.G. with the right it occupies the parallel line L.K. to its right collateral plane I.E. at point K. with which by the same proposition 28. of the first of the Elements of Euclid, also cited, the feet will remain affirmed on a right angle, caused at K. for being the external angle G.K.L. equal to the internal G.I.E. which both are right angles; and it is of such importance, as will be said in the explanation of the figure, which includes the means of proportion, and proportionate.

Figure Eight

In this eighth figure, the right angle is also caused differently from the others, regarding posture, because although the left foot occupies with the center of the heel the center of the figure I. and its left collateral plane I.G., with the right foot it occupies the line L.K. parallel to its right collateral plane I.E. Although this right angle comes to be caused corresponding the heel of the right foot to the tip of the left foot at point K., this does not prevent the same reasoning as in the previous one, since the angle G.K.L. is equal to the internal G.I.E., and thus we will say that he will be affirmed in this posture on a right angle. And this form of right angle is caused when setting aside from the nearest extreme by the posture of the Sword.

Figure Nine

In this ninth figure, a right angle is also caused differently because although with the center of the heel of the left foot the Fencer occupies the center of the figure I. and its left collateral plane I.G., with the right it occupies the line K.L. parallel to its right collateral plane I.E. The difference consists in that the right foot and the line L.K. that it occupies do not correspond to the left foot, as in the past, but it meets the line representing the left collateral plane I.G., and by intersecting at right angles, the external angle is equal to the internal angle G.I.E.

The blows that are delivered with this type of compass can be with the Sword alone, or with double weapons, both with the Fencing used in Spain and with that professed by other Nations; and not only will the Fencer attack with great strength and speed, but also will be able to retract the body with the same to the middle of proportion.

These ways of striking should not be understood as being affirmed on a right angle, but this last one, which we have explained, is to form a concept that although compasses that partake of some extreme are to be given, one should always try to conserve the body’s position, that at least the feet occupy lines that intersect each other at a right angle, as seen in this figure, and in the preceding ones, and that the feet have a distance between them of one foot, so that their centers correspond to the centers of the arms; and that in any posture, even if somewhat extreme, the rest of the body is upright, because with these precepts the utilities of defense and offense will be achieved with great speed. And in the Treatise on Tactics, special notices, and more individual precepts will be given, so that they can be formed and executed with full perfection.

Figure Ten

In this tenth figure, the center of the heel of the right foot occupies the center I. of it, and with it, its right collateral plane I.E., and with the left, its left collateral plane I.G. This position is different from all others because it places the right foot in front, and in this, the left foot is placed in front; with the right angle caused by the intersection of the two transversal lines I.E. I.G. (which represent the two referred collateral planes) at point I. This posture serves to show how the feet should be placed when the Fencer makes a movement of conclusion in the guard of the Sword of their opponent.

Special reasons for what each one serves will be given in the Treatise on Tactics for all these differences in positions in which the Fencer can affirm themselves with their feet at a right angle.

The preceding figures, which we have explained, are in order to give knowledge of the differences with which the Fencer can affirm themselves at a right angle with their feet for various purposes. Now it is appropriate to explain the third part and make a demonstration of it.

Third Part

Demonstration of the three right angles that are formed in the upper plane at the common sections of this plane with three other vertical planes, which we call principal, that the arm must occupy so that it can be said that the Fencer is affirmed with it at a right angle; and to demonstrate this, the following figure is presented.

Figure Eleven

Given is the cylinder A.B.I.H. with its base A.C.E.B.D.F. in the lower plane, and the base H.K.M.I.L.N. in the upper plane, each being one of the circles of the spheres that the Fencer causes when affirming with their arm and sword, making a revolution over the center of their right foot.

Also given is the inner cylinder P.Q.S.R. which is imagined to encompass the body of the Fencer, and the direction line of this cylinder O.G., with the base P.Q. in the lower plane, and the base R.S. in the upper plane.

Imagine on the base of the cylinder A.H.I.B. that represents the upper plane H.M.I.N. the diameters H.I., K.L., and M.N. that intersect in the direction line of the interior cylinder at point O.

Also imagine in the lower plane another base A.E.B.F., entirely equal to the upper base, with three other diameters A.B., C.D., and E.F. that also intersect in the direction line of the interior cylinder at point G., corresponding entirely to the three diameters of the upper base; it is necessary to demonstrate how these diameters cause right angles, both in the upper and lower plane, with the direction line of the Fencer’s cylinder, and we prove it in this way.

Since the two bases of the cylinder A.B.I.H. representing the upper and lower planes are parallel to each other, and the direction line O.G., as we have demonstrated in the first of these 11 figures based on proposition 19 of the eleventh of Euclid’s Elements, is perpendicular to the base and lower plane; consequently, O.G. will also be perpendicular to the upper base H.K.M.I.L.N. by the corollary to proposition 14 of the same eleventh book; from which it also follows that G.O. will form right angles with the three lines O.H., O.K., and O.M. in the upper plane representing the common sections of the three vertical planes O.H. right, O.K. collateral of the same side; and O.M. the vertical that passes through the chest’s diametral with the upper plane in the direction line at point O.

From this it also results that when the Fencer is affirmed with their arm in each of these three common sections of these vertical planes with the upper one, they will be with it at a right angle.

It should be noted, however, that only in the common section made by their right vertical plane with the upper plane, can they be, as mentioned, with their arm at a right angle; but in the other two planes—the right collateral of the same side, and the vertical passing through the chest diametral—they will occupy the common section of each one with their sword, and another mathematical line, imagined from the hilt to the direction line at point O, to be properly said to be affirmed at a right angle with the direction line.

It is also noted, if this right angle were imagined to be caused with the arm line and the right vertical line, it could in these three planes cause a right angle with the arm; however, this consideration would have a very great inconvenience because it would deprive the Art of Fencing of the use of the primary vertical plane, which is always imagined to pass through the two vertices of the two combatants and their direction lines, where it causes the common section with the upper plane, which must always be occupied to be perfectly affirmed at a right angle, and to be, as this primary vertical plane is, the principal north of all the operations of the Art of Fencing, as has been explained with demonstration in the chapter that gives knowledge of the planes, and it will be repeated where necessary, particularly in the Treatise on Tactics, because, as said, it is the guide by which they must be directed and governed for their greatest perfection.

Lamina viente y neuve del Libro ſegundo.

 

Plate twenty-nine of the Second Book.

 

CHAPTER THIRTY-ONE

In which a more universal demonstration is made of the right angle caused in the upper plane; its jurisdiction, nature, differences, and properties, in order to its reach.

In order to facilitate the understanding of this explanation, we find it convenient to first present the definition of the right angle, which is as follows:

The Fencer will be affirmed at a right angle in any part of their jurisdiction, with respect to themselves, and to their opponent, whenever with the straight line, which is imagined to pass from the direction line through the center of the arm, and through the center of the sword’s guard, to its tip, or with the line that is imagined to pass through the center of the guard (kept in these three cases as far away from their body as possible), will occupy the common section of the primary vertical plane with the upper plane parallel to the Horizon.

For the same purpose, we also present the definition of reach, and where it begins, as follows.

Having reach in Fencing between any of the two combatants occurs when there is such a distance between the center of the arm with which one intends to offend with any weapon, and the body of their opponent, that there is a point of contact on them.

Because the primary vertical plane can be caused in all the particular vertical planes of the body, and the right angle, according to our speculations, only has jurisdiction from the Fencers’s right vertical plane to their chest vertical plane, in which it can form its right angles of greater and lesser reach, as we will demonstrate through the figure that will follow after the explanation.

Let the circle A.C.B.D. represent the upper plane divided into eight equal parts, with the eight semidiameters. I.A. representing the right vertical plane. I.E. representing the collateral plane on the same right side. I.C. representing the vertical plane that passes through the chest’s diameter. I.G. representing the left collateral plane. I.B. representing the left vertical plane. I.F. representing the left collateral plane of the backs. I.D. representing the vertical plane of the backs. I.H. representing also the right vertical plane of the backs.

These planes are common sections of the four vertical planes, represented by the four diameters AB, CD, EF, and GH, which intersect at the direction line, represented by the point I in the center of the figure; and for clarity, we mark the eight planes that they cause, with their numbers from one to eight, as seen in it.

The jurisdiction of the right angle must be understood from the first to the third plane, which are represented by the lines IA and IC, which form the right angle A.I.C.

Because in this jurisdiction of the right angle, in respect to the organization and composition of the body, many right angles can be caused that have differences among themselves, it is necessary to examine it, so that the Fencer knows the nature of each one, and where they will have greater and lesser reach; and to demonstrate this, we say:

Let the same figure be given, with the same planes that have been explained, in such a way that the semidiameter I.A. is the length from the direction line, represented by point I, to the center of the guard, which is two geometric feet and three-quarters of another. Take I.K. as half a foot, and from the center I, at the interval I.K., describe the circle K.N.O.P., which will be the common section of the cylinder, in which the Fencer is imagined to be contained, and of the upper plane.

The point K will be the center of the arm, and the point A the center of the guard.

It is necessary to examine, how much reach the Fencer will have lost in respect to their opponent when the center of their guard occupies their right collateral plane I.E. at point S?

When the same center of the guard occupies its chest vertical plane I.C. at point L., which is the jurisdiction of the right angle where the Fencer can keep their arm straight parallel to the Horizon, without bending it; consequently, it can be examined, if desired, how much more reach will be lost from the chest vertical plane I.C. (where the jurisdiction of the right angle ends) in its left collateral plane I.G., which will only come to have reach at point Q, and on the line N.R. parallel to its left vertical plane I.B., which is as far as their arm and guard can reach at point R, although this, depending on the disposition of the bodies of the combatants, may have some irregularity; but whenever it is examined, there will be very little difference.

Center K, interval K.A. (length of the arm to the center of the guard), describe the arc A.S.M.L., which is the space in which the arm, without moving the body, can move over its center parallel to the Horizon (as we have said), without bending, nor making an angle at L. This arc will cut the line I.E. at point S, and I.C. at point L. We say that the difference between E and S, and C and L, are the amounts of reach the Fencer will lose in the planes I.E. and I.C., and we demonstrate this in the following way.

Draw the line K.S. because from the point S, which is outside the circle K.N.O.P. (representing the Fencer’s cylinder), two lines have been drawn to the outer circumference S.K.S.N. According to the eighth proposition of the third book of Euclid, S.N., which produced, passes through the center I, will be shorter than S.K. by the amount of S.E., which we will prove by sines, by proportion, and by geometric demonstration.

By sines, since three things in the triangle K.I.S. are known, which are the side S.K. of 36 digits, the side K.I. of eight digits, and the angle K.I.S. of 45 degrees, by the nature of the planes that are spaced apart by one-eighth of the entire circumference of the circle A.C.B.D., it will be found by this method that the difference between these two lines S.K. and S.N. will be three digits, and almost a fifth.

The other method, to determine the difference in reach between these two lines, is done in this manner.

For the construction with center K and interval K.A., the circumference A.S.M.L. has been described according to definition 13 of the first book of Euclid, meaning the line K.A. will be equal to K.S. However, I.A., by the same definition 13 of the first book, is equal to I.E., and by the same definition of the circle, the line I.K. is equal to I.N. Therefore, the remainder K.A. and N.E. will also be equal to each other, according to axiom 2 of the first book of Euclid. It follows then that K.S. will be equal to N.E. by axiom 1 of the said elements, stating that quantities that are equal to a third quantity are equal to each other: for example, the line K.S. is equal to K.A., and N.E. is equal to the same K.A., thus N.E. will also be equal to K.S. And if from N.E., the greater, is subtracted N.S., the lesser, the remainder will be E.S., which is the amount of reach the Fencer loses by placing the center of his guard in his right collateral plane I.E. at point S.

Using the Pythagorean theorem, this difference in reach can be found by dividing S.K. into 36 digits; and taking it to S.N., it will be found to be only 33 less a fifth, slightly less.

Thus, imagining the opponent positioned so that the center of his right foot occupies point E., such that it corresponds to the center of his right arm occupying his own right vertical plane, he can reach the Fencer at point N. with the same length of 36 digits, without being reached himself, because the Fencer’s reach, although of the same length, does not extend beyond point S. due to having his arm and the center of his guard in his right collateral plane I.E., and his opponent in his right vertical plane has a longer reach.

The same demonstration, using the same three methods, can be made assuming that the Fencer places the center of their guard in their chest’s vertical plane I.C. at point L. It will be found that they will lose from their reach in this position the amount of L.C., which turns out to be half a foot; and that being firmly positioned, their opponent, occupying with the heel center of their right foot the point C., will be able to reach them at point P. without being reached, for the same reason of being affirmed in their right vertical plane of greater reach.

The same demonstration can be made, as said, when the Fencer places the center of their guard in their left collateral plane I.G. at point Q., and also when they place it in the line parallel to their left vertical plane I.B. at point R.

These same demonstrations could be made in any of all the intermediate vertical planes between the referred planes, wherever the Fencer places the center of their guard, and knowledge of the reach in each one, and the amount they will lose from it, with respect to their opponent, assuming them affirmed in their right vertical plane, as said.

Corollary

It follows that the right angles that the Fencer can create in the common sections of the vertical planes with the upper plane, from their right vertical plane I.A. to their chest vertical plane I.C., which is the jurisdiction of the right angles and a quadrant of the circle, will lose reach in each one; however, it is noted that the nature of these right angles is such that as these angles are formed, more strength will be acquired, by joining the part to the whole, until reaching the vertical plane I.C., where it will have greater strength than in any other.

From this same reasoning, it follows that the right angles that are formed from the chest vertical plane I.C. to the right vertical plane I.A. will see the Fencer increasing their reach in each one, and in the same right vertical plane, they will have greater reach than in all the others; and for the same reason of the part deviating from the whole, in each of these right angles, they will lose more of their strength, until their right vertical plane, where they will have the greatest weakness.

From this, it also follows that, given that the perfection of the use of Fencing consists in having inequality with the opponent; the knowledge of these right angles is very necessary because the Fencer will use those of greater reach for the profile of the body, and those of greater strength for the posture of the Sword, to counteract with it the weakness that their opponent’s sword will have; and by the profile of the body, they will apply those of their greatest reach, which although the opponent will have in this position those of their greatest strength and lesser reach, not allowing the Fencer with it to counteract the weakness of their Sword, they can succeed in offending without being offended, and not observing these precepts, they will find themselves in difficulty.

In the different natures of these right angles, the difference in each of them is evident because the term Difference, according to our definition, is about something not being another thing, and about more and less, which is what happens with these angles since some have more strength and less reach, and others more reach and less strength.

From this follows the understanding of their properties because, according to the definition, the term property or properties refers to those that are inherently natural to the subject and remain in it, and others by accidents that stem from the use of their potential; this is verified in these right angles, because some acquire degrees of strength and decrease their reach, and others lose degrees of strength and increase in reach.

From the knowledge of these properties and the opposition they have among each other, the Fencer can regulate their operations and recognize where they fail in the use of theirs, to take advantage of their opponents’ carelessness or insufficiency.

For more clarity in these matters, it’s necessary for the Fencer to form a concept of the three main planes in which they can position themselves within the jurisdiction of the right angle, which are in their right vertical plane, where they have more reach and greater weakness; in their chest vertical plane, where they have their greatest strength and least reach; and in their right collateral plane, which, being between these two extreme planes, will partake of the reach of one and the strength of the other; hence, this posture is the most natural of all to affirm oneself in it, and the posture in the right vertical plane, due to its great weakness, is less secure for waiting for the opponent to act, as the arm is entirely disjointed from its whole, which will give them more disposition to act than in any other.

These same speculations underpin our stance of the square, from which one should not use from the medium of proportion but from the proportional, occupying with the right foot the right collateral plane, and with the left the left collateral plane, causing with the Sword, one should occupy the common section of the primary vertical plane with the upper plane, which passes through the vertical of the chest; and with the arm with the Sword, and the body, are in their greatest strength, and with a natural disposition to make the body’s movements from place to place, especially for everything that is worked through the posture of the Sword.

With the same positioning of the feet in their two collateral planes, the Fencer covers with them the depth of their opponent’s body, whether the opponent is positioned in their right collateral plane, or in the right vertical plane, or in the intermediate planes between these two. In any of these, the opponent’s arm and sword will have more weakness due to being more disjointed from their whole than the Fencer’s sword because, having it in the common section of the two referred planes and in front of their chest vertical plane, being more united to the whole as much as possible (having to hold it at a right angle) will be a significant advantage; and by having opposite the opponent’s vertical chest plane, which is also naturally stronger for the use of Fencing, for the same reason given, it will also give an advantage.

By having this positioning of the Fencer’s sword corresponding to their vertical plane that passes through the chest diameter, which is the midpoint of the two extreme planes, vertical right, and left, just as it is also of the two extreme collateral planes right and left; they can, maintaining the center of their guard in the common section of the two referred planes, move promptly from this midpoint to any of the extremes.

Although in this posture, the Fencer will have less reach with their arm and sword by a quantity of half a foot, as we have demonstrated, this not only can be compensated for to equal the posture of greater reach; but it can have more than it, and with more immediate dispositions, to enter from the proportional medium to the proportionate, and execution of the strikes, and then to exit back to it. Because being the Fencer affirmed in the proportional medium in this posture, they can enter by giving a compass step with the right foot of a quantity of two to three feet, according to the height and organization of each one, keeping it in such a way in the movement, that it always causes a right angle with the line of the left foot produced; and with the line imagined produced from the tip of the right foot, it cuts the diameter line of the circle, which was first common to both combatants; and as anyone can experiment, this compass step will be given without discomposure, in such a way, that the center of the right arm, and this without moving the left foot from the proportional medium; because although when this step is given with the right, the heel of the left will rise somewhat, and to the extent that it does, it will bring the line of direction closer to the heel of the right foot, it will still be found with immediate disposition to retract the body (after having executed the strikes) to the proportional medium, in the same posture it first had in it; and through this compass, it will reach in the quantity given, with more swiftness, and security than in any other posture, and all actions, and strikes will be with much greater violence, and force than in any other; as will be explained more particularly in its place this posture, by means of a figure, for greater clarity, and understanding.

This posture, and the way of giving the compass with the right foot, serves to enter to strike with much more security, and swiftness, both with double weapons and against the postures used in Italy, France, and other Nations, which base their Fencing on not allowing their Sword to communicate, and throwing themselves profiling, seeing some uncovered point, relying on the swiftness they acquire with long exercise; and so it is convenient that our Fencer also has it to be able to offend without being offended; requirements that do not occur in the way that the Nations have of acting, because whenever they strike they can be struck, and they have no more precepts than brevity; and if they encounter someone who also has it, it will result in being struck at the same time, which is what is not allowed in good Fencing, because the offense must always be compounded with defense.

Because it may be noted that the demonstrations we have made in this figure by three different means, in order to find out the reach of the right angle, assuming that the Fencer places the center of the guard in their right collateral plane, so that by them the demonstrations of all the right angles that occur in the vertical planes of their jurisdiction can be regulated.

We say that it has been with particular attention to make it understood that having the arm and guard in the superior plane parallel to the horizon, the Fencer can, without discomposing, with the center of the wrist, raise and lower their Sword to the obtuse and acute angle, and place it to their right and left side with much more security than if the arm and guard accompanied the Sword in these actions, because of how much the body would be left unprotected and exposed; it being so, that by keeping the arm and guard in the superior plane, the place of the right angles, with very short movements made with it to any of the referred parts, they will be able to continue defending their body, sometimes putting their opponent’s Sword on the surface of their Pyramid with their own of the arm and guard, and at other times with their Sword; in such a way, that it always contains it, on one side or the other, in the sides of the angle of their bulwark, with which we represent the two vertical planes, as terms in which the total defense consists, so that the opponent’s Sword never has direction to their body, nor cylinder, in which we imagine them, as demonstrated in the idea of our Stronghold to which we refer.

Because it is convenient that when using these right angles, it is always through the primary vertical plane, which according to its definition passes through the shortest distance there is between any of the positions in which the two combatants find themselves, by imagining passing through the two particular planes they have opposite, we say; to determine the essence of the right angle with respect to the Fencer and their opponent, in all its universality, that will be caused in the intersection of their line of direction with the line we imagine coming out of it from the center of the arm to the tip of the Sword, occupying with it, or with the center of the guard, or with the Sword together, the common section of this primary vertical plane with the superior plane, for being this plane, as has been explained, the proper place of the right angles, and observing these precepts, the Fencer will achieve to be affirmed in any of them with perfection.

With this, we have given in all that has been referred to a universal knowledge of the nature, differences, and properties of the right angles that can be caused in their jurisdiction; and of the use of them, we will make explanations in their proper places, where their utilities will be made evident.

Lamina treinta del Libro ſegundo

 

Plate thirty of the Second Book.

 

CHAPTER THIRTY-TWO

For further verification of the reach of the right angle, and of its jurisdiction, in confirmation of what has been demonstrated, I return to facilitate it in three figures of the body.

Although the demonstrations we have made of the greater and lesser reach of the right angles that can be caused in their jurisdiction are evident and clear; still, for one and the other to be seen with more distinction and to be more perceptible to the sense of sight, we have thought it appropriate to include here the three principal figures on which said demonstrations are based; in the first, the Fencer is affirmed in profile in his right vertical plane, in the second affirmed in his same side collateral plane, and the third affirmed in his chest vertical plane, so that in the difference of these positions one can judge the greater and lesser reach in each of them, whose knowledge can serve those who do not want to tire in the Mathematical demonstrations. And it is noted, that in the Mathematical demonstration, which has been made, where it is supposed that the cylinder in which we imagine the Fencer stays still, and only the arm moves from the right vertical plane to the chest vertical plane, and from this plane the arm returns to the right vertical plane, because so it was convenient to what was demonstrated; but in these three figures, which we have placed in elevation, with the considerations that must be had in the lower plane for the knowledge of them, it is necessary to suppose, for more clarity, that the arm and Sword do not move, and that the cylinder, or body is the one that moves, by means of the left foot, around the line that passes through the center of the right arm and ends also in the center of the right foot, as seen in the second and third figure, and the amount that in each one the Fencer brings the body closer to his opponent, which is what he loses in reach with him; and first we place the first figure, in which the Fencer is affirmed in profile in right angle, and on right angle, as the foundation by which the knowledge of the other two is to be regulated.

Explanation of the first figure, for the right vertical plane

Given that the Fencer is affirmed in his right vertical plane in right angle I.C.E. corresponding to the primary vertical plane, and on the base of his cylinder E.G.F.H. in the lower plane, where E.F. represents the same right vertical plane, and the line K.B. represents his right collateral plane, and G.H. his chest vertical plane, and that he has opposition to his opponent, in equal body and arms, affirmed in the same opposition without difference. In this case, approaching one another, they will be able to reach each other in their vertical lines C.E. passing through the centers of their arms, and their right feet at the points of contact corresponding to them.

The second figure is demonstrated for the right collateral plane.

In this second figure for its understanding, we say, that as in the previous one he was affirmed with the arm and Sword in the right vertical plane, and in the same plane on right angle with the feet in the lower plane; in this second, by having moved the left foot to point F. and having made the necessary motion over the center E. of the right foot, he remains affirmed in the right vertical plane F.E. with the feet on the side, as seen in the figure, with which he opposes his opponent his right collateral plane B.K. caused in the primary plane, in which plane his Sword will also be due to the movement of the left foot to F. and he brings the body closer to his opponent a little more than three fingers, which is the amount of body that comes out of the line C.E. end of his cylinder; and the same is recognized in that the face comes closer the same amount to the same line C.E. regarding the position it has in the first figure, and it is the same amount we found in the said Mathematical demonstration.

The third figure of the body is explained, representing the chest vertical plane affirmed in square.

In this third figure, as seen in it, to place the Fencer in square, he passes his left foot to point F. completing the fourth part of the circle P.F. required for it, and his vertical plane F.E. on the part that is seen in the figure, with which he opposes his opponent his chest vertical plane B.G. causing in it the primary plane; and in this position, he brings the body closer to his opponent by half a foot, more or less, by the part of him that is outside the cylinder, where we imagine him in the first figure, and to the line C.E. that passes through the centers of the arm, and of his right foot, and it is the same amount we found he lost in reach in the said Mathematical demonstration, and the same that in this figure is found to bring the face closer; and both we have adjusted by their footprints with all possible rigor.

Lamina treinta y vna del Libro ſegundo.

 

Plate thirty-one of the second book.

 

CHAPTER THIRTY-THREE

I return for the third time to demonstrate in order the reaches of the Sword in each of the three planes, and jurisdiction of the right angle, in confirmation of the previous demonstrations

Although in the demonstrations before this one, the reaches of the right angle in the three planes, right vertical, same side collateral, and chest vertical, which are reduced to the three postures of profile, half-profile, and square, have been sufficiently proven, and sufficient notice given to be able to regulate the reaches of the intermediate planes of these three; yet, desiring to provide all possible clarity to those who would not wish to tire themselves in examining these demonstrations, it seemed appropriate to us, for greater understanding, to put in figures the cylinders in which we imagine the two opponents, and the arm and Sword of the Fencer, so that immediately one can judge the amounts of reach lost, regarding the right angle, which is caused in the right vertical plane in the other two planes, collateral of the same side, and chest vertical; and with these so visible demonstrations, not only can they be perceived without effort, but it can be recognized that they conform in everything to the other two previous demonstrations, so that there can be no doubt in their reality and evidence the Fencer is affirmed with his arm and Sword in his right vertical plane.

Explanation of the first figure, for the right vertical plane

Given, then, that the Fencer affirmed in the first figure in his cylinder Q.O.M.K. divided into its eight principal planes so that A.K. is his right vertical plane, in which we imagine him affirmed with his arm and Sword A.O. his chest vertical plane A.Q. his vertical plane corresponding to the back A.L. his right collateral plane A.P. his collateral plane corresponding to his left side of the back A.N. his left collateral plane, and A.R. his right collateral plane corresponding to the back.

K.H. is the length of the arm from its center K. to H. hilt of the Sword, and the straight line of the same arm, of a length of two geometric feet. H.B. is the length of the Sword from the hilt, or straight line, to the tip, of a length of four geometric feet. And point M. is the one where the tip of the Sword has the point of contact in the opponent’s cylinder in the chest vertical plane, whose cylinder is divided with the same eight planes, as those of the Fencer, with which it will have caused in its right vertical plane of the primary vertical plane, and applied it in the chest vertical plane of his opponent.

Explanation of the second figure, for the right collateral plane.

In the previous demonstration, it is clear that with the length of the arm and Sword, the Fencer affirmed in the right vertical plane in the common section of the primary vertical plane and the upper plane, will reach his opponent in the cylinder in which we imagine him affirmed in his chest vertical plane at point M.

Now, we consider the Fencer affirmed in this second figure in his cylinder (divided into the same planes as the first) in his right collateral plane A.L. having preceded the motion around the direction line, which represents in the cylinder the point A. so that the point K. is the center of his arm, and K.H. is the length of it, and H.B. the length of the Sword, which occupies the common section of the primary vertical plane with the upper plane, corresponding to his right collateral plane A.L. It is recognized that the motion the Fencer made in moving his right vertical K.O. away from the primary vertical plane A.H. lost reach, regarding his opponent, by the amount of B.M. which is just over three fingers, and it is the same that we have demonstrated in the other two demonstrations; and in this figure, the Fencer has caused his primary plane in his right collateral plane A.L. and the tip of the Sword corresponds to the chest vertical plane of his opponent; although it is not circumstantial because any other point corresponding to the tip of the Sword will verify the same loss of reach.

Explanation of the third figure, for the chest diametral plane.

Assuming in this third figure the Fencer in his cylinder, divided into the same planes as the two preceding ones, affirmed in square, which is when the right vertical plane A.K. causes a right angle with the primary vertical plane A.H. in such a way that the center of his arm corresponds to point K. and the length of his arm K.H. and H.B. the length of the Sword, which is at a right angle, occupying the common section of the primary vertical plane with the upper plane; and in this posture, as seen in it, loses a half foot of reach, a little more, which is the amount of B.M. that is the point where the tip of the Sword would have reached to make contact in the cylinder of the opponent, and this same amount is what was demonstrated in the two previous demonstrations as lost in reach in this posture, and in it, the Fencer causes the primary plane in his chest vertical plane, and the Sword applies it in the same plane of his opponent, although it does not reach his cylinder, it does not have a point of contact on it.

Corollary

From these three demonstrations, it follows that to examine the reaches in each of the three principal planes and their intermediates, it is the same to move the Sword and arm, applying it to the planes while the body remains fixed, as in the first demonstration, as it is to keep the arm and Sword fixed and apply the planes to them through the motion of the body, over the center of the right foot, as in the second demonstration, or around the line of direction, as in this third one.

Lamina treinta y dos del Libro ſegundo.

 

Sheet thirty-two of the second book.

 

CHAPTER THIRTY-FOUR

Having given an account of the universality of the Right Angle, its jurisdiction, nature, differences, and properties in terms of its reach, it remains to demonstrate that it has a greater reach than either the obtuse or acute angles.

Mathematically demonstrating that the Right Angle has greater reach than either the obtuse or acute angle.

For a true understanding of the explanation of this demonstration, I must first base it on Mathematical Philosophy, which deals with things that have a countable or measurable quantity; given this, I (following the example of Euclid, the principal of geometers, who asked for the grace to be allowed to describe a circle with any center, and to draw a straight line from one point to another) asked enthusiasts at the beginning of this second book, in the Petitions of the sword’s regimen, to grant me that the most perfect height of a man would be two yards since Vitruvius in book three says: That a man’s foot is the sixth part of his body; and Claudius Vegetius, in book 1 of De Re Militari, discussing what stature men should be chosen for war, says: That Consul Marius chose new Soldiers of six feet in height; and for this, in accordance with Vegetius, Vitruvius should be understood in the cited place, saying that the foot of a man, is the sixth part of his body, or stature; but it should be understood that the foot he mentions is geometric, which is composed of four palm widths, and each palm has four fingers, making 16 fingers, which is a third of a yard: with the height being six of these feet, one will find that a man, according to the cited authors, will be two yards tall; following these same authors and many others, both ancient and modern, who discuss this and affirm it, according to the rule of the most wise Marco Vitruvius, who also states that six geometric feet is the proper proportion, or height of a man; although strictly speaking, a handsome man should have a smaller foot than what these authors suppose, I do not set out to contradict them, as their doctrines are so accepted, and affirmed by Alberti Durero and Juan De Arfe, in their Symmetries, as very diligent statuaries, and they consider the said six geometric feet to be the most perfect, which are the two yards.

Vitruvius’s “De Architectura”, Book 3

Vegetius’ “De Re Militari”, Book 1

 

I also asked that the sword, with which distances and measurements are to be regulated, must be according to the standard of these kingdoms of Castile, since by law and pragmatic sanction, it is prohibited to carry any but of five quarters, measuring from the guard to the tip, because with the hilt and pommel, which is its entire magnitude, it has four thirds, which make four geometric feet. Given and granted this (as it should be), I base the regularity of the demonstrations under these measures, as they are the most accepted by all scientific men, both Statuaries and Painters, who deal with the Symmetry of man; because if I had to follow the measures brought by Albert Durer, they would cause confusion, due to the aliquot parts being so minimal and lengthy for this science; thus, I make use of measuring or gauging the body of a man by feet, and by fingers, and the same with the sword, since it is the instrument with which the defense and offense (if convenient) are to be made, measuring, regulating, and proportioning with them the distances, movements, angles, actions, strategies, profiles, and aspects, etc., with such direction, that the knowledgeable Fencer may enjoy the admirable and favorable effects of this science.

Given and granted that the well-proportioned human body is two yards tall, which is its total length, making six geometric feet, and that each one is sixteen fingers in length, if the sixteen are multiplied by six, they will make ninety-six fingers for the total height of the figure.

Body 96 fingers in length

 

The arm, from the wrist line to the elbow, has one foot, and from there to the center of the arm another foot, making two feet in total; when converted to fingers, this equals thirty-two in length from the wrist to the shoulder, as stated.

Arm 32 fingers in length

 

The sword, from the tip to the pommel, being of the standard size, measures four thirds, which make four feet, which, multiplied by 16, results in 64 fingers in total length from the pommel to the tip.

As mentioned above, the arm from the wrist line to the shoulder is two geometric feet, and the sword is four feet; when held in hand, the pommel reaches the wrist line. Thus, adding the 64 fingers, which is the length of the sword, to the 32 fingers of the arm, it is found that the combined length of the arm and sword is 96 fingers, which matches the height of the man’s figure (as I have assumed), clearly recognizing the proportion between the man and the sword. By making the shoulder the principal center of the arm, one can describe a spherical surface with the arm and sword, with the arm and sword acting as the semi-diameter of said sphere.

Given all these measurements and proportions under this affinity, I present the following demonstrations to prove, both philosophically and with the mathematical evidence from Arithmetic, Geometry, and Astronomy, which angle has the greatest reach. Through the degrees of the sphere, their value will be known, adjusted by Arithmetic with clear evidence; and by Symmetry, the measurements of a man for the use and perfection of this science, as mentioned.

Proceeding to the demonstrations, I say that with the man positioned with his arm and sword, as indicated by A.B., with A being the center and interval up to B, if the arm and sword were to describe a circle over the center A, and moving the tip of the sword indicated by B, passing through F.Q.E. until returning to B, a spherical surface indicated by B.F.Q.E. would be formed. The sphere, according to philosophers and astronomers, is divided into four quadrants, each assumed to be 90 degrees, which, multiplied by four, make 360 degrees, the graduation and value given by philosophers, as indicated by the demonstration with the letters B.F.Q.E.

Demonstration

Angles of the sphere

 

They also consider it with eight right angles, each of 45 degrees, which multiplied by 8 make the same 360 degrees, as demonstrated by the letters B.O., O.F., F.T., T.Q., Q.Z., Z.E., E.D., D.B., where the same 360 degrees are found that the four quadrants have.

Value of the Angles of the sphere

 

The same will be found if the sphere is divided with two obtuse angles and two acute angles, which equal the same 360 degrees as the four right angles or the eight semi-right angles, as shown by the letters B.G., G.Q., Q.L., and each of these obtuse angles I suppose to be 130 degrees, and each acute angle to be 50 degrees, both equalling 100 degrees; and the two obtuse angles 260 degrees, which with the 100 degrees of the acute angles, make the same 360 degrees; with which it is seen that the two obtuse angles and the two acute angles equal the same as the four right angles or the eight semi-right angles. Thus, by virtue of the sphere’s gradation, the value of the angles, their quantity, and how they inherit degrees of their value from one another, as will be seen in the following form, is understood.

The angle E.A.B. is 90 degrees. For example: the arm and sword decline to the letter L, losing 40 degrees, and the same for its opposite, since each of them becomes 50 degrees, and in angle E.A.B. it rose from B. to K. so that having 90 degrees in B, it is found, by having moved to the letter K, it acquired 40 degrees, and the same for its opposite; thus, each will be found to be 130 degrees; and this is the value that each of the obtuse angles acquired, since being right angles of 90 degrees, they became right angles of 90 and are found to be 50 degrees; with which the two obtuse and two acute angles come to have the same 360 degrees as the 4 referred right angles.

The ruler that marks R.S. represents the man’s body, is divided into six equal parts, making six geometric feet, and each one of 16 fingers in length; by this ruler, the body, the arm, and the sword are to be measured, serving as a yardstick; the arm and sword are also divided into six parts, as shown by the numbers that are at the perpendiculars, falling on the flat surface, gridding the divisions of the man’s body, which is seen in the propositions so accurately adjusted to its Symmetry and composition.

The line F.A.E. is the perpendicular that divides the sphere into two equal parts, serves as the man’s right vertical side. The letter A is the center of the sphere, and of the arm and sword. F represents the Zenith. And the letter E, the Nadir. B.Q. is the horizon line, which also passes through center A, causing with its section four right angles in it, as indicated by the letters B.A.F., F.Q.A., Q.A.E., and E.A.B., all of which are right angles: with which it is demonstrated the plane at the height at which the Diestro must carry his arm and sword to be affirmed in a right angle, as he places the body and feet in the form demonstrated by the figure.

Having already provided knowledge of the most proportional measurements of the human body, according to the best Symmetry, and the length of the sword (according to the standard of these kingdoms), along with the understanding of the degrees of the sphere and the value of the angles; it is good to examine their reaches, according to Geometry, in the following manner.

Let the line C.D. be one of the verticals, or collaterals, considered on the opponent, and at the center of the Diestro’s arm A. up to B. the distance he has with his arm and sword, affirmed at a right angle; draw from point A. a straight line perpendicular to C.D. by the 12th of the first book of Elements, the point A., the Y.A.J. parallel to C.D., and A.J. will be the Diestro’s vertical, affirmed, as supposed, at a right angle, and upon a right angle; with which by proposition 29 of the same book by Euclid, the angle B.A.J. made by the Diestro’s arm and sword line with his right vertical will also be right: being alternate to the angle J.A.B. equal to two rights, center A. interval A.B. it is seen described by the vertical plane the portion of circle K.L. I say, that rising or lowering from the right angle A.B. his arm and sword, the Diestro, in any part of the sphere, causing with the vertical line Y.J. an obtuse or acute angle, will have in each of these angles less reach than in the right angle A.B. Suppose that the sword and arm lower from the right angle A.B. to the acute angle of 50 degrees at point L., so that the line A.L. represents the arm and sword; it is extended to meet C.B.D. at point D., I say it will reach less in this position than in the right angle, by the quantity D.L. and although the proposition is evident and clear, by the figure it is geometrically demonstrated in two ways.

The first, because in the right-angled triangle B.A.D. the squares of the sides A.B. and B.D. contain the hypotenuse A.D.Y. For more clarity, I examine it by numbers in the following form.

I say that the arm and sword have six geometric feet, as previously mentioned, which make 96 fingers, and the line B.D. equal to J.A. parallel between them, of five feet, which are 80 fingers, and squaring the side A.B. makes 9216, and squaring B.D. 6400, and the sum of both 15616, whose nearest square root is 125 fingers, which is the value of the hypotenuse A.D., of which subtracting 96 fingers, there remain 29 fingers for the line L.D which are one foot and thirteen fingers; and this quantity is what the Diestro’s sword would need to be longer to reach his opponent in D. as it reaches in B., and this same calculation matches completely with the previous one.

If the Diestro raises his arm and sword from the posture of the right angle A.B. to the obtuse angle of 130 degrees at C., through the triangle A.B.C. caused in this posture being equal, and its sides to the triangle A.B.D. that causes the acute angle, because the same quantity that B.D. has is had by B.C. and the angles that the Diestro causes at the center A. are equal among themselves in both postures, A.C. will be equal to A.D. and A.K. equal to A.L. and C.K. equal to D.L. In this order, any other postures, both of the acute and the obtuse angle, can be examined; and in any, it always verifies that the Diestro will have less reach in them than in the posture of the right angle A.B.

The second demonstration in the preceding supposed that the two combatants did not move, and examined the quantity that had to extend (more than the ordinary) the Diestro’s sword, to reach in the posture of the acute angle to his opponent in D. and now will be determined the quantity that the Diestro has to approach to strike his opponent in the same posture of the acute angle with his arm and sword, and it is demonstrated in this way.

Draw through point L. the line K.L. perpendicular to A.B. and parallel to D.C. cutting A.B. at point N. with which we will have two triangles A.B.D. and A.C.B. right-angled, and similar, by proposition two of Euclides, and it will be as A.L. to L.D. so A.B. to B.N. and when of four proportional quantities, the three are known, as in this case A.D. and D.L. and A.B. the fourth will be found by line, by proposition 12 of book 6 of Euclides, and by numbers will be formed a rule of three, saying: If 125 fingers which have the A.D. by the preceding proposition, give us the D.L. of 29 fingers, what will A.B. of 96 fingers give us? and following the operation, will be found the fourth proportional B.N. of 22 fingers, which is the quantity that the Diestro diminishes from his reach, being in said posture of the acute angle at A.L. than he has affirmed in right angle A.B. and this quantity of 22 fingers, is with which he has to approach his opponent so that he can reach him, giving compass of the same quantity from point J. to point M. with the center of the arm A. will pass to point V. and his vertical in V.M. and the line of the Sword from point L. to point P. and this quantity (which as said is of 22 fingers) is the advantage that the right angle A.B. has in reach to the posture in acute angle A.L. which is what was demonstrated.

The same result would occur if the Diestro were affirmed in obtuse angle A.K. if there was any part of his opponent’s body he could reach; because the triangle A.N.K. are equal in everything to the triangles A.B.D. and A.N.L. as seen in the figure, which is not demonstrated to avoid repeating the same: and it is noted, that if the Diestro varied the postures in obtuse and acute angle, that are of more or less degrees of the sphere, each one of them can be examined by the order that I have had here in the two preceding ones, adjusting the angles, and proportions and the rest, according to the postures, or rectitudes in which the Diestro can be found affirmed.

Lamina treinta y tres, y vltima del Libro ſegundo.

 

Plate thirty-three, and last of Book two.