🏠

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.

First Book

Frontmatter

To the Divine Word Incarnated

By FRANCISCO LORENZ DE RADA

To whom can the Sword be dedicated with splendor, if not to the God of Armies? (1) To whom, if not to the one who came to overthrow the aerial Powers, with the most hidden cunning schemes, (2) evacuating the Principalities (3) from their allowed usurped domains? With a two-edged Sword in the mouth, and seven brilliant Stars, you let yourself be seen after the hypostatic union. (4) The variation not used of the instruments, qualifies the success of the sites. Light in all letters has been a Hieroglyphic of Science and Doctrine: The Sword, a noble instrument of defense, or revenge and varying the places, made the Skill show off its greatest marvels: for although the site of the Sword is the belt, of the light of Science the mouth; to render rebellious, Swords of two edges are made the lights: brandishing the rays of Science, for Science is the best Sword.

(1) Book of Isaiah 1:24

(2) Gregorius Magnus. 34th homily in Evangelia.

(3) First Epistle to the Corinthians 15:24

(4) He had seven stars in his right hand, and from his mouth came a sharp double-edged sword. Revelation 1:16.

 

Scripture has no voice that does not fill the greatest scope of human subtle intelligence with mysteries: light is seen in the hands, and Sword in the mouth. Against the Prince of Darkness, the idea was cleverly forged. If the Sword were in the hands, it would defend, not teach. If in the mouth the splendor of the Stars, his doctrine would enlighten, but not defend: and the rays are moved away from the mouth, fleeing from the hands the steel; because the blazon of the one who prides himself on being Skilled consists in defending by enlightening, and in enlightening by defending, with the light of Science becoming a Sword that illuminates, and the Sword being a star that cuts; that the knowledge shines in the streaks of the adversary, and cuts the intentions that the enemy fabricates.

If the Sword were placed in the hand, in that mysterious portrait the Soldier would be seen, not the Master, separating the practical from the speculative. If the Stars illuminated the mouth; it would register to the description of a Master without the executions of a Soldier, making divorce the theoretical from the practical: and the Sword is arranged in the mouth, and the light of the doctrine in the hand; because the sovereign degree of Doctor is linked with the illustrious title of Captain General; for in the greatest battle you wielded the Sword with skill.

It was a challenge in which you defeated the devil and the world, relying on the sublime in the hidden marvels of the art with which he who fought so confidently was defeated, thwarting his schemes (achieved by the neglect of men) without resorting to power, nor majesty with whom the triumph is not so glorious, for the adversary is inferior; but in the attire of man, a fragile condition (and by weakness found in the first man) in whose duel, as nature, the enemy was judged to be superior.His malignity deceived him, blinding him with the custom of winning: and for more disgrace, according to Augustine, your Sword was not of steel, but of wood, admiring for the instrument in your crowned temples the laurels, and in it the greatest sensible confusions.

There, in the plain of Paradise, seeing man as your creation, and as yours, his adversary; devising tricks, with zero movements and wanting to test his malice to where his skill reached, guarding the Castle with all the military precautions, which you had given to Adam, and his successors; intending to enter as a spy, to choose a place and means to conquer the square.He came to capitulations with the besieged, which seemed advantageous, impossible to achieve, easy to promise in one who does not keep words, and Adam chose a means of proportion, which was not, because the compass was mistaken, from which originated the original stumble: for it was, inducing pride by a curved line, what grace had to achieve by a straight line: and thus judging the first man of the world to have subjected the Sword of his adversary (which undoubtedly he would have with a deviation) he found himself with a vertical wound, from which came and comes our lamentable pain, lost the forces, and the weapons: increasing with the challenge the glory of the insolence of the adversary, for lack of skill, the combatant was defeated in the first battle.

You felt in man how punished he was, and the art of fighting, noting the place, and the instrument with which he was left with the breaking of the clay so common; not appreciating the triumph, but learning with the same art with which he had won. You took the same weapons from the same punished nature, in which his confidence was chastised: for when he counted the triumph by the number of wounds that the body received, intense pains; he was tightening the form, to whom he took away the laurels, ending up in the conclusion without value, for the novelty of being defeated by nature, who had defeated him, gaining laurels that before paid tributes: for your Sword was not content with giving her freedom, without taking it from the same one who took it away. Not in vain the Prophet applauds you. He drags triumphs, avenging the offense of the one who committed it. It is justice that the Sword surrender, to whoever teaches skill. Even the lightness of the gift is made appreciable by one’s own esteem, not having any other better jewel to dedicate: soliciting that in your defense (being our defense) a Sword that teaches how to fight is seen, and a light with which the Skilled one, can and can defend himself; from the rising of the sun to its setting, may your name be praiseworthy.

REVIEW OF REVEREND M.FR, FATHER MANUEL de Villarroel, Doctor of Theology, Chair of Scripture, and General Preacher of the Religion of Saint Benedict,

By commission of Mr. Don Nicolás Alvares D Peralta, Vicar of this town of Madrid, I have seen three volumes on the Skill of Arms, their author Don Francisco Lorenz de Rada. Knight of the Order of Santiago, Marquis of the Towers of Rada, Chancellor Major, and perpetual Registrar of the Kingdoms of New Spain; and I confess, that the remission of the review struck me as novel, as is the matter of my state, and of my profession the Arms, fearing before leafing through the Book, the judgment in mine, which made Hannibal, hearing precepts, and rules of the Philosopher Phocion: but led by curiosity with the shield of the precept, I discovered all the argument adjusted with accuracy to rational and natural Philosophical principles, on which he erects the entire beautiful edifice of Skill, working with precision the principles of Mathematics.

Justus Lipsius; from Milit.Roman. said, that the supreme consisted in Science, in Art, and in Practice. The Philosopher in his politics reduced it to Dialectical terms, of Definition, Composition, and Resolution. Only the voices are distinguished: for the definitive corresponds to science, the composite to art, and the resolutive to practice. The Author comprehends all of this successfully in the three volumes: in the first the scientific in principles, in the second the artful in precepts, and in the last the demonstrative in conclusions and practical resolutions. The most difficult thing in the actual exercise of the Sword, is the observation of the precepts of science: that even if for another intention Cicero said: Silent leges inter arma (Laws are silent among arms). But in these volumes it reaches the non plus ultra with the tie of speculation, and exercise, explaining in what is done, and doing in what is said: passing from the generic to the specific, and from this to the individual: from science to the art from art to the operation, which is the intention; and all with scientific division, giving each other a hand the ones that were born queens, Letters and Arms.

A study without a rich vein, nor do I see what good a rough talent can do: thus one thing helps another, and conspires amicably

Horace said. Their divorce is always sadly lamentable.Spain mourns only Letters in the wise Don Alonso. France mourns only Arms in Charles VIII. It is necessary to unite them with Duarte, King of Portugal, who erected as his blazon the Lance surrounded by a Serpent. Courage is breath with faintness, if it does not have the skill of: science. Among the heroic symbols, none greater than that of Frederick III in the painting of an armed arm, writing in a Book, and the Epigraph: Hic regit, ille tuetur (This one rules, that one protects). With the precepts of the Books one learns to fight, with the Sword one defends the laws that the Books give: hence came the Proverb. Consfilum & auxilum, mens & manus, animus & gladius (Counsel and aid, mind and hand, spirit and sword). The splendor of the Sword is not risked in the hands of a scientist, rather for greater luster, science puts it in greater commitment. The Egyptians, in all mystery, learned in the academy of Memphis to paint Mercury with two faces, one aspect of an old man, another of a youth.In this age they expressed valor, science in the elderly, for the experiences of his age: and they united the extremes of science and bravery: because the greatest valor surrenders when skill jumps. What of our illustrious Solorzano case in his Political Emblems!

These are the double duties of Pallas and Minerva’s dual names
By the sword, wisdom prevails & wisdom protects swords:
These ones strike, she teaches those ones to strike back.

And Fortunatus:

With laws you rule weapons, and with weapons you guide laws:
Thus the path of diverse arts is traveled together.

No one better than our Author can boast of Mercury in such a noble glorious faculty: as Hippocrates said in arte: To discover something of those things, which have not yet been discovered, which itself is known, rather than being hidden, seems to be the desire and the work of science: achieving with ingenuity the subtlety in the application of principles, the novelty in the invention of demonstrations, and the inventiveness in the clarity of conclusions with a rational order, both in the speculative and in the practical: being able to say now of the Sword, what the other Politician of the Compass: I guide & I am guided: for there is no movement, or time in its operations, that are not governed when they govern.

Some of those who, as Seneca said, prefer to disturb the Republic rather than command, qualify bravery, not by strength in the arm. This vain opinion is dispelled by the blazon of Viliffes and the mockery of Ajax.

You carry strength without mind.
You can fight, choose the time of fighting with me,
Atrides chooses: you only benefit from the body,
We with the spirit. ― Also in our bodies,
Our chests are stronger than our hand: all vigor is in them.

Nature can make the brave, but not the skilled: and without skill, there can be no bravery. The experts will be victorious in any combat, even if they are outnumbered: for without skill, bravery is a rush that damages itself, and the larger army will account for more victims to Mars. Antigonus founded this when, on being told of the excessive number of opposing combatants, inexperienced in military art, he replied: There is not one Soldier among so many who serve. And confident in his skill, Scipion Africanus in a not different situation, said to those who counted the enemy hosts by thousands: How many do you count me for? A skilled man is worth many: in whose concept Lucan said: There were two fighters in the situation; an army, and a man;

Any page of this book is flattery for the Spanish spirit, as its mercantile genius is polished, encompassed within the bounds of the art of offense and defense, without the intrepid nature throwing itself to be wounded in order to wound, a caution charged by Vegetius: It is not a skill, he says, that in executing the intent with the sword, the opponent reaps it. It teaches not to carry the sword as an adornment or stumbling block, when for those unskilled, it often serves as an obstacle. It teaches, along with dexterity, the luster of those who honor and are honored with the sword. Not only to carry weapons, but how to carry them: I mean, only to deal with them, because a sword without dexterity is not a sword: and there’s little difference between the coward and the unskilled; as one and the other merely carry the sword to hold it, but not to wield it: with the Author aiming not only to recommend the instrument, but also its weighty and careful handling; because it makes men. I can say with Seneca in Epistle 84. Such a spirit should be, that there are many arts in it, many teachings, examples of many ages, but all in agreement. Finally, I have not found anything that could stumble the most scrupulous, as there is no proposition that opposes our Holy Faith, in whose defense directs his study, and consecrates the steel: or that contradicts good customs: for which I think it should be granted, and appreciate the license he asks: With all due respect to a better judgment. San Martin de Madrid, and July 2, 1703.

The Master Friar Manuel de Villarroel

LICENSE OF THE ORDINARY.

We, the Licentiate Don Nicolas Alvarez de Peralta, Deputy Vicar of the town of Madrid and its District, Judge in the Court of the Nunciature of these Kingdoms, and Apostolic Proto Notary, &c. By the present, and as far as it concerns us, we give permission for the three Volumes of the Skill of Arms, composed by Don Francisco Lorenz de Rada, Knight of the Order of Santiago, Marquis of the Towers of Rada, Chancellor Major, and perpetual Registrar of the Kingdoms of New Spain, to be printed and published, considering that by our order they have been seen and recognized, and they contain nothing against our Holy Faith, and good customs. Madrid, November twenty-fourth of one thousand seven hundred and three year

Lic. D. Nicolas Alvarez
de Peralta.

By his command
Domingo de Goitia

APPROVAL OF DON JUAN ALONSO, of Muxica, Captain who was of one of the Companies of the Regiment of His Majesty’s Guard, his Cavalryman, and Gentleman of the Mouth, and Lord of Aramayona del Muxica. M.P.S.

By order of V.A. I have seen, read, and observed the three volumes that Don Francisco Lorenz de Rada, Knight of the Order of Santiago, Marquis of the Towers of Rada, Chancellor Major, and perpetual Registrar of the Kingdoms of New Spain, has written on the Science of the Sword, and wishes to bring to public light. In all of them, I have found no period that contradicts the statutes of a well-advised policy, nor clause that opposes the Laws and Ordinances of these kingdoms, but rather many useful things for the public and particular interest; because the license he requests should be granted, otherwise Spain would lose the noble works of this Author, and the scholars of Fencing would be without the erudite efforts of such a great subject; Spain would lose the glorious vanity of having such a great Writer, the convenience of the ambitious of the Science of the Sword to enjoy his revelations; therefore, it is just to ask for the license, and it should be given: Salvo meliori, with which my commission expired. But the obligation of affection does not expire, firstly to his many qualities; and secondly to the role of Soldier, which we both have exercised, where the affection of a martial correspondence is contracted; and I confess with sincerity that I am extremely fond of him, for his many and superior qualities; I leave those of his known quality, in which his happiness was due to the fortune of his birth, with which the highest providence had the direction, that he himself could choose for its nobility. This, which does not matter, wanted his cradle to be illustrious, because provident (most of the time) wants high progress not to have unworthy principles: and thus, he who turned out to be so superior in matters of valor, science, and studies, it seems that he should not lack the circumstance of nobility, so that the number of his successes would be complete; His valor is well demonstrated by the positions he has occupied: From science and studies; these Books he has written: From valor; in the occasions where he demonstrated skill, which only the spirit illuminates; so that it can be seen, that what was learned in the rehearsal with the black Sword is represented in the theatre of the white ones: without valor, study is useless, since without it there would be no service in the occasion: of the sciences, or study, because without it there would be no fever in the occasion: Of the sciences, and studies, his Works will better demonstrate than my praises.

They arrived (for my happiness) his Books to my hands; and the admiration to my discourses; and although admiration in the phrase of an erudite, is the mother of silence, sometimes the voice bursts out, by the recognition of the greatness that is admired.

I will not dwell on authorizing (if I could) his proposed demonstrations, because if he demonstrates without fallacy, he makes evident what he says, and what is clear in itself does not need proof; nor will I delve into the counterpoint of his doctrines, for fear of what happened to the orator Onosander with Hannibal of Carthage, who entered to hear the orator, and wished for him to hear the soldier, and said: He who has not experienced his doctrine will know the Art poorly: for jobs that consist of execution can hardly be known with mere knowledge. This I have, for my love of Mathematics, in whom this most noble Science of the Sword has its foundation, or to whom these Sciences (according to the opinion of this Author) are subordinate.What I can say, without my judgment seeming flattery or boasting, is (for that correlation, consonance, or combination of some Sciences with others, and of them with the written word) that D. Francisco treads new orbits of this Science, or recent spheres of this Art, being the inventor of a Science and Art of an unthought-of System, and of a sphere not yet constructed, and that, as a new Columbus of the Sword, he supplies gulfs of difficulties in Dexterity, and seas of discourse in demonstration.To find the new world, in the Castle, which he points out surrounds the Swordsman with the Sword; in the System that he imagines, that he mentally constructs, his most acute genius represents invisibly, of whom we can say what of the most subtle Astronomers, that if the Celestial Systems they imagine are not thus, they could make others in that way, not lacking reason; and thus we will say of our Don Francisco, that if the Swordsman is not thus fortified with the Sword in the Cylinder that he assumes, he could be thus, without opposing the truth.

Although it seems that he stole models, sketches, or outlines from our ancient professors of this Science, it cannot be said that he who invented new courses, flaming parallels; various demarcations, different poles, would make use of the old Charts, nor of the ancient detours; although it is true that all seek an end, not all go by the same path.

Until now, the path was marked by the circumference of confusion, by the periphery of obscurity; however, in these works, enthusiasts and scholars will find new short paths to follow; and although it may seem that he diverges into the labyrinth of other sciences, and into the knowledge of different histories, which could be criticized, what is diffused is not learned with clarity, nor is what is concise good, if it is ignored because of obscurity. A short enigma that is proposed is more tiring than a lengthy explanation that is understood; and when it is a foreign concept, enclosed in the obscurity of a hieroglyph, or tiring because of an enigma, it is a secret without a key, and a treasure in the field, or the arcana of Ramon Llull, who says, he reveals the philosopher’s stone, and the more he hides it, the more he teaches it.

Here, then, those fond of this virtue, Eutropelia of the Science of the Sword, will find infinite volumes, and in them the most intricate concepts. There is no Art, or Science that does not subordinate it. Here, then, we see Plato defrocked, Aristotle refined, Saint Thomas attended, Copernicus refuted, Euclid revered, Archimedes observed, without another infinity of Authors that he handles, more as a unique Scholastic, than as an excellent Soldier, which he is.

Here, understanding will be satisfied with the sweet nectar of truth, everything tested by demonstration, without the vain error of fallacy, or the unworthy wrinkle of sophistry: In the end, in these Works, those zealous of this Science have fertile fields of erudition, beautiful hanging gardens of the Sciences, without having other volumes to dry up, or other Treatises to understand. And so, we all owe Don Francisco immortal thanks for such a universally heroic benefit; for the cultivation of agile swordsmen, at first glance, seems to have no more use than that of the individual professor; and this, which seems a unique particular convenience, becomes a universal public benefit; because who knows that the only way to save an individual from a danger, may not become a universal public convenience, because this one who risked himself, could be a swordsman of such high hierarchy in quality, and personal endowments, that his absence would be a common public loss; and when this one was nothing more than the lowest vassal, it was enough largesse, that through dexterity he saved himself, and his opponent with the conclusion of this Science, from the unhappy insult of a fall, a damage in which nature first suffers, from which an individual is taken, for whose preservation, many volumes would not be in vain; for the sole one, according to the doctrine of Saint Thomas, Christ came to redeem; if this is man in eternity, much will be the proportion preserved in humanity: secondly, the King loses a vassal, who, as father of all, it is the same as taking away a son: the People a companion; so everyone loses in the outbursts of fury: the species its individual, the King his vassal, and the People its neighbor: and if all this is taken away, saved, and removed by dexterity in the occasions of wrath, we can give, as I have said, immortal thanks to the Author, who gives rules against the errors of wrath, and against the absurdities of a fury.

From here it follows that if there were many enthusiasts for the Sword, there would be more inclined towards war, where its jurisdiction is exercised more, although in the immensity of fires that have been invented, there is little room for its exercise; however, the one trained to not fear one will generate spirits to oppose many, as it is easier for the one who does not fear one to dare against many, than for the one who has a natural horror of all.

To have Soldiers, the utilities of the Republic are evident, since peace is the effect of war, and in the cultivation of this, that is seconded, and the laws speak if the arms are silent (although they do not live without each other); Arts shine and Sciences glow, trades are encouraged, and jobs grow, Religion increases: thus, for everyone, this public display of the fatigue of this studious subject is useful. And this, in the end, is my opinion: Salvo meliori. Madrid, and November 3, 1703.

Don Juan Alonso
de Muxica.
SVM

SUMMARY OF THE PRIVILEGE

Don Francisco Lorenz de Rada, Marquis of the Torres de Rada, &c., has privilege from our Lord the King and the lords of the Royal Council to be able to print three volumes of the Science, Art, and Experience of Spain, as more extensively stated in its original, dispatched in the Office of Don Bernardo de Solis, Secretary of our Lord the King, and his most senior Chamber Clerk of those residing in the Council. In Madrid, on the 10th day of the month of November 1703.

ERRORS CORRECTED

I have seen these Books, titled Nobility of the Sword, whose splendor is expressed in three Books, composed by Don Francisco De Rada, Marquis of the Torres de Rada, &c., and it is in accordance with its original. Madrid, and June 9, 1705.
Don Jachin Benito
del Rio y Cordido.
General Corrector by His Majesty.

PRICE

Don Bernardo de Solis, Secretary of our Lord the King and his most senior Chamber Clerk of those residing in the Council; I certify that having been seen by the lords of a Book titled Skill of the Sword, composed in three volumes by D. Francisco Lorenz de Rada, Marquis of the Torres de Rada, &c., which with permission of the said lords has been printed, they priced at twelve maravedis each sheet of the said Book; which appears to have two hundred and eighty-nine, without beginnings or tables, which in this regard amounts to three thousand four hundred and sixty-eight maravedis. And they ordered it to be sold at this price, and this Certification to be placed at the beginning of the Book. And so that it is known, I signed it in Madrid on the tenth day of the month of June of the year seventeen hundred and five.
Don Bernardo de Solis

TO THE WRITINGS, AND ADMIRABLE DEMONSTRATIONS of the Skill of the Sword and Dagger, both in Spanish and Italian, brought to light by the most skilful and distinguished Don Francisco Lorenz de Rada, Marquis of the Torres de Rada, by Don Joseph Garcia Hidalgo Alvarez y Barruezo.

SONNET

Destreza has arrived at the last end,
Its accuracy reached the heights sought;
From theory to execution it’s brought,
With certainty and truth it does defend.
Now the author who came last is first,
With discourse and proofs so well wrought,
So geometrically designed and taught,
That in Rada another Euclid immersed.
With his teachings, one cannot ignore,
How to defend and how to strike,
In studying his works, one will explore,
And find amidst danger, how to thrive.
To the skilled executor, nothing more,
Is left to do, nor to contrive.

OF AN AFFECTION TO THE AUTHOR

SONNET

Your subtle arguments, shown with such grace,
Are, Skilled Rada, a sight of sheer delight;
In lines and angles, I perceive the trace
Of geometric axioms, sharp and bright.
But with your sword and hand so well applied,
The doubtful will admire, seeing the true,
For deceit and falsehood, they have died,
In sight of such elevated marvels anew.
What was once much, now appears as none,
Seeing your knowledge, your discerning mind,
Crowning the empire of the Sword, well done;
And since you’ve ensured its greatness, well defined,
With theory and practice, under the sun,
“Non plus ultra” to your skill, we find.

BY THE SAME AUTHOR, SO SKILLFULLY adept at wielding the sword, as well as writing about its use in a mathematical and philosophical manner.

D. Felicianus Gilber of Pisa Fernandez

DODECASTICHON

The Olympic laurel yields to you from the arena’s spear;
A blooming Palm adorns your palm.
What the compact [sword] covers, you reveal its secrets, Pyragmon;
You’re accessible, and Mars shows you a safe path.
So easily you reveal what’s in the sword and in the volume; how
Pallas Athena loves your warfare; cultivated Minerva cherishes [you].
Your right hand is as good in camps as it is in writings; it first
Occupies the place in the twin fortress of Pallas.
You prove your writings by the sword; you fix conflicts on the leaf;
In the matters of sword and leaf, you have sharpness.
You fight writing; you argue contesting: hence,
Undoubtedly, you shine like Caesar in both ways on the page.

FROM THE SAME TO THE AUTHOR. TENTHS

If the portrait of the valiant Macedonian could be made by anyone who experienced any fortunate event: whoever presents your valor here fearlessly, since you are, if not the first, a second, and without a third, Alexander with the Sword.

Seyano could well be the swift, ominous brute; and against the name, unlucky could be the Tholosan gold: but that which (oh Rada!) your hand wields the Sword skillfully; without luck on the left (which could not be a crown) will achieve, as in Bellona, the advantages of a Master.

It was taught by some, reigning in honorable peace; at all times glorious is the Skill of the Sword: doubled glory is acquired with the wonders of such Art, the one your valor shares, since you generously bestow it, burning in funeral pyres all the noise of Mars.

Who, then, will be idle, even if they do not feel encouraged by such a generous study? Let useless rest cease; let homage be paid to Pallas: and since you mark the exercise of the Sword; let us leave the vice of idleness, let us give wings to Steel.

And since in a public fair you generously flood the world with your doctrine, which is no less wise than it is serious: no one in such a noble matter; no one in such grave matters, folds the keys of money; because if he spends freely before, in the one who instructs and learns, the world will see what you know.

The Temple of Fame, open (reward for your deserved sweat) although divided in many, offers you all its doors. You find both paths of Arms and Letters: the entrance cannot be denied to you; since you know how to overcome it in sum, to the sheaves of a Sword.

To this Book, then, which carves an immortal Temple to your name, in which where man learns, one and another example is engraved: I contemplate it so happily, that in the leaves of eternity, your heroism elevates, through Lines that the World praises, from the Temple of Fame, to that of Immortality.

TO THE READER, HEALTH, AND HAPPINESS.

Polidoro, Virgil, and other worthy men dignify, how much they rejoice in common and public benefit.

The ancient philosophers, the more arcane they were, seemed to elevate their knowledge more, not divulging the height of their concepts, and the interior of their speculations: for this they used fables, hieroglyphics, terms, and means that their intelligence required, consistent study from which caused various interpretations, being a single truth of the Sciences.

Plato had Socrates as his master, and he distinguished himself by forming new ideas: what he esteemed as divine, he hardly explained it to acquire such renown. Aristotle, the great disciple of Plato, did not emulate Plato, but revealed himself to be opposed in style, in logic, in arguments reduced to more precision, to more categories, and distinctions; thus fitting the name of Philosopher by antonomasia: and yet they noted him as obscure, and he needed the comments of Theophrastus his disciple, Alexander of Aphrodisias, Averroes, and others, which were perfected by Saint Thomas: adding afterwards so many, and such learned men as in public schools multiply opinions, however those are valued, that with greater evidence convince with demonstrable reason to the understanding, as much as our limited human capacity admits, which being so, can advance more and more in Sciences, and in the Arts.

Its nobility is qualified, either by the superiority of the objects, or by the infallibility of the means by which they are investigated. By the object, the first degree is granted to Theology, to Metaphysics, to the grand construction of the elemental and ethereal regions, the structure and composition of man, a brief world in the physical, and great in the powers of the Soul, capable of reason and free will, with aptitude for successes and errors, merit and punishment, prepared for defense and offense, both in singular combat and in aggregation of many, operating with Mathematical Science: which, if not the most noble by the object, is superior in the infallibility of its means reduced to demonstrative arguments.

And if Philosophy embraces all subjects of nature; Mathematics includes all continuous and discrete quantity, and in it movements and operations; its division admits various species, the main ones are Geometry, Arithmetic, Astronomy, and Music.

Geometry is subdivided into Cosmography, Geography, Hydrography, Chorography, Topography, Geodesy, and Stereometry.

Cosmography comprehends from the first movable, to the center of the earth. Geography the part of its globe, whose surface is habitable. Hydrography the seas, and the waters. Chorography the Regions. Topography the Places. Geodesy the fields. And Stereometry the buildings, towers, hollow bodies, vessels, etc

Arithmetic has discrete quantity as its subject: it is subdivided into collection of numbers, subtraction, multiplication, and division; these are the first four species, from which the others are derived, as from the multiplication of one number by another, the area is produced, which if square, arises from the number being carried in itself, or in another equal to it, and if unequal, gives the length of the larger number, and the lesser the width: and to the square power is named “cenloz” and if the number is carried twice, once in itself and another in its product, the result is the solid, which they call cube, or “censo”, recognizing, and finding by the root the power, and by the power the root, which results from multiplication, subtraction, and division, and the same in the roots of various species, and their powers, with which the other terms, or names, are considered and recognized, from which the major art is formed, which they commonly call Algebra, or rule of the thing; and from one and the other, we proceed to the exact knowledge of continuous and discrete proportions, as Euclid teaches, and is done by sines and logarithms; and from all this follows the Symmetry of distances, elevations, and depths, and of plane and solid figures, spherical, cylindrical, and conical.

Astronomy is divided into two terms, or species, according to the authors have used differently at various times: in modern times the term, named Astronomy, includes the consideration of the movements, and the places of lunar bodies, and stars, their magnitude, and placement.

Astrology is considered the observation and judgment of the influences, aspects, and qualities of the Stars, and how they operate on the inferior elements, and bodies: and to the professors they operate in the Judiciary, Genethliacs, and Chaldeans, etc. Celio Rodiginus considers Gnomonics as a species of Astrology, which works in the knowledge of the shadows, caused by the lights of the luminaries through dense bodies, from which results the construction of clocks: and it is given as the inventor of this species to Anaximander, disciple of Thales of Miletus, as Diogenes Laertius reports.

Meteoroscopy is that species of Astrology, which inquires about the distances of the Planets, and Stars, the differences in their elevations, courses, and movements, according to various hemispheres.

Dioptics is that, with which are investigated the circles, and the intervals of the Sun, Moon, and Planets, caused by different aspects, of which Astrology makes so much use, in which is granted Astrolabe, with tympanums, and spider, is attributed to another Ptolemy (who they called Synesius) according to Andrés Diucio.

Music is divided into Theoretical and Practical; the speculative which is the Theoretical, is based on harmonic proportions, different from the Geometric and Arithmetic, that these are caused by discrete or continuous qualities; and Music of proportional harmonic numbers, as in the Double of the Diatessaron to the Diapason, which is like from 4 to 8 will be a harmonic proportional number, exceeds the first number 4 by 1.⅓; and it is exceeded by the number 8 by 2.⅔, which is the same Double; proportion in which the extremes 4 and 8 are, in which the excesses 1.⅓ 2.⅔ have.

The practical, or multivariate Music, is the one that through diversity of organs expresses and produces concerto, and harmony; and as the human voice exceeds in sound the other voices (not by nature, but by Art), it is reduced to compound proportions in the mind, where the harmonic concepts are the nerves, or index of formal harmony, which all together is called Music. This is what the Ancients signified in the fable, and from them the name Music was derived, as Andrés Diucio explains.

From such principles, making use of Geometry and Arithmetic as subordinate, the knowledge of machines, mechanics, military art, and the Skill of Arms, down to the most individual, Queen of all, which is the Sword, corresponding to the Sword, adornment, strength, and defense of man, used and esteemed by the Ancients and Moderns, with the qualities, and differences that will be shown among the introductions of these Books. As in Philosophy, Sciences, and Arts, the distinguished men in them, have sought to immortalize themselves with their writings; so too there are many who, driven by such glory, have written and brought to light various works of the Philosophy, and Skill of the Sword alone, and defensive and offensive weapons, which usually accompany it.

In Spain, imitating Plato in the dialogic method, the Commander Geronimo de Carranza wrote with the erudition, and eloquence that is notorious, titling his Book (which came to light) Philosophy, and Skill of Arms, showing in it his great talent, and knowledge he had of other Sciences; although as obscure as his contemporary in Italy Angelo Vigiano, who with the same Platonic method wrote on the same subject, forming trees to conceive the quality of the movements of the Sword, in parries, and blows: and both authors proceeded with such obscurity, that Carranza needed to refer to other Books, offering in them the individual precepts for perfection, and teaching of this Science: and as this work (which was expected) was not printed, nor is there any news of him leaving it in manuscript, the most essential of what was achieved by such a great subject is lacking.

And Don Luis Pacheco de Narvaez (like Aristotle to Plato) succeeded him, reducing to more precise and clear terms, with which he came to be greatly esteemed in the nations of Europe; and in Spain, for his merits, Don Luis (like the Philosopher of the great Alexander) was a worthy Master of our lord King Philip IV (who enjoys God’s favor), the Great, the greatest of the Monarchs of the Orb, who accepted the name of disciple of such a wise Master, as Botero demonstrates, and I (like Theophrastus) while not presuming wealth to comment on his writings, fulfill (at least) by writing in the same Science of the Sword, owing most of my encouragement to the affection that the writings of such a great man put in me: for having been born with a martial inclination, not completely disfavored by Minerva, nor viewed with bad aspects by Jupiter, and Mercury; I was barely eight years old when the name of the great Don Luis, whom everyone venerates as the Prince of this Science, struck my ears: this was the cause of awakening in my tender age such a passion, that it forced me to collect all his works, studying them with such fervor, and affection, that although I was not fortunate enough to be able to hear his live voice, I was favored by the same Planets as Don Luis; with these, and more than 28 years of study, that I have in his writings, and in those of all the other Authors, who have treated this Science, to whom I have examined the most hidden of their thought with all mathematical rigor, demonstrating it with my arm, and Sword for more than 20 years, both in this Court and throughout Europe, seeing if not the whole, at least a large part of what it cost Don Luis more than 50 years in the speculative and practical, in giving as he did, knowledge of the power of man in his parts, for the use, and perfection of the individual operations both ordered and disordered, deduced from his organization, and body composition, with rules, and observations so adjusted, that in order not to touch on his perfection, I refer to the much that in so many Books he did not leave taught; where the most curious will find, to his desires, always falling short of my praises in his praise, without admitting passion (for the affection his writings deserve) since the estimation is due.

I omit much (in order not to prolong this discourse) the repetition of the names and works that Italians, French, and Northern Europeans have published on such a great subject, each one applying themselves to the form and use of the Sword, according to their Nation, following various opinions in postures, and in movements, defending, and offending, that in order to compile them in a brief summary, large volumes are needed, as can be seen in Gerard Thibaut, a modern author, native of Antwerp, whose book is so large, and with so many prints, and so costly, that when it had nothing more than the decoration of them, it deserves worthy esteem, owing much to all those who have stayed awake to communicate the fruit of their labors, to find the perfect Skill of the Sword; noble instrument, frequent, and necessary to every honorable man.

And having seen so many authors, and through them recognized, that despite so much having been written about this Science (which it is), it has not been fully understood, as there are so many different opinions in speculation and action without complete satisfaction of Philosophers, Mathematicians, and practitioners, with only one goal in mind: self-defense, in offense against the opponent, in which by reason the means of achieving such should be so certain that they become infallible; since the Skill of the Sword is reduced to the combat of two, which is called a duel of Duela currency, which is commonly named two to two, according to the feeling of Paulo, and I to the intended argument thus.

In the Art of War (which is combat of many against many), the precepts, maxims, and method should be one. In the duel (combat of two), which is more abbreviated, the same reason applies, and even more strongly, due to the known equal weapons: therefore, in the Skill of the Sword (accompanied or alone), which is the main instrument of combat, the precepts, maxims, and method should be one. The greater is proven, recognizing in the Writers and Historians, the times, and the ways of warfare, which are ordered for combat, according to the weapons, persons, and positions; varying only as they are varied: the lesser is manifest, the consequence is inferred.

With this knowledge, we can qualify the Skill of the Sword (accompanied or alone) as a Science, in which the mathematical disciplines are subordinate, just as in Philosophy: from which it results that the Skill is a demonstrable Science, and most noble for the subject (which is the man with the Sword in hand) and for the certain way of proving, which is mathematical. This conclusion is true, and by it, and other foundations, I decide to take up the pen, without limiting the spirit of so many, and such learned ones who have written, since I follow the infallible means of mathematical demonstrations; both in composition, as in resolution, which are the two poles, or bases on which the Sciences rely; the former because it is a means of teaching, and the latter of achievement, and those who have deviated from these Mercurys, or courses, have lost the way, drowning in the stormy sea of various, and confused opinions, caused by the different thinking, and acting, without having achieved the infallible by the mathematically demonstrable, recognizing by Geometry the species of continuous and discrete quantity, which are reduced to line, angle, surface, and body, and the subject of Skill admits the same consideration: from which it follows that the means of proving Geometry, and the Skill can be one, insofar as both make use of the continuous, and discrete quantity, and of the mathematical entity, and demonstration that is produced from it.

The Skill is achieved through straight and curved movements, with the body, with the arm, and with the Sword; and these cannot be formed without the species of quantity: linear, angle, surface, and body. It follows, then, that Geometry and Skill admit certain demonstrable means: and if they are infallible in Geometry, they are also infallible in the Skill of the Sword, accompanied or alone.

That the movements of Skill, with the body, arm, and Sword cannot be performed without causing some of the species of quantity, is evident; because any point that moves, forms the trace of its movement: for example: The end, or point of the Sword moved straight or curved, necessarily forms its vertigo according to the species of its straight or curved movement; being mathematical, although not perceptible to the sight, the lines, surfaces or solids that are caused by the movement that only tears the air. But if these same movements were made and formed in dense matter, they would be physical and perceptible; from which it follows that if the thread of the Sword is moved, it must cause a flat or curved surface, according to the nature and trace of the movement: and consequently, if the surface is terminated, the movement of the surface or surfaces is demonstrable, by the definition of the cylinder that Euclid gives, saying it is a solid figure, caused by the revolution of a right parallelogram in circulation of one of its sides to the fixed one, until the moving one returns to the point where it began its movement.

And defining the right cone, he said it is the vertical point caused by the pyramid, whose base is a circle of a solid figure, caused by the revolution of a right triangle, on one of the sides that includes the right angle. Nothing in the exercise of the Sword is more proper, and its knowledge more necessary (in my opinion) than these pyramids, of which I have found no written Author in this Science of the Sword instrument, but in Don Luis in folio 26. line 6: of his New Science, where he names cylinders, and pyramids, etc. without applying them in all his works; being their knowledge as necessary as I said: and these figures being so well known by the Philosophers professors of the Mathematical discipline, and their speculation and demonstrations being very ancient; in which Menechmus, a disciple of Eudoxus, and contemporary of Amiclas, very familiar with Plato, is admitted as the inventor, of whom Proclus, and Diogenes Laertius, certify was the first, who put in demonstrable method the conic and cylindrical sections, found by Analysis (as reported by Andrès Diucio) illuminating them with superior accuracy Apolonius Pergeo, from whose Book the last ones were missing, which have been supplemented, and given intelligence to all by the Most Learned Reverend Father Claudio Ricardo noble, native of Burgundy, Religious of the Insigne Company of Jesus who in the most famous Imperial College of this Court of Spain has read Mathematics and brought to light such a useful, and lucid work, that has been printed in Amberes, as a crown of many that he has written: with which in the speculation we will find the most estimable, that benefits the purpose of the Science, and Skill of the Sword, with which the man can hardly make movement, that is not forming some pyramid, or portion of it, whose base many times describes the tip of the Sword, and the cut the surface; and in the centers of the arm, elbow, vein, and wrist are the vertex points; and in the intersection of the Swords, when an aggregation is made, and a contract of one in another; whose axis is imaginary.

At other times the hand describes the base; and the vertex point is considered at the tip of the sword, when it reaches a specific point on the opponent’s body (as will be explained in due course). The definition of the sphere also serves the intention, which (according to Euclid) is caused by the revolution of a semicircle, until it returns to the point from where it began to move; although this definition is more about the structure of the sphere than its essence. This leads to the definition of Theodosius, who said, it is a solid body, contained within a surface, in whose middle is a point that is named the center; from which all lines drawn straight to the circumference are equal. From one and other solid figures, sphere, pyramid, and cylinder, the learned Archimedes discovered and taught the most that we accumulate, deservedly earning, that as an insignia they placed one figure inside another, as Cicero refers.

These principles (so far little noticed in the Art of the Sword) are of such consequence and consideration that without them (in my opinion) the possibility of achieving them becomes quite impossible. This is corroborated by the common maxim of Philosophy which perceives understanding through the organs of the senses, or understands through some analogy of the visible. In the Art of the Sword, the former method is used, understanding through movements, which due to the speed at which they are made and formed, since the sword does not leave a visible trace where it passes, it is very difficult to comprehend with the sense of sight, from where it has to be transferred to understanding; because it cannot be proportioned with visible distinction what physically takes place and is seen due to the accelerated movements of the sword, as is experienced in the rigor of combat, as far as the act is concerned. And consequently, neither can the understanding comprehend, nor can it conceive a formed discourse, from which evidence results in the visible.

However, what is so inaccessible in the physical is supplemented by the means of metaphysical imagination, by the similarity of pyramidal, cylindrical, and spherical figures, or their portions; due to the similarity they have with the proper and contrary movements, no matter how vehement and accelerated they may be, facilitating understanding with mathematical demonstrations that make physical representation perceptible to the eye. In this way, they can come to understand the differences in movements that are made and formed with the Sword: thus more perfectly regulating defense and offense in man, who is the object of this Science.

For greater understanding, let’s take the first example of optics, which through the imagination of lines, angles, surfaces, and bodies metaphysically formed in the air, without being comprehended by the visual sense, produces marvelous effects in perspective; as demonstrated by Vitellion, and the Archbishop of Canterbury in the common work he left written, whose demonstrations confirm our intention: just as painting also demonstrates; with the value of straight and curved lines, light and dark, produced by the outlines of imagined bodies, according to visual proportions, placing them in such a way, that the result of their operation on a plane, deceives the eyes with illusions of light, that perceive apparent things as true. Therefore, sculptural painting was first before brush painting, as inferred from Pliny, and others in different places, conceding the first brush to Apollodorus of Athens, in the opinion of Juan Rungio Gripwaldense; and both methods were born from lines, surfaces, and bodies premeditated ideally for physical works; as also in the speculations of celestial movements, both of the prime mover, and of the other spheres and stars, their appearances, and courses, knowledge results from various figures, found in fantasy, and operated in demonstrations. As can be seen in Ptolemy, in the Great Construction, and in his Expositors, who imagine circles, caused by different stars, and points, and granting eccentric and concentric orbs, different equants, and epicycles, come to exact knowledge of the course of the Planets, aspects, distances, and eclipses, caused by the pyramidal shadows that the Sun produces for the earthly body, which is also seen in Gnomonics, which through the same means of conical shadows gave diverse designs of sundials.

In Cosmography, circles and triangles are also investigated, which distinguish and demonstrate the zones, climates, and places, from where the elevations of the Pole, the diversity of the artificial days, and everything else that includes the knowledge, and use of the natural and armillary sphere is derived, achieving the art of navigation by course and altitude in which there is no little to discuss with regard to the intention.

In speculative Music, from which the practice is produced (as has been touched upon), the harmonic proportions are found in the mind, from where we come to the knowledge of what are the harmonic proportional numbers between their extremes, from where in action the concept, and harmony is formed, just as also in the combat of the Sword, first it is known in the mind what is the means of proportion between the extremes, and what is the proportionate; with which a certain species of harmony in movements reduced to two compasses and proportions is achieved, in which the more skillful is more victorious. In this consideration it is worth noting the introduction, form, and sound of the war instruments, their differences, and compasses, found, and reduced to the Military Art in combat, ordinance, and fight, both in the singular contest, and its trials, jousts, and tournaments, in which skill is learned, as in the realities of duel, and war, recognizing that in one, and the other there is harmony.

Assuming this, it is not unreasonable and without discussion that the Skill of Arms is dealt with, inquired into, and achieved with the very means of the examples referred to; and that as Mathematics are subordinate, it chooses from them what is convenient for speculative and practical regulation, and movements of the arm, and of the Sword reduced to method, that straight and curved lines, circles, surfaces, and solid spherical, cylindrical, and pyramidal solids, means of proportion, and proportionate are formed in the air; and that by the proper order of everything, postures, dispositions, movements, and operations of the body are regulated and executed on the horizontal planes on which it moves, or elevates, imagining, and choosing such circular, or straight paths, as in calm, or stormy navigation, that conceding in the understanding, without perceiving with distinction in sight the wake of the Ship, serve as a guide in the great sea of the Skill of the Sword, in which although the whole seems almost incomprehensible; I will try to advance as much as I can, reducing power to determined acts, with such brevity, and clarity, that neither burdens the memory, nor disturbs the understanding; but facilitates it in such a way, that with average ingenuity, and agility, one can recognize, and achieve what with many years of studies, and experiences, exercise, and communications has been accumulated, to form this work with all perfection, keeping in it precepts, and rules of Philosophy, and Mathematics, proceeding by principles, arguments, and demonstrations, from the universal to the special, constructing this building to perfection, making firm bases the definitions, requests, axioms, hypotheses, and analysis, as accepted in Philosophy, and Mathematical disciplines, as well as the ones of Skill, conforming in terms with the most accepted in the Sciences, and Arts, to achieve the greatest clarity, in which I put special care, wishing to be understood, and to make myself understood, excluding the affectation of phrases, and exquisite words, because it is not in the sonorousness of words, and locutions the essential, but in the substance, explained with pure, chaste, and proper language, as the Philosopher teaches, noting the differences. Readers and students, receive my affection, which is to succeed, so that my greatest reward is your censure adjusted to reason, which I will appreciate as a teaching.

Farewell.

FIRST DISCOURSE.

ON OFFENSE AND DEFENSE

Desiring to perfect the subject of the Exercise of the Sword (Queen of the Weapons, the one who wears it, also binds himself to the obligations of honor), it is necessary not to omit the difficulties; because the intention is to include in this Book the most essential to such a commitment; and the most forgivable is the knowledge of offense and defense.

If one inquires in antiquity about offensive and defensive weapons, one will find, by force of reason, and from Sacred and Profane writers, that their use was occasioned by discord and war; the former admitting singulars, such as Gaius and Titius, duel or contest: and the latter extending to the fight of many against many, multitude against multitude.

Provident nature in plants, animals, birds, and fishes, granted them weapons for offense and defense broad field has discourse in individuals. Cicero noted it, Anacreon touched it, whose sense is this in our language;

The Bull strikes with the hard point,
The Horse has its weapons in its foot,
The Hare takes advantage of the swift course,
That provident nature gives them,
As well as to the Lion, fierceness, and teeth.
From the bravest to the most timid of animals, they act as they can, in offense and defense; why wouldn’t the same be found in man? Thus Lucretius noted, that in the primitive:
The ancient weapons were
Hands, nails, and teeth.

Marco Tulio elegantly confirmed it, speaking for Milon: This is not an exercised law, but a native one; we did not learn it, nor read it, but received it; for truthfully we seize and operate it from nature itself; as if our life fell into some traps, like between force, among the offensive weapons of thieves, enemies, it would be permissible for all our reason to save ourselves.

From this natural precept, Ulpian drew the common maxim, accepted by the Jurisconsults: it is lawful to repel force with force. Or according to Cassius: This right is compared to nature. From this results the permission in defense and offense, admitted by common laws; and in this part the precept does not hinder. Do not harm another, to which it is responded, is understood only in the manner prohibited by reason and justice, as it follows from Canon Law, to whose validation the words of the Pontiff Clement V are useful, declaring whether or not he incurs irregularity the one who in his defense gives death to his invader? Comparing it to the furious, he says: If the furious, or the infant, or the sleeper injures or kills a man, he does not for this reason incur any irregularity; and the same we declare in the one who kills another, not being able to save himself in any other way, because he injures or kills his invader.

From this principle to our intent, it follows to discuss the point of offense and defense, in which it is not a little disputable which is first, the offense, or the defense? Those who admit that the defense precedes, base themselves on the fact that man, as a rational being, first seeks a repair that will defend him: therefore he dresses against extreme cold and heat. That’s why he builds dwellings, opposing the inclemencies of the weather. That’s why he seeks to live in the company of others: that’s why he surrounds populations with walls and fortifications: that’s why he constructs Towers, Castles, and Fortresses: that’s why he arms himself before he fights: that’s why he first puts on the breastplate, and the other pieces of armor, and takes up the shield, before the steel is drawn, nor is attacked: Military Ordinances come before the onslaughts: first one learns, and practices the use of the spear, and the Sword, before executing the strike on the contrary; first nature, the Teacher of the Arts, arranged in the Elements, in the plants, in the animals of all species (beasts on earth, birds in the air, fish in the waters) with which to defend and repair themselves. Trees and fruits are defended with bark and peel; whoever looks attentively at the spike, finds it surrounded by sharp awns, which, like spears, surround it, sees the dense tunics, which surround the grain, constructing a safe dwelling for it. What branch, what flower, what fruit is there without defense, the thicker, or impenetrable, the weaker the pith, seed, flower, or fruit, which it preserves? The seed, which is essential for propagation, is always defended. The pear, the quince, the apple, the peach, the apricot, the pomegranate, the plum, the cherry, teach, demonstrating their prepared defenses: beasts, diverse in various skins (according to their natures) are dressed, and disposed to defend themselves; birds with feathers, fish with scales, and the most delicate with shells. The Elements in the opposition of qualities have their defenses. Therefore, primacy in defense must be conceded: hence it was appropriate that the Soldier, who lost his shield, should be given greater punishment than the one who lacked the Sword.

This concept admits an even more expansive discourse, if not entirely omitted here, at least limited. However, opening the door wide to the amplification of brave minds, many recognize offense as primary, granting it a preceding degree: its primacy is qualified because it is the principle of occasion, for without offense, defense would be in vain.

Man, because heat offends him, because cold bothers him, dresses and repairs himself. Because the temporal inclemencies harm him, he builds dwellings: against expugnations, he constructs walls and fortresses; against offensive weapons, he chooses and uses defensive ones; he uses a congregation of people to defend himself from an aggregation of: people he uses Military Ordinances to defend himself against Military Ordinances: and in the end, from the premeditation of the offense, the defense is investigated and produced. Therefore, offense has the first degree, the first antiquity, than defense.

Well, offense is divided into just or unjust: the just can be called correction, punishment, or satisfaction: the unjust, crime, grievance, or insult, in respect to equal or lesser. The angels, in the retinue of Lucifer, committed the first crime and were punished, not offended, because the offense was against the Supreme Highness, the Supreme Justice. The same happened to man, who committed a crime against his Maker, who corrects him, punishes him, and does not offend him. The trees, the plants, arm themselves against man, dressing in offensive instruments, sprouting thorns, and poisonous points: even the Rose, Queen of Flowers, produced thorns, all being executors against man. Offense and defense are correlative; and it is not a small dispute, which is more noble, assuming that offense does not become a crime.

This concept dies in the definition of one and another species, as Angelo Vigiano feels, saying: That offense is action, and defense is resistance; hence in Philosophy it is common, to be more the agent than the resistant; and by this maxim, offense is nobler than defense: because action comes from form, and passion from matter.

This is understood in proportionate action; in respect to the subjects, since action in abstract will always be nobler than passion; but in concrete terms it may sometimes be less: let’s take an example from elemental nature. The active opposing qualities, heat, and cold, are nobler than the passive ones, wet, and dry; although when combined they alter, so the passive ones can be active; because physical agents, in doing, suffer, just as water through humidity corrupts fire, etc. From this doctrine it can be deduced (speaking naturally) that offense is nobler than defense, as long as defense is considered mere.

Applying this to the purpose at hand, it is reasonable to question whether human artificial offense is nobler than human artificial defense? Not everything that is granted in nature is granted in art; for its explanation, we turn to the qualification of acts in offense and defense, in which virtue or vice can be found in both; thus, offense and defense can be just or unjust; and in such a difference, the offense may exceed the defense, or the defense may exceed the offense; and in this consideration, one or the other can be understood as noble, or vile.

For greater clarity, offense can be called impulse, and defense can be called repulsion; and in such terms, offense and defense can be proportional, not exceeding each other: from which it follows that both in offense and in defense, magnanimity and strength (related virtues, comprehended in a tight bond) are involved. For he is magnanimous who resists and defends himself against all the cases that occur to him, whether prosperous or adverse; he is neither vain in the former nor annihilated in the latter; he remains tranquil in both: just as the excellent pilot in the greatest storm, neither the tumultuous seas, nor the furious winds, nor the rocking of the ship, nor the confusion of the sailors disturb his spirit, nor does he abandon the governance of the helm and the sails: he attends to everything, anticipates everything, and in everything executes with accuracy: just as in the calm, he does not trust, does not surrender to rest, does not forget the danger: he acts with magnanimity in tranquility and in storm, breaking the waters, overcoming the contrasts, to lead himself to the port, without which he is headed. The same effects are proper in strength, for this reason the Doctor Angelico defined it, saying: It is a moderating virtue of fear and audacity.

These virtues (strength and magnanimity) are admitted in defense and offense, because the one who defends himself strong and magnanimous, persists in difficulties, and the one who offends against oppositions, seeks victory.

It follows, then, that offense and defense are equally noble as long as they are proportional to what is just and upright; just as they can also be vile, insofar as offense stems from unreason; and defense, if it turns into a cowardly flight.

From all the foregoing, it is deduced that offense and defense are equal in nobility, proportionate to what is just, as much as one offends and defends within decent limits, conceding that offense will be more generous when it is of such valor that it overcomes and does not pursue; and defense more praiseworthy, and a shield, when it is not only mere defense, but repulsion of the offense, offending the aggressor, as Angelo Vigiano well defined it.

From these principles (specific to individual contests) comes the reason for numerous conflicts between peoples, which is called war, since there is offensive war and defensive war: in the offensive, the reason for justice is qualified, from which the terms “just war” and “unjust war” resulted; and in the defensive, flight is not admitted; but repulsion, in which extensive discussions are offered, which are omitted, as they are not the subject of this discussion.

More to the point, one must investigate which is more natural, offense or defense? Since both are natural in their own right, as an effect produced by nature itself, understanding offense in the sense and acceptance mentioned above.

This is demonstrated in the Elements, in plants, in terrestrial animals, in birds, in fish, and in everything that is capable of quality, instinct, or impulse, to offend and repel their counterparts. The same is found in humans with greater perfection, for being rational animals.

From the perspective of defense, it seems more natural; and on the contrary, there are foundations for offense, in addition to those touched upon at the beginning of this discourse; to which it is added, that nature itself, since the first sin of man was committed, inclines, moves, and violently leads to offense due to the excess of passion; Job recognized this, saying: The life of man on earth is a battle.

Not only does this definition encompass humans: all life of the living is a battle, the predatory birds tearing through winds, just like fish in the seas, sustaining themselves through predation, offending each other, and even swallowing each other: The Eagle flies, the Swordfish cuts through, swiftly (according to their wings), the former through the clear air, the latter through the liquid Element, to offend, the former the birds, the latter the fish: The terrestrial beasts have an innate antipathy, maintaining a constant battle among themselves. There is a struggle in all species, making it difficult to determine which is more natural: in this, the high providence is recognized, which gave natural aptitude to offense and defense. The Elements do not cease their natural battle among themselves, sometimes they offend, sometimes they resist, sometimes they persist in the continuation of their fight, with offense always preceding, as Ovid said: Hot fights against cold, Dry opposes the wet. In the sentient beings it is the same. Each one recognizes its natural opposite, each one is impelled by instinct, and nature to offense, and even to treachery against its opposite, moving to offend, and to resist: and man, although reason corrects him, rarely overcomes himself, because he does not lack the inclination, taking more pride in being an offender than a resistor: differentiating himself, as in human qualities, that the choleric is opposed to the phlegmatic, the sanguine to the melancholic. Entire Nations, in general, are contrary to other Nations, as Histories show; and everything proves that in human warfare, offense precedes defense, by nature itself, with reciprocal action.

In light of this understanding, exploring their definitions by genre and difference, one could say: that offense is a natural offending impulse: and defense is a natural defensive and offensive repulsion. These definitions seem more proper (in my view) than those given by others, like Angelo Vigiano, saying: that offense is an action of violence, or violated: and in admitting such terms, the clear reason is destroyed, that there is a natural and just offense; just as it is, and can be defense in its own terms of natural defensive and offensive repulsion; since as has been demonstrated, offense and defense in their decent limits, are natural acts, produced by necessity in beasts; and reason; and necessity in man, who must act as a rational being, restraining himself to moral virtues, with which he makes offense and defense nobler: because in exceeding the licit limits, virtue turns into vice, as the Philosopher widely proves, just as the strong; exceeding in strength becomes reckless: and the prudent, if he is overly fearful, becomes a coward, the liberal becomes prodigal, and the measured becomes miserable. From which Celio Rodiginio recognized that virtue rests on two pillars, or elements; one, the hope of honor; another the fear of infamy (which he called penalties) by the authority of Cicero: and between these two terms operate offense and defense, which admit our definition, both of one and the other; and for both (perfected science, and the art the nature) instruments are found, which generically are named Weapons, because man is rational, and therefore nature did not give him offensive and defensive instruments; like the beasts: granting him greater perfection in the discourse, and in bodily movements, which together with the armigerous instruments, acquires superior means for offense and defenses; making him, according to reason, according to art, and according to science: and as this act is acquired by habits, and precepts, from antiquity the most political used contests, which they named, games, or exercises, being the most celebrated the Olympic; exercising in the races, and in bodily agility, operating between the two terms, or elements, hope of honor, and fear of infamy; or penalty

And out of care I omit here to explain individually how many species of offense there are, which are committed without weapons, which with bodily operations; which cause injury to honor, to Majesty, or to Office, which to the person alone. In this there is so much to discuss, and to dispute, and it admits entire books, not of my intention.

In the same way, I omit to deal with each species of Weapons, because the proper assumption is not general, but specific to the Sword alone; or accompanied, of which its principle, its dignity, its perfection, science, and skill in offense, and defense, noble, and decent will be investigated.

SECOND DISCOURSE.

ORIGIN OF THE SWORD, its qualification, use, estimation, and dignity, in various times, and Nations.

From the Holy Scriptures, the origin and nobility of the Sword can be inferred, but as it does not pertain to my faculty, its omission is necessary. Among the Gentiles, their Gods were adorned with a Sword, a custom prevailing especially among the Lacedaemonians. Among the Romans, the act of girding oneself with a Sword was so esteemed that despite the military belt being a honorable insignia for the Soldier, it was not permitted in ancient Rome, except when they were actually going to war, signifying that they were to act with the Sword, from which originated the privilege, and it being solemn for the honor of the Sword, calling it a Military testament, as Aulus Gellius reports; lending the Sword the prerogative to the belt, or baldrick, from which it hangs, girded by the Soldier: Converting the terms of girdle, or military readiness, committing the synecdoche figure, and all military insignia, honorable by the Sword.

From which in the Judges, as noted by Pedro Gregorio, it is said that the girdle is because it grants them the faculty of jurisdiction, in which greater and lesser girdles are considered, for the greater or lesser power of the Sword, from which resulted the proverb, or term: Exercise, judges, in great girdles. And from such high considerations, Lampridius ponders the sentence of Alexander Caesar, who said. Never will you sell the honor of the right of the Sword, because he who buys, sells.

Dion Cassius writes of Octavius Caesar, that for the greater honor of the Provincial Praetors (corresponding to the Governors) he granted them, while exercising such preeminent Offices, to wear military attire and gird themselves with a Sword, representing in it the entire jurisdiction: and to the Proconsuls, and Prefects, and the others, who had limited jurisdiction, they were not allowed to gird themselves with a Sword, nor wear military attire. Giphilinus, in confirmation of the great prerogative of the Sword, noted against Parthenius, that being in the Chamber of Domitian (who granted him the honor of girding himself with a Sword) he treacherously killed the same Prince who had allowed it, thus multiplying the atrocious crime.

Herodian relates of Emperor Severus that when asked: What was the greatest honor Paucianus, Prefect of the Roman Courts, enjoyed? He replied that it was to continually carry a Sword at his side, as it was the insignia of the Supreme Dignity. Tritemius writes of Besançon, King of the Sicambri and later of France, that great deed against his own son Sedamo, because having promulgated the laws of Chivalry (which he observed rigorously) and Sedamo being accused and convicted of committing adultery, the King drew his Sword, and with his own hand, to give him the most honorable death possible, cut off his head, saying: It is not I, but the law that takes your life. For this action, he was called the Just, as he did not fail in legal rigor, nor allowed the executioner to carry out the punishment, nor was it done with a less noble instrument than the very same Royal Sword. The reason and antiquity of the ceremony of auguring and entering into the greatest applause the Kings and Sovereign Princes with the naked Sword before them, carried by a great personage, I will touch upon.

Bautista Ignacio argues that the practice of Kings and Sovereign Princes carrying before them the Ense (which signifies Sword, or Royal Rapier) unsheathed, symbolizes the increase of supreme power, which does not need the sanction of others for the effective use of high jurisdiction. To this point, it’s noted that the Duke of Venice, although carrying a sword before him representing the supreme jurisdiction of the Republic he governs, does not however have it unsheathed, but instead sheathed in a golden scabbard; signifying that he does not punish hastily on his own, but with the mature counsel of the Senators. In place of a sword, the associated Consuls carried before them

From this, Pedro Gregorio adds that the Sword and the Safe preceded the Kings, signifying that the highest power of jurisdiction lies within themselves, without associates. Thus, Romulus displayed before him twelve Lictors, who preceded him in the manner of the Etruscans, because twelve Peoples elected the Kings, and for each one gave to the King a Lictor, a royal insignia that he could wield the power of his Sword in each jurisdiction, in which Titus Livius and Dionysius of Halicarnassus agree.

And even earlier than the Romans, among the Persians and Greeks, the Sword signified supreme and royal power, as Quintus Curtius notes. The Chaldeans (a rank among the Persians equivalent to the Egyptian Priests) seeing that Darius at the beginning of his empire abandoned the form of the Persian sword and imitated the Greek one, prophesied that Darius’ empire would pass to the Greeks, whose style of sword he had chosen. Such must be its importance, so esteemed it is in the common consent of people, Princes, Kings, and Monarchs, that in all political nations, and at all times, the Sword has been, and is, the most noble, most distinguished, and most considered military and political instrument.

Thus, in the auguries and coronations of Emperors, Monarchs, Kings, and Sovereign Princes, the most esteemed demonstration is with the Sword, as can be seen in the Western Empire, which is crowned with the Diadem, Sword, Scepter, and Golden Globe, as Pedro Gregorio writes, referencing others.

Suetonius Tranquillus in the augury of Aulus Vitellius recounts that upon receiving him as Emperor, the military people, divided into troops and occupying the most important posts, unsheathed their swords and acclaimed him equal to Mars, and Julius Caesar: and Vitellius greeted them with great demonstrations, because the Sword is the insignia of supreme power, jurisdiction, and dominion in offense and defense.

Carlos Sigonio, describing the augury of Julian Augustus, says that having been acclaimed Emperor by the military, following the death of Constantius, he made an eloquent prayer to those in his retinue. As a demonstration of their loyalty to him to the last moment, they congratulated him with their shields embraced and their swords unsheathed, placing the edges on their necks. In imitation of this, the Rectors and Princes present at the act did the same as a sign of obedience and loyalty to the Imperial dignity.

Saxon Grammaticus considers the greatest act of fealty to their Prince for clients to touch the sword and to kiss it with humility and reverence, thus acknowledging the supreme power in their King, and the supreme obedience in themselves.

In the Christian Religion, the Supreme Pontiffs consecrate the Sword, which in great honor, with a Legate, they send to the Prince who fights against the enemies of the Holy Catholic Faith, as a symbol of victory, and as an incentive to greater deeds against Infidels, as noted in the Ceremonial.

This action is very ancient in the Church, as Hector Boecio notes, referring to the example of William, King of Scotland, to whom the Pope sent the sacred Sword in the year 1202, with a sheath adorned with gold and precious stones, and it was sent with a Legate. The same favor was done for Lord Juan of Austria by Pope Pius V, as a symbol of the naval victory he achieved with a significantly smaller fleet against the numerous Turkish one.

Not only in the auguries and honors of Emperors, Monarchs, Kings, and supreme Princes is the superior dignity displayed with the Sword, but it is also used to bestow the investitures of the highest titles, offices, and honors, as Ammonius, Godfrey of Viterbo, and others relate. Pedro Gregorio, by the authority of Otto Frisingensis, notes as a general rule that the symbol of the tradition of every Feud is the Sword, or the Standard, with such distinction that the investiture of the Kingdoms is given by the Sword: and thus, when the Pope solemnly gives the investiture of King, before the Gospel, the blessed Sword, which is on the Altar, he himself girds it on the King, as a symbol of the defense of the Church, and the punishment of wrongdoers.

And the investiture is given by the Banner, or Standard, when it is not of Kingdoms, but of Provinces, as the aforementioned authors and Pedro Gregorio Toledano note in his Syntagmas iuris, and here are omitted the many examples that the Histories offer, for what he intends to gird this discourse

In Spain, the investiture of Admiral is given, according to the laws and ancient laws, with the Sword, Ring, and Standard, as well as to the Vassal, and the Leader, and of the Rich Men was their insignia Sword, Banner, and Cauldrons granting them maintenance, as found in our laws, laws, and ancient Writers.

The knighting in all political Nations is with the Sword, which was watched over with the other arms; and in Castile, and Leon in antiquity the Knight was given a blow to the neck, and he gripped his Sword, with the demonstration of drawing it against the one who knighted him, in whose respect he contained himself; but now only the blows with the Knight’s own Sword are used, which is taken from him by the one who arms him; and once the ceremony is done, it is returned to the sheath.

The institution of Military Orders, whose admission and honor is associated with the Sword, is performed with the ceremonies of Knighthood, as stated in their Constitutions.

The Order of Santiago is named after the Sword, not so much for the qualified title, nor for the form of the Red insignia they wear on their chest, but for a special dignity and acknowledgment of the Military Institute’s obligations. In this regard, it is worth remembering that the Templars, among the constitutions of their Knighthood (highly esteemed during their time), the primary ones were to die for Christ, be the first to take up arms against Infidels, not to turn their backs having drawn the Sword, nor return to their quarters without their Captain. And if they were to be captured, they would offer no other ransom than their belt and Sword. They observed this precept so strictly that when Saladin captured a nephew of the Master, asking for more ransom than the belt and Sword, the Master preferred him to die in captivity rather than give more ransom than the belt and Sword, in accordance with his Templar Knight status, as related by John Villembrochio Dantiſcano.

The Teutonic Knights, a chivalric order, were known as Gladiators, because of their sword and the skill they professed with it, as Mnuster recounts. In conclusion, to highlight victories, it is common in Scripture to qualify them with the term, “ln ore gladij,” which is the same as “in the wake of the sword”; in Spanish it corresponds in the same sense to say: “He entered the strength with a sword in hand,” which means the same as by force of arms. By the way, it is worth pondering that in all times, in all nations, and in all symbols and paintings, the sword is, and has been, in the shape of a cross, which its guard has required, and not without great mystery, which is not of this subject.

Regarding the makers, shapes, qualities, and material of the sword, one could expand the discussion into a volume; but here it suffices to adorn, that of the sword that Ascanius gave to Euryalus, its creation was attributed to Lycaon Genosto, as Virgil describes.

Demosthenes, the father of the orator, was nicknamed “Makeropio”, derived from “Makera”, which in Greek is the same as “Sword”, because he had a large workshop, where very fine swords were crafted, having for its manufacture expert officials and servants, as Plutarch narrates. Suidas says that the Romans in the second Punic war, imitating the Iberian Spaniards, used swords with a point and edge, which they made for both hands.

Diodorus Siculus notes that the Celtiberian Spaniards, to manufacture swords and other weapons, stopped the iron (according to their ancient custom) making it into sheets, and hiding them in the ground, where the weaker parts were consumed over time, and from the most purified they made very fine swords, and from the less pure the other pieces of armor, so the swords came out so strong that no shield, helmet, or loriga could resist them. And Suidas notes that although the Romans in the war of Hannibal, reduced to a better measure, and form the swords, leaving those they used in old times, imitating the Spaniards; however, they did not achieve the purification of the iron, nor the goodness, nor the art in the tempering, and manufacture, in which the Spaniards exceedingly surpassed the other Nations. It is therefore recognized that in the manufacture, in the measure, in the perfection, and in the skill, nobody equaled the Spaniards, because the weapon sword is more ancient, and more proper to Spain and of greater esteem, and dignity, than in the other Kingdoms, and Provinces.

From all this it is concluded, that Sword is named with different voices (according to various languages) and it is the instrument, and weapon of the highest dignity, of the highest nobility, of the highest symbol, and of the highest esteem. Then its science, and its exercise should be speculated, known, and exercised by every Prince, by every noble, by every Soldier, and by every man of reputation, who girds a sword, in peace, or in war.

THIRD DISCOURSE.

INTELLIGENCE, AND EXERCISES, of the Sword, if it is a science, and of what kind

Having recognized the antiquity, estimation, and nobility of the instrument, which we commonly call Sword, it is necessary to discuss the understanding of its intelligence and exercise, if it is a science or an art, and of what kind, if of the liberal or servile? For in this we see varied opinions; since the professionals, some lean towards that it can be a science, and they name it as such, like Don Luis Pacheco de Narvaez in his latest works, and Geronimo de Carranza more confused, without determining a fixed conclusion.

The modern Philosophers, with obscure knowledge, insist on the division of sciences, which concern the handling of weapons, in the preliminary questions of Logic, and Metaphysics, investigating as to the universal, its antiquity, properties, and distinction, which Aristotle, Saint Thomas, Saint Isidore, Hugo de Sancto Victore, along with the stream of Logicians, and Metaphysicians deal with, and with special curiosity Julius Caesar Scaliger, and Eugubino.

Regarding the antiquity of sciences; some want them to be derived from Adam, passed on by traditions, rather than in writing, thus passing from one age to another, to the Greeks, and from these to our times. Others, with Eusebius Berossus, and Josephus admit that the first sciences were derived from Adam, and later concede various inventors, as reported by Polydore Virgil.

Regarding the discourse and reason (in which the philosophers do not disagree), it is inherent to man, that his understanding is like a blank slate, in which nothing is shaped, because he is born without any knowledge; although, with the propensity to know, the desire being more insistent for the necessary, or for the useful: the former, which moves, not only for comfort, but for reason: and the latter, for self-interest.

Both are the origin of sciences, with speculation being first, from which the speculative or theoretical terms resulted, whose end is the contemplation of the truth: and from this first consideration, the active, or practical ones were produced, which have their proper end in the work itself.

These are subdivided into two more adequate terms, because the active ones guide the actions that are in the same potential agent, on the part of intelligence: and the practical, or effective ones, guide the operations that are external, or outside the same potential agent, because they pass to extrinsic works, like playing instruments, etc. from where Aristotle concluded, that sciences, some are contemplative, others active: those effective, by means of which man with understanding recognizes, perfects, and guides actions, preparing in himself what is necessary: these, by which in effect pass to the extrinsic operation.

The strictly philosophical divide contemplative science into Metaphysics, which focuses on the spiritual and the common being; Physics, which deals with the sensible, such as humans, etc., and Mathematics, which looks at quantity, subdivided into continuous and discrete: continuous by Geometry, discrete by Arithmetic. Astrology, which contemplates the number, movements, and magnitude of the Heavens; Music, the number, proportion, and harmony; Perspective, the visual lines that distinguish the various ways of seeing, due to the varying position of objects. These are more accurately mathematical means rather than proper mathematical sciences: hence, they can be reduced to Physics, these four species, Astrology, Geography, Music, and Perspective, which originate from Geometry and Arithmetic, just as to Metaphysics are reduced the speculative, active sciences, which direct interior actions, such as Logic, and Dialectics: and those that touch on Moral Philosophy, widely discussed by Aristotle in his Ethics and Politics.

From these common principles, as parts of the active sciences, resulted the Arts, which distinguish humans in the common animal genus (as touched on by Pedro Gregorio) directing towards the necessary and useful in human society, either by voice, by letters, or by works: by voice, by the congruous means of words in various languages, which explain concepts: by letters, in Rhetorical and Oratorical eloquence, either for permanence in writings, or for communication with the absent, letters being elements that, in right arrangement, stand for words, forming syllables, dictions, periods, etc., from which History and Poetry, etc. achieve perfection. For these works, philosophers classify the seven liberal and noble arts, which are included in the common Latin verse:

Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, Astra.

Lingua, signifies Grammar: Tropus, Rhetoric: Ratio, Logic: Numerus, Arithmetic: Tonus, Music: Angulus, Geometry: Astra, Astrology.

The first three, which are called trivium or trivial, look at and are directed to eloquence, and explanation of concepts.

The last four (which are the quadrivium) are directed to continuous and discrete quantity, and all seven earn the reputation of Liberal arts and science.

To these, the Logicians add another seven Arts, which they call servile, included in this verse:

Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates.

Rus signifies Agriculture: Nemus, the Hunt, or Art of Hunting: Arma, Arms: Faber, Architecture: Vulnera, Surgery: Lana, Woolwork, or Art of Weaving: Rates, Navigation.

They tend to call these Arts servile, because they serve the body, just as the Liberal ones serve the soul: and both are considered worthy in a noble person: and to both, they add the mechanical arts, which are the operators in different species, widely and specifically discussed by the Philosopher.

Those who materially look at the term Arms, like Friar Pedro de Oña in his Logic, and other moderns, understand by the term Arms the Gladiator, or Laniſta Art, which they judge to be the skill of the Sword, without considering that the term Arms is a material generic, and not specific, as will be proven in its place, demonstrating that the understanding and exercise of the instrument named Sword is not only a Liberal Art, but also a science; making use of Logic, as the science of sciences, for being the investigator of the true and the false, as Boethius and Saint Thomas teach, and all the current philosophers; although some moderns, like Fathers Pereyra and Fonseca, want the investigation of sciences to touch on Metaphysics, because the metaphysician is like a craftsman, from where the investigation is consequently. But in this part, we follow the most received opinion of Boethius and Saint Thomas, and others, with Averroes, who calls Logic, the common instrument of all sciences. But the dispute here is not about that, but whether it is a science or art, and what kind, the understanding and exercise of the Sword.

Proceeding, therefore, radically, we consider the cognitive powers, which Celio Rodiginio named (taking the term from pure Greek) in science, art, and experience, recognizing them as analogous to each other, and all three species are proper to the understanding and exercise of the Sword, as will be demonstrated in these discourses.

Aristotle teaches that to discourse in the sciences, above all things, one must distinguish the equivocal terms, thus avoiding confusion in the terms, because the division of the sciences is recognized by the variety of instruments, and ways of knowing; that is, by the organs and means by which science is acquired, reasoning by topical places, by demonstration, to cause and effect, or vice versa. Where it is argued in the understanding, and exercise of the instrument Sword, it is also investigated by the same means: therefore, the understanding and exercise of the Sword is a science: the major premise is proven, because in the conclusion, the terms are Syncategorematic (that is, as Saint Thomas explains) consignificant, which are imprinted in the mind, in relation to the instruments and organs. The minor premise is noted: then the consequence is valid. To clarify further: the science of the Sword is distinguished in Docens (Teaching) and Vtens (Using), that is, intellectual and practicing. The teaching, which is Docens, is separated from the things, as intelligence is. The Vtens, or practicing, is that which is joined with the instruments. Therefore, the science of the Sword is both teaching and practicing; teaching, that is in Docens: and practicing, that is in Vtens.

Although in this division it seems that there is a place for the difficulty that philosophers present, noting that one dividing member is not formally whole of a division because one thing is not another. Then one dividing member is not formally the other, as Saint Thomas, Cajetan, Scotus, and Scaliger prove with effective reasons. Valduíno makes the example in Logic, by the division of Docens (Teaching) and Vtens (Using); and understands by Docens, that which measures; and by Vtens, that which is measured. From which it appears that the understanding of the instrument Sword, as far as it is Docens, can be a science, because it is measuring; but the practicing, which is Vtens, will be art, because it is measured.

But the difficulty is answered, that the understanding, and the demonstration, which is the same as Docens and Vtens, are one single acquisition, knowing by different organs, which are in themselves integral in a subject, as from Logic by Platonic doctrine, it is considered to be the first of all sciences, because it makes, reasons, and argues about the being, and the subject; the being and the subject are one aim, or final object: then Logic as Vtens, as well as Docens, is one single science; and the same consequence results in the understanding, and exercise of the instrument Sword, which is Docens and Vtens

But for the purpose, I argue thus: Science is a habit of the intellectual power, which considers the subject in its entirety: the understanding, and exercise of the Sword is a habit of the intellectual power, which considers the subject in its entirety; therefore, it is a science.

But I argue more clearly thus: That faculty is proper science, in which two requirements concur; one, that by certain, and first principles (certain, and evident) known, the terms are known; another, that from such knowledge certain, or evident conclusions are inferred, by certain, or evident consequences. In the understanding, and exercise of the Sword, then, such requirements concur, so strongly, that they are by themselves manifest to the understanding, because with its explained terms (without other proof) the understanding assents to the certainty of the conclusion, by the certainty of the consequences; from where a certain evident habit of necessary thing is caused by its known causes: therefore, the understanding, and exercise of the Sword is properly science.

A more evident argument is as follows: That faculty is a proper science in which two requisites concur; one, that through certain and primary principles (which are certain and evident), the terms are known; another, that from such knowledge certain or evident conclusions are inferred by certain or evident consequences. In the understanding and practice of the Sword, these requisites concur in such a way that they are manifest to the understanding by themselves, because with its explained terms (without other proof) the understanding assents to the certainty of the conclusion, by the certainty of the consequences; from where a certain habit is caused, evident of a necessary thing by its known causes: therefore, the understanding and practice of the Sword is properly a science.

Let the minor of this argument be a corollary: that is certain, or evident knowledge of necessary thing, investigated by its causes, which is acquired by mathematical demonstration. The understanding, and exercise of the Sword, then, is investigated by causes with mathematical demonstration: therefore, it is science, as a habit that is produced evident of necessary thing, investigated by its causes.

This is confirmed because the understanding and exercise of the Sword, as far as it is a teacher (Docens), mathematically demonstrates that it cannot have a true antecedent and a false consequence, although the topical syllogism produces opinion, and the sophistical error. In the mathematical argument, then, whether it is a problem or theorem, no fallacy is admitted, because its proof is demonstrative, and not by tropics and sophistics: therefore, the understanding and exercise of the Sword is a science that admits evidence.

From the perspective of the object (which is man in his entirety, and in his parts) understanding, and acting with movements known by their causes, from which the understanding and practice of the Sword demonstrate inherent passions, it is also proven to be science, as it clearly results from the common doctrines of Aristotle, Saint Thomas, Boethius, Cleanthes, Rodigino, and the Arabs; Algazel, and Alpharab, and others, proving, that Logic is science, and part of Philosophy, for the same reasons, which occur in the understanding and practice of the Sword.

Nevertheless, there are such sophistic minds that strive to assert that the understanding and practice of the Sword is not science, but Gladiatorial Art, and they argue thus

By the principles of secondary intentions, neither knowledge is given nor acquired. The understanding and exercise of the Sword are principles of secondary intentions: hence, the understanding and exercise of the Sword is not science, but Gladiatorial Art. This is demonstrated by the fact that the use of a thing is not the same thing, nor the use of the operation, but the operation itself: thus, neither will the use of science be science, and consequently, the exercise of the Sword, which is Vtens, will not be science. Moreover, the understanding and exercise of the Sword are reduced to the use of a physical instrument, to demonstrate the passions of the subject; and what is the principal cause (which is the instrument) is the one to produce science or art: then the understanding and exercise of the Sword (which is the causal instrument) is not science, but Gladiatorial Art. Furthermore, they justify themselves, assuming that between the principal agent and the instrument, which produces a similar effect, thus in the species (which is the instrumental), in truth it is not the same in the effect, which simulates the principal agent, to whom it should simulate, not the instrument. For example: it is explained in the generative power, which generates man, which is similar, not to the same generative power (which is instrumental), the same is seen in the artificial, because the statue is not similar to the saw, nor to the hammer (which are instruments), but it is only the likeness of the existing art, which was in the mind of the Craftsman, from where it is argued thus.

Science is according to the act of the scientist, chosen for the same science by its principle, which generates science. The Sword, then, is the chosen instrument, which instrumentally demonstrates its effect: therefore, its understanding and exercise is not science, nor can it generate it, much less in its own instrumental exercise.

The term Arms; which is generic; includes, and encompasses all species of its genus; and the term Arms is not of the seven Liberal Arts, but of the seven servile; and thus the Logicians, by the term Arms, understand the Gladiatorial, as carried by Oña, and others. The understanding and exercise of the Sword is a species of Arms, included and understood in its genus: therefore, it is not science, but Art of the servile, and not of the Liberal.

In these five acumen, many others are compiled, which are gathered from various writings and opinions, both of logicians and those who discuss what is commonly and vulgarly called Destreza or Fencing, which logicians reduce to the term Arms, not to its proper meaning, but to the Gladiatorial Art, where they are clearly deceived, as will be proved in its place, first responding to the aforementioned contrary arguments, which are the most sophistical and subtle of all I have read and communicated.

To respond more clearly, it is noted by the doctrine of Scotus that science is acquired by any adequate method, which is a means of knowing. Thus, the same Doctor resolves that Logic is called science because it commonly teaches and can be applied to various things, through which it reasons, argues, and proves; because the way of knowing can be common in application. Assuming this, we respond against the first contrary argument, denying the lesser, and saying that the understanding and exercise of the Sword is not acquired by the principles of second intentions, but by the radical causes teaching and practicing (which is the same as Docens and Vtens) that are adequate means of science. The understanding and exercise of the Sword, then, are not principles of instrumental second intentions, but of first radical causes, which are adequate means of knowing, Docens, and Vtens: therefore, the understanding and exercise of the Sword, Docens, and Vtens, is science and not Gladiatorial Art. Along the way, it is noted with the Philosopher Alexander, and others, that Lemus refers to, that before all things, in any science it is absurd not to first know what is the method with which one proceeds in it, to which cause it was shown at the beginning of this discourse, and its place will be demonstrated.

The major premise of the second argument is false, understanding it universally, because the natural entity (e.g., man) says a greater entity than that of its material cause, as Father Oña concedes because it is a perfect entity in its own species, as is also the object in the material cause of science, being matter about which science is exercised, from which it is not inconvenient, that science exceeds the entity in operation. The understanding and exercise, with which it is not the same operation: then it is science the understanding and exercise of the Sword, because it is Docens, as well as Vtens.

For further clarity, it is noted that the true and proper object by itself, although it does not cause science (because it does not influence it, but the science in the object) but says that the object is the cause of science, because it is specified by intrinsic order, for any knowledge (in a certain way) is measured by the known object, because it is the adequation of the object by the understanding, as philosophers feel: therefore, it is not absurd, that from such a cause, and measure of lesser entity is measured (in a certain way) the greater entity, and with this distinction, it is easily recognized, that although the understanding and exercise of the instrument Sword (for being an object) by itself does not cause science, because it does not influence it, but the science in the object; but it will be said that it is the cause of science, which is specified by intrinsic order; for any knowledge (in a certain way) is measured by the known object with which it is adequate: therefore, it is not inconvenient, that from the material object (which is of lesser entity) is caused science in the understanding (which is of greater entity) with which all the sophistry of the second contrary argument is convinced.

To the third, it is responded that the scientific act is resolved to be in it some principle by itself noted (as is common in all science) so in the understanding, and exercise of the Sword will be the first principle by itself noted the same instrument Sword, and its knowledge will be its first principle by itself known; however, the Sword will not be the same science, since the physical instrument does not fall under the scientific habit; because the knowledge of the instrumental principles does not fall under the scientific habit, as this does not need another regulating instrument but regulated. The instrument Sword is, then, the regulated instrument of the understanding and exercise of man, the main subject capable of science, to which only the Sword is a causal instrument, with which the passions of the subject are demonstrated, which is Docens, and Vtens: therefore, the understanding and exercise of the Sword (which is the instrument) although it is causal, as it has been said, is science, and not Gladiatorial Art.

In response to the entire apparatus and syllogism of the fourth opposing argument, a distinction is made between the instrument with which the effect is performed and the first agent (which is the science that regulates the same operation). From this, it follows that science is not just the act of the scientist, but the very science, in the likeness of which the act is directed and the instrument is chosen. The Sword, although it is the chosen instrument with which the first agent instrumentally directs and performs the effect, is not, however, the same science, nor similar to it, just as the saw or the hammer is not similar to the science existing in the idea of the scientific agent. Therefore, the understanding and exercise of the Sword, moved and directed by the understanding, arm, and hand of the scientific agent, is science, because science is not regulated by the act or the instrument, but the instrument and the act are regulated by the science.

The fifth contrary argument is answered conclusively by distinguishing the term Weapons, which is generic in terms of the pieces that make up all Military Weapons, as widely and skillfully demonstrated by Pedro Gregorio Tolosano; and specifically those corresponding to the Gladio, or Sword. In this regard, in terms of the manufacture of all weapon pieces, their species are included in their generic category Weapons, and their manufacture is indeed an art, and one of the seven servile arts; but for that reason, the term of the same Weapons, nor the Gladiatoria, as poorly explained by Father Oña, speaking like a pure scholar, but not as a military scientist. The same absurdity is confirmed in the term Rates, by which the same Author (and others who follow him) understood the Art of Navigation, erring in the lack of knowledge; because the term Rates, as a generic, only includes the species of Vessels, whose manufacture is one of the servile arts; but for that reason it does not include the science of navigation, which in itself is the most scientific part of Cosmography, which is subordinate (to what the common misunderstanding calls the Art of Navigation), being, as it is, a most noble science because of its causes. The understanding and exercise of the Sword, then, is not of the manufacture of the Weapon instrument, but of the science acquired in the understanding and exercise of the agent subject: therefore, it is a science, and not one of the seven servile arts; rather, it is the most noble science, as proven by the following reasons.

Firstly, because that science is most noble which is desirable for its own sake, like the Ethical, or Moral sciences, because they direct towards virtues; the Political, Economic sciences, because they direct towards the perfection of sociable life; and Medicine towards the health of man, etc. as can be inferred from the teachings of the Philosopher, and Saint Thomas, and many others: therefore, the understanding of the instrument Sword is desirable for its own sake due to the qualities referred to in the previous discourses, and those that any average intellect recognizes: therefore, it is a most noble science.

Sciences are also characterized by their subjects, and the subject of the understanding and exercise of the Sword is most noble, because it is man known in his entirety, and in his parts, and movements by power, and practiced act: therefore, the understanding and exercise of the Sword is a most noble science by the subject. Similarly, sciences are characterized by their own end. The understanding and exercise of the Sword, therefore, has its own end in defense and offense in man: therefore, it is the most noble science for its own end to which it is directed.

The certainty of the means with which an argument is made and knowledge is acquired is a great qualifier in sciences, as the Mathematics are estimable, and most noble because of the certainty of the means with which they argue and demonstrably prove, as philosophers concede. Therefore, the understanding and exercise of the Sword argues, acquires, and proves its knowledge by means of mathematical demonstrations: therefore, it is a most noble science because of the certainty of its means.

That science, as Aristotle says, is more qualified in its totality, which teaches the subject and object more intimately, and demonstrates its effect with greater certainty, than the one that only teaches the object to exist; but not being so demonstrable in its effects, as the Philosopher concludes. Therefore, the understanding and exercise of the Sword both teaches and demonstrates with certainty the subject, object, and their effects: therefore, it is one of the most noble and qualified sciences in its totality.

As a corollary of such a maxim, the same Philosopher considers the science that most infallibly manifests its certainty, like Geometry, Arithmetic, and Music, to be superior in its totality. Therefore, in the understanding and exercise of the Sword, the same demonstrations occur, because Geometry, Arithmetic, and proportions are subordinate to it: therefore, it is one of the most superior sciences in its totality

I avoid ostentatiously adorning this point, due to the brevity with which I proceed; however, it should not be omitted whether the understanding and exercise of the Sword is one science, or diverse. It can be proved that it is one science, in which Aristotle’s definition is admitted, to which I adhere, with the most concordant of his Expositors, saying: That is one science, which is of a single genus, and which is composed of its first principles in its parts and effects considered by themselves. The understanding and exercise of the Sword is of a single genus, which is composed of its first principles in its parts and effects considered by themselves: therefore, it is one science, and not diverse sciences.

The consequence is proved: The diversity of sciences is in the diversity of genres, and of their first principles, and in that the first principles of one are not demonstrated by the first principles of the other (as is inferred from the same text of the Philosopher) and the principles, when in themselves are diverse in the demonstrable to which they are directed, are not of the same genus: and they are of a genus, when they demonstrate it by themselves: although there may be many demonstrations of a same genus, but not by means of an order, but by means of diverse orders, as everything is looked at under one reason, Sub qua, as the Commentators of Aristotle widely explain, most of them, and those of most authority, agree on these principles. From which it follows that the unity of science is considered in three ways, either generic, or specific, or numeric, as Master Zumèl discusses, with the common current of the Logicians, with whom I say:

Generic is a science, with respect to the union in the same genus, although from distinct and diverse parts; even though they differ in essence and nature, they agree in the definition of the superior. Exempli gratia: Man and Lion (whose common reason is the comprehensive definition of Animal) are one genus, in as much as they are of the same reason; but such generic unity, although in the union of the genus is one science, is not therefore in the species; because it is called specific unity in the science, whose definition is proper, and adequate to a common essence of nature; so, they only differ in accidents, as Porphyry taught in the example of many men, who by the participation of one species are defined by one man in relation to it; and this in as much as the species is one specific science.

Numeric is that science, which according to some singular thing (although it is diverse in itself, and can be in any other singular thing) as in its entirety can be considered one, looks at diversity, according to a formal reason, as in the collection of numbers, whose sum is one, indivisible in itself, because the whole is no more, nor less, than the collected numbers; even though in another singular thing it can be considered division (as in the parts, or numbers of which it is composed) but not in the collection itself, which in it will always be one, with respect to Numeric science; and so in other considerations, as results from the doctrine of the Philosopher, who considers Grammar a science, although it is a collection of many voices. In the broad sense, all agree in one reason, which includes the mode of proceeding by demonstration, although by different modes of arguing: therefore, in as much as the understanding and reason in which they agree, demonstrating all the sciences, they unite among themselves: therefore, it can be said that they are one science in this consideration, as Mirandulano admits.

To our purpose, following the teachings of the Philosopher, Saint Thomas, Scotus, Zumel, and others, we will maintain that the truth and unity of science result from the abstraction of the object, which is acquired by the habit, which they call Scientific; and this, is not only achieved by the reason and species of the object, but requires facility and ability on the part of the acting power, to properly arrange the species to judge correctly by the ordered demonstration, as is required in the understanding and exercise of the instrument Sword, which being one science, needs facility and ability on the part of the acting power (which is the scientific man) to arrange the species for correct judgment, by the ordered demonstration in offense and defense, by a demonstrable science.

Those not very versed in Philosophy, presuming by sharpness of intellect, find it difficult to concede the life of science in the understanding and exercise of the Sword: and they say, that this is a material instrument of different genus, species, and number, than man: and so, the understanding and exercise of the Sword is not one science, with respect to man, and with respect to the instrument.

This enthymematic argument in appearance, the common people find it effective, but it is very fallacious, and sophistical, noting what the Philosophers call intention, and extension, in which Aristotle, and his Glossographers discourse, concluding, that intention is the power, or active quality in a subject individual, or compound, as in our purpose it is man with the Sword in hand, which for the understanding and exercise is a compound only the man armed with the weapon Sword.

And as the Father Oña shows, by intention the Philosophers understand, when in a subject, or part of it there is some quality, as heat, or movement: and extension, when the heat, or movement extend in another part. Exempli gratia, extension is when degrees of facility, or movement, are added with respect to another common consequent, as is the instrument Sword in the hand of man, who governs, and moves it, from where science is communicable, as in a whole heterogeneous, whose similar parts are degrees of facility, with respect to a same conclusion; and dissimilar, with respect to different conclusions, which nonetheless are called parts of a species, or of a compound, as is given in intelligence, as in movements, which look with diversity to an end, and understanding regulates them by a reason: thus the man with the Sword in hand should be considered, whose movements are governed by a single active power, which acquires, and works in understanding, and exercise with a single science, and extensive movement: Ergo habemus intentum.

Intellectual habits, unlike simple qualities (like a point), have different components and therefore are considered complex. This is because, instead of being confined to a single individual or matter like the human body, these habits involve a complex interplay of factors, enabling more flexibility and scope in our actions, whether towards a single conclusion or multiple ones. These actions don’t precede the act itself; instead, they are the product of the act. For instance, in using a sword, the intelligence and practice involved determine the outcome, whether it’s a single wound (a conclusion) or multiple ones. The actions aren’t produced before the act; they’re produced by the act itself. Thus, the ease of one action over another falls under the same category because they all stem from the same reasoning, embedded in a scientific principle or active power.

Nevertheless, as a crowning of this discourse, it remains to see whether this science of understanding, and exercise of the Sword, insofar as it looks at its object, is a real being, or a being of reason.

According to philosophers like Aristotle, Saint Thomas, Scotus, Durandus, and others, the concept of being can be divided into four types: substantial (the most perfect), accidental (less perfect), generative, and negational or lacking. All four types can be understood through reason. Aristotle further clarified that being can be real or existent in the mind. The latter is conceptual or rational, while the former is physical reality. In simpler terms, a being of reason refers to knowledge we gain through understanding, whereas a real being denotes the actual, physical manifestation of truth according to science.

Assuming so, avoiding controversies, and questions, in which Logicians, and Metaphysicians dilate, the following conclusions are formed to the purpose. The object specifies, and terminates the science: the understanding, and exercise of the Sword is a real object, for being the same Sword governed correctly: therefore its being is a real being, and not only a being of reason, because it is not limited to its term.

Demonstrable understanding is the greatest physical perfection of science, and thus is a real being: the understanding, and exercise of the Sword is demonstrable mathematically, because Mathematics is subordinate to it: therefore it is a real being.

Real science involves specific changes in the subject it’s studying. For example, the visual ability at a particular distance can accurately identify color and shape. In the same way, the skill and understanding of using a sword can be considered real science as it involves specific actions in relation to the object (the sword). So, the knowledge and practice of using the sword is a genuine entity. I’ve kept these discussions brief, and could have added more detail, enough to fill a book. But, I’m satisfied with showing that the understanding and practice of using the sword is a notable science in its own right. It’s unique, specialized, provable, and valuable both for its own sake and for the object it studies, which is a real entity

FOURTH DISCOURSE.

ART AND EXPERIENCE of the sword

In the preceding discourse, Celio Rodiginio’s cognitive powers were noted, signified by the Greeks as conditions corresponding to thought and opinion. In the twist of meaning, Celio himself explained them as Science, Art, and Experience, which are analogous powers that include perfect human knowledge.

On this basis, which allows for extensive adornment (omitting it for brevity) we content ourselves, having proven that the understanding and exercise of the Sword is most noble science. We reserve for this place the demonstration of the terms, Art, and Experience, from which perfect knowledge of the formal truth of the understanding and exercise of the instrument Sword can be achieved. The result of all this is what is commonly held as true Dexterity, which Geronimo Carranza called the Philosophy of the Sword, with demonstration of its definition; and Don Luis Pacheco de Narvaez, science, for its common principles of being investigated by its causes; and the Italians, French, and Northerners grant it as Art, without saying what kind; whether Liberal, or servile, noting only that it can consist of rules and precepts, as is gleaned from Angelo Vigiano, Tibaut, and Pedro Gregorio.

From these confusing lights, through continuous efforts, studies, and operations, I have come to inquire what is Science, what is Art, and what is Experience. Enough has been demonstrated about science, so I will proceed to the rest.

It is common in all good Philosophy, that from science comes art, because it is nothing other than a collection of precepts, reduced to method and order, which is granted in Logic, and Dialectic, which look to an end, which is reasoning, and the argument for inquiring the truth: Logic is science, and from it is produced Dialectic, which properly is art, collected from various rules and precepts for arguing: and as in Logic, and in Dialectic, different circumstances are considered, with which the former is science, and the latter is art, this one produced from that one; also from the science of Teaching, and Using, of the understanding, and exercise of the Sword is produced the art, with which its formal operation is disputed.

Plato, through the etymology of the terms, Logic, and Dialectic, explained their difference, suggesting the former as science and the latter as art. As he noted, Logic comes from Logos, which means probable reason; and Dialectic (according to Diogenes Laertius) comes from the Greek word Dialegiste, which means altercation in question and answer, from which Plato defined Dialectic, saying it is the skill of disputing, questioning, and answering.

According to my intention, the same can be considered in the science and art of the Sword. Because the teaching and practicing science, reasoning for real being, achieves the probable and demonstrative reason of the understanding and exercise of the Sword. In this part, it can be universally considered science. But in the operating use of the Sword, which is reduced to rules and precepts, strictly produced from science and opinion, it will be only art, as exemplified in Logic and Dialectic.

For example, Aristotle granted Dialectic to be part of the Topics, that is, the Art of discussing the probables, thus he said, Dialectic is a discursive action, which is concluded from the problems. From this, the same Philosopher taught, “It is useful to confirm the principles of sciences by problems;” and he himself concludes that “It is the Philosopher’s task to treat theorematically through necessary discourses: and the Dialectic through problems.” From this, it is resolved by Aristotle himself in all his works, that Dialectic is Art, which disputes or debates through problems. I apply, then, in the science and art of the Sword, when reasoning theorematically Teaching and Using, it is science; and when operating by precepts and rules collected by the probables, it is art.

But there may be a curious one, who raises the objection that is touched upon in Dialectic, which I have taken as the cause of the example, and will say: Aristotle, either deals with the syllogisms of Dialectic as a whole, or in its parts. If of syllogisms as a whole, it touches on the Analytics: therefore, Dialectic will be part of the Analytics, or the Analytics will be called Dialectic. And arguing to the point: or does the art of the Sword deal with its intelligence and exercise as a whole, or in part? If in its entirety, it will be the same science, or the science will be the art: it cannot be part, as it is clear.

In greater clarity; the counter-argument is answered: Aristotle called parts of the Analytics part of the Dialectic, not because in true reality it is part of it, but because out of necessity, for the perfection of Dialectic, it uses its absolute terms, with which it extrinsically leads to the consummation of its end, acquiring parts of the Analytics, but not because it is part of them. An example is found in Aristotle himself, who says: The analytic parts, and civil science, are parts of Rhetoric, not because in true reality they are its parts, but because extrinsically Rhetoric needs them, to lead itself to its consummation, and end.

And by the same analogy in the Art of the Sword, it makes use of the reason and means of its science, from which it is produced, just as Dialectic does from Logic, to achieve its greatest perfection, working by the rules and precepts of science and opinion: not because art is science, nor science art, nor opinion one or the other, but because to lead the Art to its consummation, it makes use of all the means, sciences, and disciplines it needs, just like Geometry and other parts of Mathematics, not because the Art of the Sword is part of Mathematics, nor Mathematics part of the Art of the Sword, but for the same reason that the Philosopher exemplifies in Rhetoric, with respect to the Analytics and civil science.

According to the Platonic doctrine, received by all Philosophers, in every dispute it is necessary to define what is being discussed, so we will say: Art of the use of the Sword is a habit with which man, observing rules and precepts, produced from science and experience, acts effectively in defense and offense.

This definition is more proper and quidditative than descriptive; as can be recognized, the genre is the habit in common, observing rules and precepts, which generically fits every Art: the difference is, to be the precepts and rules, produced from science and experience, that direct man to act effectively in defense and offense, of which Aristotle can be seen in book 6 of his Ethics, chapters 4 and 5.

It is proven by the definition of the definition that Aristotle gives, saying: The definition is a statement that explains the essence of what is defined; see St. Thomas in the same place, Cayetano, Alexander of Aphrodisias, and the current of the Scholastics. Cicero, agreeing with Aristotle, said: The definition is an explanatory statement, because there is a defined subject.

Both definitions of the definition are equivalent to the same concept, because it is the same to explain the essence of what is defined, as to explain what the subject is that is defined. The common objection that is put forward in schools is to say that neither one definition nor the other explains whether it should be long or short, from which the Moderns do not rest, pretending to hallucinate more, as will be touched upon in its place: summarizing here by the most concordant, that the definition of the definition is, to be a statement explaining the nature of the thing defined, included in the shortest ambit, which satisfies the objection; so Father Oña compiled it, saying, a definition is a collection of the properties of what one is, which is not found in another.

Assuming this, imitating the old common style, it is also necessary (in the art and experience of the Sword) to define the instrument, and generically it will be said: An instrument is that which, intervening, makes the action and exercises the office, as the instrument of seeing are the eyes, the instrument of cutting wood is the saw, the instrument of the Orator is the voice, articulating words, and placing periods, with the qualities, that Quintilian, and Rodolphus Agricola, who defined the speech by the effect, according to the reason of the argument, that explains to be speech, or instrument, that convinces the adversary, and leads him to the consequence of the leading. This can be applied to the instrument Sword, governed by a collection of rules and precepts, in such a way that, convincing the contrary, it forces him to the consequence of the leading.

This (according to the doctrine of the same Rodolphus) is achieved by two means, which are, disposition and controversy, just as with Dialectics, by the disposition of arguments, and dispute, which also admits the term Contest, like that of Swords.

It is doubted (with all that) whether the instrument Sword belongs to the Art, or to the Artisan? To this it is said (with the Philosophers) that as the instrument is of the Art, and of the Artisan; the same judgement is made of the instrument Sword, which is also of the Art, and of the Artisan.

The consequence is proven by the authority of Quintilian, who carries the common understanding, that the instrument is the intervening party, with which the action is perfected; and that one alone is the Artisan, to whom the instrument belongs. But if it is said that one is the reason for the instruments of Art, and another for the Artisans; the solution is easy for those who understand the terms, Qui, Quo, and Quod: Qui, is the Artisan: Quo, the instrument: Quod, the intention, or effect, which all compose a whole physical in concrete accidental, perfecting the action the agent Qui, by the instrument Quo, which is the Sword: from which it follows, that the instrument is of the Art; because in the benefit of the Art, the Artisan, and the instrument are directed to an intention. Therefore, the instrument Sword, governed by the man, who is the Artisan, by the rules, and precepts of the Art, composes no more than an accidental concrete, which is formed, or results from the Art.

For example, the bridle in the horse is an instrument with which the whole compound (although of different bodies) arm, hand, agility are a cause for victory: so in the accidental compound, man, and Sword; The skill, or ability used, cause victory: therefore the Sword, as an instrument, is of the Art, and of the Artisan. This will suffice for now as to the Art, since from the pointed out, one can discourse with extended adornments, which will perfect those knowledgeable in the exercise of Arms, for what they are Art.

As for experience, the field is no less expansive, where we will pick some flowers. Flavius Vegetius, a highly erudite author, and rightly esteemed in the science of war, recognized as a principle, or certain axiom, that in all fights, whether many against many, or singular (which all are embraced by the term Omni Prælio) not so much untrained forces, but art and experimental exercise, achieve victory: therefore the mere speculation of Arms is not sufficient, if art and experience are lacking, since the ideal is useless without operation.

What does it matter if he who prides himself as a Geometer, because he is adept at the placement of lines and figures, seeming to him that Geometry is subordinate to the intelligence and exercise of the Sword (as also to Physics, Metaphysics, and Philosophy) makes propositions that seem demonstrable to him, with the rule and compass, if in the operation of the Sword he lacks Art, and experience? Let the most speculative know that for the perfection of intelligence and exercise of the Sword, all the three cognitive powers, Science, Art, and Experience, are necessary; for as Vegetius himself concluded: Although the science of fighting increases audacity, because no one fears to do what they know they have experienced, nevertheless, in the contest of warlike actions, the small number of trained soldiers is more prompt for victory, than the rude and unlearned multitude, who are always subject to flight and wounds. The proof is given by Flavius himself, saying: That there is nothing that does not become easy with constant meditation and use.

From this, it can be inferred that science, art, and experience must coincide in what is commonly called the true Skill of the Sword: and to such a degree is the experimental operation imperative, that to achieve it, various methods were used by valiant Nations; particularly with the instrument of the sword and shield: this (as described by Flavius Vegetius) was made circular, from wicker, with double the weight of the ordinary ones used in the armies: and in place of swords, at the beginning, they gave new soldiers, called Tirones (and our common term, ‘greenhorns’) clubs, which were like wooden swords, also double the weight of the common ones; and so that they could be taught from their own experience, they set up wooden poles, shaped like swords, each one six geometric feet high, with the pole being movable towards the part of the Tirone. In this way, a pole was attached for each one, and against it, as if it were another adversary, with the shield and club (which served as a sword) they trained, finding themselves in opposition, trying to hit either the head, face or sides, teaching themselves to enter and exit, and to experience all movements of the feet and legs, defending, attacking, and retreating, as if the pole were another enemy man, executing all impetus, and all art in fighting, with such meditation and caution, that they recognized and experienced how they had to strike, without being offended.

Vegetius himself notes that this practice of using poles was not only extremely useful for soldiers, but also for gladiators, who required the highest skill in swordsmanship. He emphasizes that no man has ever been recognized as invincible in the arena or on the battlefield without having practiced with the pole.

Great example! It’s a grand disillusionment that conclusively convinces those who presume that they can fully understand the art or the science of the Sword without agility in action and experiential learning! In whose effects alone, lines, figures, circles, and conical sections, premeditated in the imagination and described on paper or print, are of little value. While a knowledgeable and experienced person achieves a collection of rules and precepts that form the art, they also recognize with disillusionment and evidence, that formalities of lines and conical sections, etc., that pure mathematicians describe on paper or in prints, are not useful among the actions of defending and offending in execution against another human adversary. Rather, they rely on other methods that, although originating from geometric ones, are performed with the sword and arm, adapting these terms to the understanding and practice of the Sword, varying the centers and positions according to the movements compelled by the operation; and this with such speed that neither the sight perceives them well, nor always do they align with the imagination: and if this is necessary against a pole, how much more against a rational adversary? And how much less useful will be theorems and problems of precise lines, circles, and figures, especially when they do not fit the operation itself.

From science and experience, the rules and precepts of art are perfected and gathered, and lacking any of the three cognitive powers, one will barbarically presume to grasp the understanding and exercise of the Sword (which is commonly called Skill) that to achieve it among the Romans, they not only relied on experimental practice with the pole, but also noting (as Vegetius himself points out) when it is important to know how to strike more with the point than with the edge.

Furthermore, in the type of exercise that the Field Doctors (who Vegetius signifies with this name as experts in the science, art, and experience of the Sword) called ‘Armatura’, they examined the Tirones, recognizing that in all battles, those trained in the Armatura fought better than the others. From this, he draws the conclusion, confirmed with estimation, saying: From this it must be understood, how much better the trained soldier is than the untrained one, and learned in the Armatura, and how much they precede their comrades in the art of fighting.

And he adds: The discipline of exercise was so severely enforced among the elders that, as for the Doctors of Arms, they were rewarded with doubled annonas (which were military rations): and for the soldiers who made little progress from such exercises, in place of wheat, they were given barley, compelling them to accept it, and they could not return to enjoy wheat annonas until in the presence of the Prefect of the Legion, and of the Tribunes, and of the General Prince, they could demonstrate that they knew everything they were obligated to in Military Art. And he concludes with such emphasis. Nothing is more stable, happier, or more praiseworthy in the Republic than an abundance of skilled and learned soldiers: it is not dressing in gold, silver, or shiny stones that inclines enemies to reverence or grace; but only the fear of the weapons by which they are defeated. Thus, I say with Cato: Errors can be corrected, but not in the crimes of battles, which do not receive amendment, because in them those who ignorantly oppose perish, either fleeing from the victors or showing themselves to be inferior.

We can already see the causes and examples, worthy of commitment in the studies and operations of intelligence and exercise of the Sword, that for everyone is noble, useful, and necessary; also being a great honor for the Nation, a significant ornament in public order, a great strength in the Army, and a great reputation in weapons, as the Sword is preeminent and a significant cause for victories.

In this consideration, the Ancients, even in their rudeness after the Universal Flood, in need of defense and offense, not only premeditated ways to introduce science, art, and experience into fighting with different warlike instruments, making men agile, but they also encouraged them with rewards, honor, and fame, dedicating places and times for such exercises. This resulted in the diversity of military exercises, in wrestling, running, jumping, spear throwing, and other bodily exertions, with honorary rewards, crowns, and other decorations, from what they called the Olympic Games, into whose terms they later substituted contests, as from some and others, large volumes can be formed. Here I have omitted what is not of my subject, referring the curious to Pausanias, Athenaeus, Suidas, Caelius Rhodiginus, Natal Comite, Strabo, Herodotus, Ravisius Textor, and the extensive Johannes Villembrochius Dantiscanus. It is found in the cited authors, and in ancient and modern historians, that at various times, nations, and provinces, there were contests of arms with judges and prizes (in the manner of the Olympics) which Pausanias talks about: and to our purpose, we find the one that was most anciently instituted, called Grave Armatura, which was of the Sword, the shield, and the warlike tunic, as is recognized in Flavius Vegetius, by the term Armatura, and of this Villembrochius says that it was later instituted, accepting the course of the Infantry, because they considered it useful for war; and the first victorious in such a contest of the Sword, was declared Demeratus of Hera, crowning him in the manner, and rite of the Gymnic contests, in which the prizes were only crowns of leaves from different trees, or plants, with honor being the true reward of virtue. Hence the famous saying of Tigranes, son of Artabanus, who upon hearing from the Greeks that skill, dexterity, and valor in the handling of arms, was received with only crowns of Celery, Olive, or Laurel; when Papeo Madronio was persuading Xerxes to wage war against them, he exclaimed: Oh Prince, against what men do you induce us to fight, who do not agitate contests for money, but for virtue?

With this end in mind, Alexandro in his Genial Days advises that the Gladiatorial Games (that is, of the Sword) were instituted to instruct youth in Arms, thus becoming accustomed to not fearing the congress of enemies, this exercise being all the more honorable, and all the more proper for the nobles, as they are more dedicated to warlike actions by obligation.

So Xenophon notes about Cyrus, in a great action, that he took away the bows and arrows from his soldiers, leaving them only the sword, shield, and breastplate, so that they would fight more skillfully and bravely: and to this end, he introduced among the soldiers contests with such weapons, acquiring in them intelligence, exercise, and skill, rewarding the victorious with valuable gifts, and remunerating them with dignities.

Suetonius Tranquilus relates of Julius Caesar, that he valued the Skill of Arms so highly, that in the game and exercise of the Sword, he would not permit his recruits to be taught by common Masters (who were called Lanistas) but rather he obliged the Roman Knights, and the very Senators skilled in Arms (who for this reason were called Doctors of the Armies, according to Vegetius) to teach the Military in their homes; for this purpose he made public requests in his letters, encouraging them to acquire the science, and skill of the singulars, so that they could thus communicate it.

From this principle could arise the consideration of Valerius Maximus, who, making memory of the Military competitions, highlights that Publius Rutilius Consul, and Gaius Manlius, his colleague, valuing the exercise of Arms (and especially the Sword) brought to Rome, from the School of Gaius Aurelius Scaurus, the most exercised Teachers of the Gladiators, so that with their science, art, and experience, in defense and offense they could teach to avoid contrary wounds and execute their own; because thus, mixing virtue with art, and art with virtue, the former would provide the strong impulse, and the latter the knowledge to the former, resulting from both the cautious brave operation.

The insistence on the terms Gladiators, and Lanistas, so used in the Ancients, and so little understood by the common people, who, confusing the exercises, actions, and people, do not distinguish the honorable from the reprehensible, nor the contrary; for this purpose, it is necessary to investigate in the depths of good letters what is essential to our intention.

Seneca, writing to Lucilius (speaking of the Gladiators) makes mention of three species, and without distinction, considers all of them reprehensible, naming them, Ordinaries, Equals, and Postulatics, for whose verification, some rely on Festus, and Ulpian, also confusing the term Postulatics with Supposititious, by the verse of Martial: Hermes is also supposititious.

But Celio Rodiginio, great inquirer of the ancient voices, against Seneca, and the rest of his opinion, considers as Ordinary Gladiators those who were in the first place experts of the Gladiatura, and who, instructed in their appearance, and rite, produced the Gladiators, who at the will of the spectators, constitution, or custom used to exhibit. And he makes an example in the Jurisconsults, and Ordinary Consuls, concluding: Because Suetonius called it a just and legitimate spectacle of the Gladiators, by the formula, and ordinary rite given.

And to greater evidence, he proposes the Ordinary Judge, who by his right, or of the Prince exercises entire jurisdiction, as also to that one to whom is committed the university of causes, and that by the College is chosen, and by the Superior is confirmed, who is named Ordinary, and the same the Legate in the Province over decree, in which Celio admits two types; some, who have administration; and others, who do not have it; as also there were two Ordinaries of the Militia (as in the History of the Emperors, dealing with the Empire of Tiberius, writes Flavius Vopiscus) as it was used in the Cavalry, where there were Ordinary Consuls, which is all from the same Celio.

The same author understands “Postulaticios Gladiatores” to be those who, due to the requests or petitions of the people (beyond ordinary obligation), out of kindness or concession by the Prince, provided some Gladiators for extraordinary events. This is what Suetonius Tranquilo implies when he says that, in addition to the ordinary obligation of the Questors, the people always petitioned and were granted the power to have more ‘Pares Gladiators,’ who brought about a new, courtly spectacle. The same Suetonius explains this more clearly in his description of the extraordinary spectacle of Gladiators.

Celio corrects the lesson in Seneca, who reads ‘Pariarios’ for ‘Pares’. He argues against Seneca’s understanding, as Seneca considers ‘Pariarios’ to mean ‘Proxenetas’, which is the equivalent of Mediators or Conciliators in purchases, sales, disputes, etc. He also notes the custom that when Emperors went to war, they staged spectacles of Gladiators and ‘Venaciones’ (wild animal hunts). The Gladiators fought before the image of Nemesis, believing this would dispel the force of fortune, or so that the soldiers would dismiss their fear of giving and receiving wounds.

Pliny, when discussing the spectacles of the Elephants, reports the culmination of the Gladiators during the time of Claudius and Nero. Celio Rodiginio, grappling with the difficulty of what the culmination of the Gladiators could be, concludes (citing an author he calls ‘most learned’) that these were the veteran Gladiators who, due to their art and daily practice, needed to rest. If you agree, they could also be called ‘Rudiarios’. Prisciano, the interpreter, named them as such - those who, upon receiving a staff or bar, leave the Gladiator life and receive public sustenance. Cicero alludes to this when he says to one, “You have been such a good Gladiator, why did you receive your staff so soon?”

Celio concludes that Gladiators were called ‘consumed’ when they were recognized for their science, art, and gladiatorial experience (which is the same as being skilled with the sword), like soldiers who were dignified by their deeds; they were called ‘consumed’ due to the strength of their merits.

Thus, Julio Frontino notes that after Curcio defeated the Sabines, by Senate Consultation they expanded his lands, as to the seasoned soldiers, although he was content with the ordinary portion that was granted to veteran soldiers. So, not all who practiced gladiatorship were blameworthy, but distinct among themselves, according to their occupation and skill.

Thus, different types of Gladiators are found, regarding the common weapons (as noted by Juan Ravisio Textor, and the Theater of Human Life) were those they called Reciarios, Sectores, Mirmilones, Hoplomachias, and Thraces. And they generically named the Masters of all these Lanistas, which corresponds to public Masters of Arms, because they had public Schools in the squares, or fields: but there were others, who in their houses taught the science, art, and experience of the Sword.

Those who were public Lanistas, taught the Fiscal Gladiators, and others, who sold to the Munerarios for public Venatory and Postulatic spectacles, and those who for pay, or for public ostentation fought under the Sun in the arena.

Munerarios was properly called those who were the exhibitors of the Fiscal and Venatory Gladiatorios for public spectacles, which corresponded to those called Agonethas by the Greeks: apart from the Lanistas, there were other persons skilled in meditation and exercise of the Sword, very different, and so they called them Sciamachios (because as Celio Rodiginio explains) they knew and taught the science, art, and experience of the Sword, not in the squares, nor to the common Gladiators, but to the Milites, as sensed by Plutarch, from where Juan Ravisio Textor, explaining the term Sciamachia, the exercise, said, that under a roof they feigned a shadowy fight, not a real one, like that of the Lanistas, but teaching the Art of the Sword in all its ways of attacking, and retreating, striking, and avoiding the wounds, as well as where with the point, where cutting, they had to execute the blows: and so they taught their disciples, so that on all occasions, now in the dust, now in the injurious contest they would better assure themselves, and with more art attack the enemies. The curious see, and note the words of Textor himself, which being so broad, although proper of the intention, are omitted.

This place expresses our intention, demonstrating how different were the Lanistas, and common Gladiators, who were produced for public spectacles, to those who nobly taught and learned the intelligence and exercise of the Sword, to defend themselves, and offend their opponents in honorable occasions: from which, learnedly, Celio Rodiginio, recognizing the distinction, reproves those who, like the commoners, confuse the terms, rudely understanding by the Sciamachia, which is the perfect Skill, and meditation of the Sword, what they call Fencing, which is very different, as the same Celio points out, calling semi-learned people those who confuse such distinct terms; in whose consideration he disputes the terms, and the exercises, and applies to the Sciamachia the history, and the statue of Glaucus, a man distinguished in virtues; and especially in justice, and in the meditation, and operations of the Sword (which is commonly called Skill) and thus, those who professed it (in contrast to the Lanistas) had, as a noble insignia, the painting of Glaucus, according to his statue, as Celio refers, where with more breadth the curious will find all satisfaction.

And although those famous in the intelligence and exercise of the Sword, generically (by the instrument Gladio) were called Gladiators, and divided their species by the weapons they used (as noted above) from the Retiarius, Secutores, Murmillo, Hoplomachus, and Thracians. Because in public spectacles these kinds of weapons and exercises were admitted, it does not mean that those in Sciamachia, who learned them with greater perfection and for better purposes, did not use the same weapons, finding among all of them extremely noble and famous men, as will be proven by the memory of worthy examples. It is assumed, for clearer understanding, that the Retiarii fought with a net, which they hid under the shield, and with it, in the conflict of the fight, by throwing it, they entangled the opponent, and these also had the name of Murmillo (so called, because they were opponents of the Retiarii, and they had as insignia on the helmet a fish, as Turnebo says) and they were differentiated from the Secutores, in that using a shield, armigerous tunic, and Sword, some, and others put on helmets, and the Retiarii hats, as Ravisio Textor and Carlo Zerotino touch on, making use of Juvenal’s verse: He did not hide his forehead with the cloak, nor did he move the trident. Herodotus tells of Phrinon (whom he qualifies as a very clear Captain of the Athenians) who was so skilled in the kind of Gladiator Retiarius, that in a singular contest with Pithaco Mitiline, in the greatest conflict of the fight, with the net, which he hid in the shield, he threw it at him on one side with such skill that, enveloped in it, Pithaco was surpassed by Phrinon, and he honorably defeated him.

Juvenal also mentions Gracchus, a famous Retiarius:
Even when Gracchus fought, he didn’t move his shield.
They called the Gladiators who used swords in the Thracian style ‘Thracians’, a skill that was highly esteemed in antiquity; they are thus placed among the others, and Spartacus the Thracian is mentioned for his renown, as Cerotino and Textor say, he was famous.

For further verification, I will compile some notable examples of experts in the science and art of the sword, to whom the Ancients gave the name Gladiators, not because they were Fiscal, Venartorian, or Postulatic, but because of their practice and skill with the instrument of the sword.

Suidas says of Polydamantes, that Artaxerxes gave him great rewards because in a public contest he alone fought with three very strong Persians, and killed them all; such is the value of experienced skill.

Eliano celebrates the skill and strength of Dioxippus, a soldier of Alexander the Great, who, challenged by a Macedonian soldier named Coragus, killed him in a one-on-one duel.

Josephus appreciates Sabino, a notable Gladiator, who because of his knowledge and skill, Emperor Gaius appointed him his tribune and made him the prefect of his army.

Solinus and Pliny make a point of admiring Tritanus, a Samnite gladiator, of whom Varro affirms that he not only had transverse muscles in his chest but also in his arms. This natural constitution gave him such strength that with a light touch he could overcome any adversary, perfecting his physical aptitude with exercise and knowledge. It’s also said that he had a son very similar to him, who, being a soldier of Gnaeus Pompey, killed his enemy with one finger.

Leaving aside many other examples of notable and famous men in swordsmanship, we’ll conclude with the famous Vito and Bachio, who were equals in skill and audacity. Having always been victorious against their adversaries, they challenged each other to a duel. Neither won the victory; both died in the arena, giving rise to the saying, Vito against Bachio. as noted by Erasmus and Carlo Cerotino.

Ersenio and Pacidiano, whom Cicero and others called the most noble Gladiators because of their science and skill with the sword, always emerged as victors. Neither was defeated by the other even though they fought, giving rise to another saying to signify two excellent equals, Ersenio with Pacidiano.

No less notable was Eschines, who, like Ersenio, fought with the same Pacidiano. They made peace during the combat, recognizing themselves as equals, as Cerotino notes.

In antiquity, it was allowed when two experts in the sword entered into a duel to compose themselves, remaining honorable, either because they both learned from the same Master, or because they were notable in skill and valor. This can be inferred from the case of Eschines and Pacidiano, as expressed by Celio Rodiginio and Cicero.

And what adds great and distinguished consequence to all this is the most exemplary and admirable case found in history, particularly in honor of Spain: the case of two distinguished Spanish knights, Rui Paez de Viedma and Payo Rodriguez Davila. During the reign of King Alfonso the Eleventh of Castile, having challenged each other (according to customs), the King granted them a field in the Arena of Jerez de la Frontera and was present at the fight. They entered the arena and fought continuously for three days from sunrise to sunset, retreating each night to their respective tents set up within the arena, where they were treated for the wounds they had inflicted on each other, and given bread, meat, and wine for dinner. The following day they returned to combat with the same courage, fighting ceaselessly until the afternoon of the third day, when the King himself separated them and made peace, declaring them equal in skill, courage, and loyalty, recognizing them as distinguished knights, worthy of military exploits, in which they earned renown. He declared them both free from the obligations of the challenge, like both victors, as is extensively referred to in the history of the same King and in other books and noble records. It is noteworthy that in such duels, the Kings were present with a golden rod in hand, symbolizing supreme justice, and the combat was carried out with swords. The last example of this was the challenge that took place in Valladolid, attended personally by the great Emperor Carlos V, who separated the fighters by throwing his golden rod at them, and declared them both good, with the circumstances that Don Fray Prudencio de Sandoval relates.

From all this, it can be clearly inferred how significant, illustrious, and noble the science, art, and experience of the sword is; and the distinction there was in antiquity among its professors and masters, and which were deplorable and which were noble and esteemed. This justifies the resolution of Pedro Gregorio Tolosano, who, discussing the gladiatorial spectacles of antiquity, said that exercises of arms and fights should not be understood absolutely, but with moderation, because some look at the interest, or price, and others at virtue: those are undoubtedly depreciated; these do not admit infamy, even in athletes, as noted by Ulpiano, and Alexandro de Alexandro. And it is consistent with the doctrine of Plato, who confesses: No man achieves renown if he does not engage in honest exercises from childhood.

Thus, no one is more suited to nobility than the understanding and practice of the sword, as all civilized nations adorn themselves with it, arm themselves with it, and honor themselves with it; this is especially true today, where common gladiators are completely excluded, resulting in the proverb, They advised in the arena, because they fought there in public spectacles, or as fiscal officers, or as those excluded by the Lanistas; and even among these, composition was accepted (as noted earlier) for having learned with a master, as Quintilian also points out.

Also excluded since antiquity is the combat that was introduced at banquets, as Nicolas Damascene reports: the Romans used gladiatorial spectacles, not only in public theaters but also at dinners and banquets in the rite of the Tyrrhenians, from whom they learned, choosing up to two or three Gladiators (those they called Pares) for their skill; and these, after being satiated with the dishes and drinks, fought fiercely each seeking victory, even if they killed their opponent or opponents; and this action was considered very festive, as Atheneus also writes about the Celts.

Not only in banquets did they introduce gladiatorial contests, but they also offered a beautiful woman as a prize to young men, for whose love they would fight spiritedly; seemingly taking imitation from irrational animals, as per Ovid’s observation, who said: I saw two sturdy bulls fighting for a beautiful cow, who was present, infusing vivid valor.

And this rite went so far, to encourage the skill of the sword among the youth, that in their wills, some left that for such beautiful women, they would fight with swords, and give themselves to the victorious as a prize. This custom lasted until the Roman people themselves abolished and prohibited it, as Carlos Cerotino expresses.

The use of gladiatorial contests and combats was also so widespread that they were not only introduced at public festivals and banquets, but also at funerals. The Roman Republic and other nations had public masters at great prices for so many and various types of Gladiators, who (according to Juan Villembrochio) they generically called Lanistas, very different from the Sciamachios, imitators of Glaucus, whose painting (in the style of his statue) they had in their houses, where they taught those dedicated to war. For this just cause, the premeditations and exercises of the sword were instituted, so that the educated youth would become accustomed to not fearing hostile fights, as Alexandro and Celio Rodiginio noted. Celio gives Theseus as the inventor of Pancratium, in memory of the victory he obtained from Minotaur, and understanding by Pancratium that fight, in which the skill of the sword was not aptitude, also attributing to him the palaestric exercise, in which the main practice was of swords, hence the masters of such combats were later called Doctors of the Palaestra in court.

And if we were to discuss all types of contests, whether Olympic or others, introduced for the agility of men in different weapons and movements, all for the purpose of human defense and offense, it would be necessary to write entire and large books, which for not being my subject, are omitted.

It is understood that in place of Sciamachia, there has remained meditation, operation of intelligence, and the practice of the sword, where those with knowledge, art, and experience reach their excellences, having virtue as their main reward. Even the Doctors of the Armies, Tribunes, and Consuls, who strive to achieve a true understanding of the noblest and most honorable instrument wielded by men for the defense and honor of the kingdoms, can be correspondingly recognized.

And those who commonly, even if not through all their principles and cognitive powers, at least through acquired and experienced rules and precepts, engage and practice the teaching of the sword, deserve the honorary title of Masters in Arms. They gain more esteem, the less they frequent and appear in public squares.

FIFTH DISCOURSE.

LOGIC OF THIS SCIENCE: of the Definition, and Division

Having demonstrated in the previous discourses that the understanding and practice of the sword is a science (from which art is produced), with experience contributing to the practicing part, it is not to be omitted the method and precepts by which it is governed. This includes the rational logic, which is common in all sciences, as well as the disputable dialectic, which looks at the rules and precepts with which experience is perfected, resulting in what the common people call Skill.

Philosophers, logicians, and dialecticians consider the definition and division as principal terms to all science. With the understanding of these, one can better engage in the predicables, predicaments, categories, etc., in which the understanding becomes accustomed to guiding towards demonstration, acquiring what is probable or evident, which is the aim of all science, art, and discipline. This is also recognized in the understanding and practice of the sword, where the terms: Definition, Division, etc., are necessarily integral parts of the argument and demonstration.

It is commonly touched upon in schools as a difficulty, which comes first in order: the Definition or the Division? They consider that if they refer to different things, the division is first in the order of nature, because by the division of the superiors the definition of the inferiors is investigated: e.g. by the division of the substance the definition of the animal is sought; and thus, the division is first, before the definition, because it is first to divide the highest genus than to define the species.

On the contrary, if the definition and the division refer to the same thing defined, the definition is first before the division in natural order, and of doctrine; e.g. if the animal to be defined is considered, the definition is first, then the division. The reason is clear: the definition is a certain composition of the thing defined, and the division, indeed, is the resolution: and according to the order of nature, it is first composed, then divided, and resolved.

It is commonly touched upon in schools as a difficulty, which comes first in order: the Definition or the Division? They consider that if they refer to different things, the division is first in the order of nature, because by the division of the superiors the definition of the inferiors is investigated: e.g. by the division of the substance the definition of the animal is sought; and thus, the division is first, before the definition, because it is first to divide the highest genus than to define the species.

Therefore, when talking about the precepts of defining and dividing, the principles of defining should be disputed first in terms of doctrine and dignity: in terms of doctrine, because the concept of division cannot be properly understood without the definition: and in terms of dignity, because the definition explains the essence of what is defined: just as in the science of the Sword, the essence of what is defined in it is not explained by the division, but by the definition in the first place, as will be demonstrated; and here for the sake of brevity and clarity, we present the naked conclusions without the disputable apparatus, and various opinions of authors, because, as it has been said, our aim is not to show off, but to explain what is necessary for our endeavor, trying to stick to what is necessary in what is written.

Aristotle teaches that there are not many quidditative definitions given of a defined subject, just as there are not many essences, because if there were, its supreme whole would not be definable. From this, Scotus concludes that there are not many definitions of an absolute (of which the definition indicates its being). From this, it is argued: the definition is one absolute, etc., therefore the definition of Definition must be one, and not many.

For this reason, the same Philosopher defined the definition of the Definition, saying: It is a sentence that explains the essence of the thing. In this substance, Philosophers and Rhetoricians agree in different phrases, from which we deduce the definition of the definition, being: It is a sentence that explains the essential nature of what is defined in the shortest possible number of words.

We say that it is a sentence because it is not a simple word; if you were to say, the Gladius is a sword: it is a sword, it would not be a definition, but a simple or identical proposition. In a sentence, there are more words; one perfect, which consists of one word, such as White man; another imperfect or compound, which does not consist of one word, but many, such as Man is an animal participant of reason; and so, although it is a sentence, it is not only a definition but a definition and the defined, because for the definition, the genre and difference are enough, which is explained by Animal participant of reason; the word man is not part of the definition, it is the defined.

Therefore, the definition should not be obscure or ambiguous, but lucid, clear, and proper, so Quintilian said: The definition is a sentence of the proposed thing, proper, lucid, and comprehended in brief words. From this, Aristotle named it Oros, with Quintilian explaining that it signifies Term, in allusion to the boundaries in the fields, which are also named Terms, because they include what they comprehend, distinguishing one from another.

Boethius considered fifteen types of definitions, not by essence, but by the manner of composition: the Modern Scholastics are content to divide the definition into two modes; one, definition of the thing, which is that which explains it, according to its own being, and essence; and this they call Essential, and they divide it into causes, and effects, etc. Another mode they name definition of the name, because it explains what the name signifies: and they consider it in five modes.

The first, when an obscure word, name, or term is demonstrated by another clear, intelligible one, like Fretum, which is a narrow or strait of Sea, placed between two continuous lands: Zero Movement, which signifies a certain way of acting with the Sword.

The second mode is when the etymology of the name or term is explained, like Parricide, the one who kills his father: Triangle, that figure which consists of three angles: Cuchillada, that wound made with the blade of the Sword.

The third mode is when it is explained by analogy, or metaphor, like Adolescence, is the flower of age: The mind, in the soul, is what the eyes are in the body: Estocada, for that wound made with such a form of Sword, which has no cutting edges on the blade, like the Estoque, to which it alludes by analogy, or metaphor.

The fourth mode is when it is explained by example or comparison: for example, the brute animal is like a man in sensitivity and in movement, etc. The Cut and the Reverse resemble each other in delivering a cutting strike.

The fifth mode is by negation, such as virtue is to avoid vices. God is not a created substance, He is not finite, etc. The Reverse is not a Cut, and even less a Thrust.

These principles moved the Philosopher to consider the division of the definition, in that which looks at the reason for the thing defined and in that which looks at the name, so he said: The definition of the thing defined is that which is the means of demonstration, either by the nature of the subject defined, or due to causes, and this is called essential. The definition of the name is that which is not a proper means of demonstration, like definitions from offices, elected, etc. of which Aristotle speaks broadly, and the Dialectics discuss.

There are three types of definitions different from each other, not by essence, but by the mode of the definitions; which are a means in the demonstration; the first, which is by genus and difference, is raised with the name of essential by antonomasia: the second, although it is also essential, is called ‘sought from causes’: the third is the description, because the defined is explained by passions, or properties, like ‘Man is a laughing animal’: which is only property, and not constitution: the same is the Equilateral Triangle, Vertical Cut, which are essential definitions of a mathematical figure and of a cutting wound; because all, and the like, manifest the intimate of what they define: all three are embraced by the Definition, which explains the essence of the thing defined by that which is intimate in it itself: and in the one in which these qualities concur, it accepts the term or qualification of essential.

For understanding this, it should be noted that there are some considerations that are accidental, meaning the subject defined can exist without them, and others are such that without them the subject cannot subsist. In those that are so accidental that without them the subject can exist, they do not provide essence to the definition, such as being seated or standing; sleeping or waking; these considerations, and the like, do not take away the subsistence of the subject, or the thing defined; for the man standing or seated; in stillness, or movement; sleeping or waking; subsists in all his being, and is defined without them. There are others that are not accidental, but essential, because without them the subject or thing defined does not subsist whole, such as wings in a bird, which is not physically complete without wings; but with all this it can be defined, and understood by Genus, and Difference proper to the subject.

There are other considerations, without which, neither the subject can exist, nor can it be defined or understood: these are properly called intimate, like rational animal, wound in its lowest species, which are the lowest considerations in the subject; because man cannot subsist or be known without them; nor the wound, but by its lowest species, in which its lowest and intimate difference is explained, like Stab of Quarter Circle, where the term Stab is genus, and Quarter Circle is the lowest and intimate difference: the same can be said in every defined thing, just as the Triangle does not subsist in its figure without three angles; and more essential, if it is declared by its lowest, intimate difference, Octagon, Isosceles, etc. because Genus is that which includes different species: and Difference is that which separates, and represents the intimate properties of the Species; and therefore we resort to the intimate, and lowest differences of the subject, that separate it from the other species, which are included in the genus, from which it is understood what the Philosophers commonly say, that the genus must be constituted from the matter, and the difference from the form, in which what properly belongs to the genus is known; and what properly belongs to the lowest, or intimate difference in the subject, to form the essential definition; e.g. Vertical Cut, Diagonal Cut, etc. which are defined, and known by their lowest, intimate difference, with respect to their lowest genus, which is why it is considered, that there are also very general genera, that include, and embrace in themselves other genera, as in the science of the Sword there are very general genera wounds, movements, which are capable of including in themselves other genera, not so general, as in wounds, slashings, stabbings, which are genera for other lower genera, such as Cuts, Backstrokes, etc. and so in movements. For example: in the straight line of a category, or predicament, descending from a high genus to a lowest species, it will be said wound: or is it cutting, or point. Cutting? Slashing: Slashing? Cut, or Backstroke, Backstroke Diagonal, or Vertical. And ascending, it will be said Diagonal Backstroke: then slashing. Slashing? then cutting wound.

The same method is considered in Philosophy, as if we were to say: Vegetable, only man, brute, and plant, etc. and these general and more general Genres in the definition require more considerations, going from a highest Genus to a lowest Species, or conversely, ascending from the lowest Species to the highest Genus of its predicament, as will be demonstrated in its place: noting here, that there are highest Genres, or principles, that do not admit essential definition by Genus, and Difference, because the simplest Genus or principle does not admit Difference in itself, like the point, which is the principle of quantity; but it is not quantity, because it does not have parts, and thus lacks difference: but not for that reason is it indefinable (since everything finite, be it highest Genus, or principle, is definable) but due to lack of Genus, and Difference From Causes, or by description: thus Aristotle compares the essential Definition to the number, because just as with the number, if something is added or removed, it changes the species; e.g. in the ternary, if one unit is added, it becomes quaternary; and if one is removed, it becomes binary; so also in the essential Definition, if something is added or removed, the definition is inverted, or passing from a less general genre to a more general one, or vice versa, as Logicians and Metaphysicians broadly dispute: the same is experienced in the science of the Sword, in which removed or added an intimate, or lowest Difference, inverts the Definition, as has been pointed out, and is evident.

The second mode of essential Definition is From Causes, or by one, or by more, or by all: for understanding this, it is assumed with the Philosopher, his Expositors, and the current of the Schools, that there are four causes, material, formal, efficient, and final, and we place them in such order as to nature, that first is the matter, then the form is introduced, and then the efficient and final cause are considered, always recognizing that natural agents, making, suffer: because only God is the first efficient cause, and so Cause of causes, Creator of prime matter; and the others that are considered, are physical causes, and subsequent: e.g. in man, it will be said, that he is an animal, whose physical matter in the first was the slime of the earth, and in propagation the prolific matter: in the formal it will be said, that he is a rational soul, which gives him being, and form, produced, by the efficient; and it will be said of man, that he is an animal, consisting of a human body, and a rational soul; and in this definition, the body is matter, and the soul is form, and by supreme efficient we recur to the essential principle, which is God, who in the slime of the earth, disposed, inspired the rational vital form, from which the essential end of man is to achieve the end for which he was created, and by all causes it can be said, that he is an animal, consisting of a human body, with a rational soul, created by God, the principal efficient cause, who created him for the most perfect end he should aspire to, which is to see and love Him in Beatitude.

In the rest of the sciences, causes are investigated according to the order of nature, and through it, an essential definition of what is defined is formed. Similarly, in understanding and practicing Swordsmanship, being a science, definitions are found by causes and they are also essential, as will be demonstrated in its place when dealing with the causes of this science.

The third form of essential definition, which can be demonstrable, is description; and although this is not as quidditative as the one resulting from genus and difference, or causes, it does not lack essence, as it explains it in a brief sentence, which describes it in such a way that it is a means for demonstration, and thus it is defined, saying: Description is a brief sentence that explains what the definable thing is through some or some of its properties, or by the collection of many accidents, and proper of the subject.

By some of its properties, such as when a man is defined as a laughing or admiring animal, or all together: because admiration is a property of man, and laughter is also, and the subject of admiration is laughable, and the one who is laughable is admirable, which are properties of man, and sufficient to define him by description; but it can also be done by the collection of many accidents, like a two-legged animal that lacks feathers, which are accidents, that each are properties of other animals; because birds are two-legged, and fish lack feathers, these accidents do not occur together as properly as in man, without having a place for the Ecce homo Platonis in the featherless rooster, as Achilles Bocchio tells. In the science of the Sword, many definitions are made by description, such as of the Sword itself, which is an instrument of two edges in proportional length and width, consisting of a sharp point, and such ornament at its beginning, that provides defense to the hand that guides it, and gives it aptitude to impede the opposing instrument, to which it has to oppose. And so, other described definitions can be formed.

Aristotle, recognizing the precepts of many to find the correct definition, gave the following: the first rule is that it should be distinct and clear, and this precept is violated in two ways; the first, if the thing to be defined is included in the definition, such as saying: The rational is an animal partaking of reason, Dialectics is the skill of arguing dialectically, where the subjects rational and Dialectics are what is being defined, which should not be included in the definition, as for this, the genus and the difference are sufficient, and essential, and on the same defined subject, like saying: A stab, or Vertical Slash, where the same mistake is committed.

The second error is if an obscure, ambiguous, or homonymous voice is included in the definition, such as saying: Generation is movement from non-being to being; such a definition is faulty, because Movement is an ambiguous word, and does not form a distinct definition; obscurity is committed when obscure words are used in the definition, such as saying: The earth is the nurturer of the living, the error is committed in the word Nurturer, which is metaphorical with respect to the earth. Obscurity is also committed in improper ways of speaking, such as: The Law is the image of those who are just, which is an improper phrase for the definition, from which unusual words are also excluded.

The second rule in the definition is that it should not be greater or smaller than what is being defined; this means that it should not apply to more than what it defines, because what is extraneous is faulty in the definition, which will be greater when it expands to more than necessary, with redundant terms: and smaller when it lacks some term necessary to the understanding of what is being defined.

The third rule is to match the subject, or thing being defined, with such property that the intimate of what is defined is understood; in such a way that what suits it, suits the definition; and what suits the definition, suits what is defined reciprocally, as is recognized in the accepted definition of man as an Animal participant of reason, which suits the definition, and the subject: all this the Philosophers explain briefly, saying, that defined, and definition are convertible.

The fourth rule is that in the definition there should be nothing superfluous, which will be recognized when, if any word or particle of the definition is removed, it remains sufficient, as in saying: Rational, admiring, and laughing animal, which is superfluous, because even if the words, Admiring, laughing, or the like are removed, the definition remains sufficient, saying: Rational animal.

The fifth rule is that what is defined should be recognized if it is capable of genus and difference, so that the essential results, because lacking true genus and difference, one will have to choose by causes, or by description, and this is achieved by ascending and descending along the straight line of the categories, as will be demonstrated in the Predicaments.

Aristotle found two means of investigating the Definition, one through composition, another through resolution, because the first order is to compose rather than to resolve.

For the composition, the genus must be sought; and once found, it is divided by contrary differences, and from these the proper and immediate ones of the thing being defined are chosen, excluding the repugnant ones, proceeding in this way until a proper sentence can be formed, suitable to what is being defined; e.g. in man, the highest genus of his category is sought, which will be Substance, and this is called the highest genus, from which it is derived: therefore, the substance will be divided into its differences, which are, corporeal, and incorporeal; and because the incorporeal is repugnant to man, what suits him is chosen, which is corporeal, and it will be said: Man is a corporeal substance; and because the intimate difference of man is not achieved with only being a corporeal substance, one proceeds to the immediate difference of the corporeal part, which is, being animated, or inanimated; and as the inanimated is repugnant to man, what suits him is chosen, which is to be an animated corporeal substance: but as the animated can be sensible, or insensible; and the insensible is repugnant to man, what competes with him is chosen, which is, being sensible, and it will be said, that he is a sensible animated corporeal substance; and as the sensitives differ in participants of reason, and in those lacking reason, and it is repugnant to man to lack reason; it is convenient for him to be a participant of reason, for which reason the intimate difference that competes with him will be chosen, which is, being a participant of reason; and from this difference, and from the immediate proximate genus, which is animal, the essential definition by genus, and difference, found by the composition of the Predicament, or category of substance, will be formed, discoursing along the straight line of the Predicament, because in the parts of the definition such an order must be observed, that the genus is placed first, and then the differences, and among the general ones, the least general ones are chosen, until the most intimate to the defined is found. And by this method, everything that admits an essential definition by genus and difference is investigated, finding what properly competes with the definition, according to the definition of the Definition, as will be demonstrated in the science of the Sword in its predicament, or category.

In creating a definition based on causes, you compose it by finding the properties that are unique to the subject being defined, investigating until you find the most specific or most intimate differences that result from the causes.

When creating a descriptive definition, you examine the specific characteristics of the subject. You then describe the subject or the thing being defined in a brief scope using the most unique characteristic or a few equivalent ones. It is important that this description should not apply to any other subject or thing but only to what is being defined. That is why Porphyry says that the strictly proper predicate applies to every single one, and always. The examples mentioned earlier can be applied to this principle.

Focusing solely on the essentials of Division, we will try to limit ourselves to what is necessary for its understanding, avoiding an ostentation of debates and various opinions of which so much has been said that it forms volumes. Among the vast writings, we choose what is inexcusably relevant to our task. But before we delve into the intrinsic definition of Division, note that this term, taken broadly, is homonymous. When considered in particular, it is distinguished by enumeration and partition, because division originates from various types of wholes, which should be the primary consideration and discussion.

There are many types of Wholes, and among them, because they serve our purpose, we select two: one, what is called a Whole Integral; the other, the Whole Universal. The Whole Integral is one that consists of its integral parts, like a house, which consists of foundations, walls, and roofs, etc., and Skill, which includes complete perfection. The Whole Universal is what is predicated of its parts: like an animal, which is a universal whole with respect to man, lion, horse, etc. because a man is an animal, and a horse, and a lion.

Between these two types of wholes, there are three differences: the first is that the Whole Integral is not directly predicated of its parts, because it would be false to say, the wall is a house, or the foundation is a house. However, the Whole Universal is rightly predicated of its parts, as if one says, the man is an animal, or the horse is an animal, or the lion is an animal, which is a true conclusion. The second difference is that the Whole Integral is posterior to its parts, and the Whole Universal is anterior. The third difference is that the Whole Integral, even if it perishes, some of its parts can remain, while in the Whole Universal, the parts are destroyed when the Whole is destroyed.

Thus, in the science of the Sword, the whole integral can be called the whole Skill, which is composed of different integral parts; but because in the Integral, the definition can be made by the Whole, and not by the parts rightly; and in the Universal, it can have differences, which are referred to (all are applicable to the science of the Sword, which is commonly named Skill, which needs so much of distributive divisions from the most general, and common, to the less common, and more special) it will be recognized, that the kind of Division is the partition, or enumeration of degrees, or numbers, etc.

Division is in two ways, by name and by entity, like Thrust, Cut, Reverse, which make division by name, and by thing, with the addition, which makes the Division more individual, constituting it in the lowest species, like Vertical Cut, Diagonal Cut, Thrust of Quarter Circle, that by the addition of the lowest difference, they not only achieve the difference that individualizes the species, from which it results that the Division is subdivided into two terms, Name, and thing, which are explained thus.

Division of name is, when the name is shown, which can be in two ways; one, when the voice is homonymous, and it is distinguished in its significations, like Cut, which without addition, is a homonymous voice, which includes various species of cutting wound, signified with only one term, or name.

Another Division is found in the amphibolic sentence of the name, when it is distinguished and divided in its true senses, as in the Delphic Oracle, asked: Quomodò vincendum? Responded: Hasta Romanos, which can signify contrary senses, understanding, either ‘The Romans to be defeated with a spear,’ or ‘With a spear, the Romans are victors.’ And in the science of the Sword, Cut, Avoidance will be amphibolic, which can signify such a sentence contrary precepts, as if they are constructed, dividing the significations, one could understand Cut as one, and Avoidance as another: and if they are made of one signification, they will understand one Cut against another Cut, placing them, disjoining the A. And these amphibolic, which are usually committed, either for lack of explanation, or for affecting brevity, should be avoided in the science of the Sword, in voice, and in writing: and we point it out, so as not to omit the complete explanation in the terms.

Division of the thing is, when it is distributed in its parts, which is done in three ways: the first, by essential division: the second, by accident: the third, by partition. Essential division is subdivided into division of the genus, and division of the species by the genus, like Animal, which admits division into man, and brute; by the species, man into Peter, John, etc., the brute, into lion, horse, etc. However, it should be observed that the division of the genus by differences is not completely different from that which is divided by species, because in truth the genus is not divided into differences, as in parts, but as in species by names of differences, like the difference of rational, the one of brute, etc. Hence the very division, which is made of the genus animal into man, and brute, is the one that constitutes the difference of species.

For our purpose, such divisions are recognized, caused by the distribution in parts, respecting the genus to the species, as in the proximate and remote genera of wounds, that a Knife cut looks at the genus of cutting wounds, which by the force of distribution, are divided into also generic species, and these into the lowest differences, which make the meanings more individual with the additions, Vertical, Diagonal, etc.

The above is proven with two reasons; the first is that in every good essential division, every divide must be understood, and repeated in the dividing parts, as in animals, some, who participate in reason; others, who lack it: then the divide Animal Genus must be understood, and repeated in the dividing parts; e.g., Some animals are partakers of reason, some lack reason. From where the animal participant of reason, is not only difference, but the very species of man; and also animal lacking reason, is not only difference, but the very species of the brute, because the division of the genus into species, by name of species, and another by name of differences; and one, and another in an equivalent essentiality. The same reason is valid in the science of the Sword, as has been demonstrated in the preceding example, which, being so clear, is not duplicated

The second reason is that the whole should be predicated of its dividing parts, therefore it is not predicated of differences, as Aristotle taught: hence, the division of an animal into those possessing reason, and those lacking it, is not a division of the general into differences, but it is in species by the name of differences. This is why Boethius was moved to say that the genus must be divided into species by the names of species, not by the names of differences.

For our purpose, note that the essential division (which in another way is usually called division of the genus) is called essential because the whole divided is of the essence of the dividing parts, as in the highest genus, ‘Wound’, in all its parts, it causes essential division into the lowest genera of wounds, to the most specific species of them.

The second essential division is by accident, considered in three ways: the first is from the subject to accidents, and in this all the divided, subject, and dividing parts are accidents; for example, of men, some are white, others are black, others are not entirely white, nor entirely black; and in this way, the subject and parts admit accidents, not separated from the essentiality, just as in accidental movements, some are violent, others are slow, others are between slow and violent, which can be called natural, and all are admitted and divided, without separating from their essentiality.

The second way is the division of accidents into subjects, in which all the divided is accident, and the dividing parts are subjects, for example, the habits of the mind, some are situated in the soul, others inherent in the body, as far as their accidental operations; so that a division of accidents into subjects can occur, in which the divided can be an accident, and the dividing parts subjects, which can be experienced by the expert in the accidents of combat.

The third way is the division of accidents into accidents, in which all the divided, and dividing parts are accidents: as in the actions, one is erroneous, another is correct, the former due to ignorance, the latter due to study, and practice, as in this science of the Sword, that acting in the conflict of combat by its proper and contrary actions, where the division is forcibly from accident to accidents, being all the divided, and dividing parts accidents; because the combat is reduced to operations, which are accidents, and these operations, some are done correctly, others with error; those that are done correctly, result from the understanding, and practice of the Sword; those that are mistaken, are caused by ignorance of this science, or the art; which is produced from it, or the experience with which it is perfected.

The division by partition is double, considering one of the whole integral into homogeneous, or similar parts, which admit the name Whole; as when water is divided into its parts, and air into its own, any part is water, and any part of air is air, and any part of movement is movement.

Another division is by partition, and this is considered of the whole integral into heterogeneous parts (that is, dissimilar) which by themselves do not admit the name of Whole, as in the house divided into foundations, walls, roof, etc., and the wall is not a house, nor the foundation is a house, etc., and in the structure of the body, the arm is not the head, etc. Thus, in the science of the Sword, which is all composed of dissimilar parts, as in types of movements of the body, arm, and Sword, dissimilar among themselves, by their divisions, and differences, regulated with such proportion that, together with the other parts that contribute to the actions, they perfect this science, which the common people call Skill.

To conclude what pertains to the Division, we take from much that has been written on such a wide subject, the following rules. That the Division be made into nearby parts, and not distant ones, because the animal is not divided in the first term into Pedro, Juan, etc., or into horse, or lion, etc., nor the wound into Diagonal Cut, or Vertical, etc., but first is the division of animal into human, and into brute, and then into its lowest differences, as wound in the first term, or genus, of cut, or point: in the second of cut, into Slash: in the third Slash, into Cut, Reverse, etc. and in the lowest difference, Vertical Cut, etc.

The second rule is that, just as the dividing parts, each one taken by itself, are smaller than the whole divided, and all of them collected together should compose the whole, so it must be with the integral division, like the whole genre of animal divided into man and beast; because man considered by itself, has fewer terms than animal and beast; but man and beast in collection fall under the term Animal, because the term Animal divided, is either man or beast, and any man or beast is an Animal: similarly, a Sword-stroke, is either a Cut or a Reverse; and Cut and Reverse together, fall under the generic term Sword-stroke, because any Cut or Reverse is a Sword-stroke.

The third rule is that the dividing parts should be opposed to each other, as the entity and the reason that oppose each other: e.g., Animal, one is a man, the other a beast, which are opposed to each other, because it is not possible for a subject to be both man and lion. And in terms of reason, as with actions, some are honest, others useful, others enjoyable, and are divided into the genre action; e.g., the practice of letters is honest, insofar as it is considered a virtue; and being a virtue, it can be useful, as it helps to achieve some useful end; and being honest and useful, it can shine and cause delight, as proven by the Philosopher.In the practice of the Sword, in terms of reason and entity, the dividing parts are opposed to each other. In terms of reason, because the understanding theoretically divides actions to investigate in what they differ and in what they oppose, achieving through such division its knowledge by intimate and ultimate differences: and in terms of reality, which is reduced to effective operation, it regulates the dividing parts, like the Thrust, the Cut, the Reverse, which are dividing parts of the genre Wound, and descending to their intimate and ultimate differences, qualifies in what the Cut is opposed to the Reverse, in what the Vertical is to the Diagonal, etc.

The fourth rule is inferred from Cicero, who says that it is not appropriate for a part placed under a Genus to agree with another part, which is placed under the Genus divided; this is, it is not appropriate for the dividing part, which is contained under a Genus, to agree with another dividing part: because it will not be a good division of animals, one Human, another Beast, another Lion; because Lion is already contained under the dividing part Beast. Thus, Plato taught that the division should consist of two parts, because if it consists of many parts they have to be reduced to two, by negation, or privation, as in this division of animals, some terrestrial, others aquatic, others flying, which are reduced to two parts, by negation, distinguishing, either it is terrestrial, or it is not terrestrial; either it is aquatic, or it is not aquatic; either it is flying, or it is not flying; and Boethius follows this sentence, arguing thus: The Division must be made by opposite parts: are they opposite? then two: then the Division must consist of two opposite parts. But Aristotle seems to refute this opinion, and rightly so, forming a broad discourse (which the curious can see), that if the Division had to consist of only two parts, it would result in the multiplication of the Divisions; e.g., virtue is divided into justice, strength, prudence, etc., and by Boethius’s doctrine, it would necessitate multiplying the divisions, saying: Justice? its opposite is injustice, and so on in the others, which would cause inconvenient laboriousness in the division.

It is not obligatory, nor necessary to reduce the Division to only two opposite parts, as Boethius implies; for his opinion can be understood and saved with the term Repugnance, even if the species are many and different from each other, as in beasts, lion, horse, bull, etc. These species, due to their repugnance, are divided without the need for negation, as can be inferred from the doctrine of Aristotle, which we follow in the science of the Sword, where the Genus Injury is divided into various differences, which are divided by the term Repugnance, such as the Cut and the Reverse in their lowest species. The same in movements, in postures, etc. which can be divided by their repugnance without inconvenience, without resorting to negation, or to two singular opposites; with which we have sought to encompass what pertains to the Division, its understanding, and precepts in relation to the science of the Sword, providing for greater clarity, not only philosophical examples, but ones specific to this very science, judging that in this way, more demonstrably with both, the discourse will comprehend, that in this exercise the precepts of science have a place and are necessary: and with such foundations we will come to the demonstrations, and topical and mathematical arguments, which will produce what is probable, and the evident from the understanding, and exercise of the Sword, which is commonly called Skill, and to the one who achieves it, Skilled; and accommodating ourselves to the most common, we will use, in many parts the same terms, Skill, and Skilled, and we will pass with such attention to the explanation of the words, that name Universals, or Predicables.

SIXTH DISCOURSE.

LOGIC OF THIS SCIENCE: Universal voices

Logicians and Metaphysicists agree that every science is of Universals, because there is no science of singulars, as Duns Scotus indicated, and is deduced from reason, because the Universal has its requisite conditions for the subject and object of science: this consists of a definable entity, and this should be considered with demonstrable passions; and the Philosopher proves that the Universal is Being, and under the condition of Non-being, science cannot be understood: and he gives the reason, because the intelligible moves the understanding to understand, being a passive virtue of the same understanding, as the Philosopher pointed out, and Scotus explained, saying that by reflecting on itself, the understanding knows the reason for its opinion, due to the strength of its intellectual operation, conceiving concepts as universals, with which it proceeds to the rest in operation, as is experienced in this science, by first and second intentions, not only in understanding, but also in acting, perceiving the first concepts with distinctions by universals, because as Torrejon said: Those things, which according to their entities, are signified, are of the first intention; and those that declare the affections of things (because the understanding participates in them) are of the second intention: and this way of understanding and acting in principle, originates from Universals; from which science is given, deriving from understanding by first and second intention the acting in this science by first and second intention, the fundamental thing being the understanding of Universals, in which Porphyry, an Apostate of the Catholic Faith, Greek by Nation, is considered the inventor (in terms of method and explanation), who flourished in Sicily around the year 280. after the Birth of our Redeemer, being a public Preceptor of Philosophy, moved to such work at the request of Chrysaur, a Roman nobleman, who wished to understand the categories of the Philosopher with sufficient principles, which were the Predicables of Porphyry, commonly called voices in the Schools, reduced to five, which are, Genus, Species, Difference, Proper, and Accident.

In schools, questions are raised, whether these Universals, or Predicables are voices, or entities; or if they signify entities, and voices? Opinions concur, recognizing that the most received in Universities, is to call them voices, because Logic, and Dialectic are considered as debate, which is achieved with words, speaking: and speaking, signifies voices, and things, with which the term is suitable to one, and another sense, as it is proven by Cicero, and expressed by Saint Augustine, that the curious can see, from which the overcoming of the difficulty is derived.

Given that the Universals can signify voices, and things, omitting the lengthiness of the questions, in which the Logicians dilate, the essential that makes this science will be sought to be girded, following the most received in the Schools, and most in agreement in the serious Authors.

With such resolution, three divisions are found in the voices, noted by the acuity of Logicians, and Metaphysicians: the first, and most generic is in simple voices, and in compound voices. A simple voice is that which does not consist of many sayings, and a compound voice is the one that is composed of many sayings.

It is said that a voice will be simple, the one that does not consist of many sayings, because it can consist of some, and be simple, signifying a single singular.

On the contrary, a voice will be compound, which although it adheres to few expressions, signifies many singulars, or many things; e.g. Thrust, Slash, insofar as they signify a singular species of wound, thus being a single expression, and because of the specific meaning, they are simple voices. On the contrary, it is a compound voice that is constituted by a number of expressions, and signifies various things, like Cut, and Reverse, which are species of the genus Slash, and signify various things. But it should be noted that there are compound voices by the number of expressions, which are simple by the singular they signify; e.g. Diagonal Cut, Vertical Cut, which are compound voices as to the number of expressions, and simple, by the singular meaning, that this happens, when the Genus, and the Difference join in the composition.

Another division is considered in two other modes, resulting from the voice, and the term, like synonymous voice, and homonymous voice. A simple synonymous voice is one that signifies many singulars in a same generic reason, like Thrust, Slash. A homonymous voice is the one that signifies various things with a single voice, which in vulgar is called equivocal.

Another distinction is considered in common voice, and in singular voice: a common voice is properly generic, because with a predicamental term it signifies various singulars, such as Thrust, which is a common voice to puncture wounds: and Slash, to cutting wounds. A singular voice is the one that is assigned to a singular species, like Cut, Reverse, Thrust. Other differences are found in Logicians, and Metaphysicians, which are more suitable for other sciences, than for that of the Sword, where the proposed ones are sufficient.

According to Porphyry, and his expositors, the voices (which they call Predicables, or Universals) are reduced to five, which are, Genus, Species, Difference, Proper, and Accident, as has been said.

Scotus, in proof of the production, and number of these voices, resolves (by authority of Porphyry) that they are five, and no more; although, placing them in different ways, considering that the Universal, either signifies substance, or accident. If substance, in whole, or in material part, it will be Genus: if formal, it will be Difference: if in all substance, it will be Species, which tells the being of the immediate individuals to the Genus: if accident, either it is convertible, or it is not convertible? If it is convertible, it is Proper; if it is not convertible, it is Common Accident, and thus the fifth Universal: and concludes, that as it is not possible (to our understanding) to signify what is said of many, except by these five ways, the Universals are no more than these five.

It is recognized by the doctrine of the Philosopher that in three ways two things are said to agree, or to be of the same reason; this is understood in Genus, in Species, in Number: Because that is said to agree, being of the same genus, which is contained under the nearest Genus; such as Cut and Reverse, whose nearest Genus is Cut, which includes the wounds of cut. The nearest Genus is called that, between which, and the Species there is no other intermediate genus, as you see, that between the Genus Cut, and the Species Cut, and Reverse, there is no other intermediate.

Agreement in species is said, when under a same lowest Species, singular species are contained, such as Diagonal Cut, or Vertical Cut, etc. which are singular species of a same lowest Species, which the Logicians call Individuals.

A singular lowest Species is, when the Species cannot be Genus, but precisely it is contained in its very species or singular, like a Quarter Circle Stab, which cannot be Genus, nor Species in common, but in singular specific.

Agreement in Number is understood when one and another thing agree numerically, which can be in five ways: one, when they agree in the same name, and number, such as First Intention Stab, Second Intention Stab, which agree in the generic name, Stab, and in the number for First Intention, and Second Intention, which although they differ in the lowest Species, they agree numerically.

Another, when being different names, they agree in one meaning, like Diagonal Cut, Diagonal Reverse, although the names, and species, are different, they agree in one meaning, which is Diagonal.

Another, when the definition and the defined are of the same number, like defining the Cut, it will be essential, saying: That it is a wound caused by the edge of the Sword, which agrees with Cut, for being due to the blade, and not to the point, with which the definition and the defined agree in the essence of being a cutting strike.

Another, when the Property and the subject agree in one enumeration, as the subject, and the property, that in this science, the subject is the man, and the property to wound the opponent, by movement, or movements, which are proper in the man, or violent, or natural, etc. which can agree in one enumeration.

Another, when agreed in the same accidental number, like combatant against combatant, who agree in the accident of the Sword, with which one and the other are armed, etc.

Just as it agrees in Genus, Species, and Number; so also it differs in the same three ways, because to differ in Genus is when the nearest genera are different, like Stab, Cut, etc.

Difference in Species is when, although they agree in the proximate or remote Genus, they differ in the Species, like Cut, and Reverse, which agree in the genus Cut, and differ in the species.

In various modes of agreement and difference, a certain order or analogy is found in diverse proportions. Because those things that agree in Number are said to agree maximally; those that agree in Genus, are said to agree less; and those that agree in Species, are said to agree medially.

In various modes of agreement and difference, a certain order or analogy is found in diverse proportions. Because those things that agree in Number are said to agree maximally; those that agree in Genus, are said to agree less; and those that agree in Species, are said to agree medially.

Conversely, those that differ in Genus differ maximally; those that differ in Number, differ less; and in both modes, those that agree or differ in Species, differ or agree medially. Like Stab and Cut, which differ maximally by differing in Genus; Vertical Cut and Diagonal Cut, which differ medially by differing in Species; and Cut and half Cut, which differ less by differing in Number from whole to lesser movement.

With the previous principles in this Discourse, the understanding of each of Porphyry’s Predicables, necessary in this Science for the Predicaments of the Philosopher, is facilitated. From his doctrine it is inferred that the Genus is considered first due to the continuous generation that is produced from it. Porphyry defined it, saying: Genus is what is predicated of many different Species: e.g. Stab. The term in Genus is caused by the instrument with which it is executed, considering it as the material cause of the wound, which is made with an Estoc, a type of Sword, which lacks a blade. Therefore, the generic name of Stab is given to all wounds made with the point of a Sword, including such a Genus all wounds, executed with the point of a Sword, reduced its term to the Estoc, because with it you do not wound by cut. Likewise, for the instrumental material cause, all those species of wounds that are committed and executed with a short instrument, moved by the efficient cause of the man’s fist, belong to the genus Dagger Strike. Therefore, the instrument suitable for such generic movements is generically called a Dagger, even if in the lowest species it has another name, like Knife, Dagger, Almarada, etc.

The Genus is considered in two ways, which are Supreme and Interjected, which is the same in common speech as interposed or intermediate. Supreme Genus is understood as That which is such that it cannot be a species. Interposed or Intermediate Genus Is the one that between the Genus and the Species admits the interjection or intermediate of another lower Genus, and this is called remote Genus; e.g., wound is a remote term, because what it produces is the first division into lower genera, such as Cut and Stab, etc. Thus, from the Genus Cut (which is intermediate), the division results in lower genera, which are Slash, Reverse, etc. and these produce species, such as Diagonal, Vertical, etc. up to the most specific.

The questions raised by Logicians and Metaphysicists, whether the meaning of the Genus is material or formal; or if the Genus in common has a material meaning; or if the relation of the Genus is one with that of the Species, or the same nature of the Genus, as to its definition; or if this is descriptive or causal; and if it is descriptive, if the most proper is that of Porphyry: in what way are the Genus and Difference considered and separated; and if the Genus is in potency or in act; and if it is predicated of the Species, as part or as a whole; or if of one or if of many Species: how it is the principle of the Species, and what is the definition of the defined in relation to the Genus? Thus, a multitude of doubts and questions, which the curious can see in the Expositors of Porphyry and Aristotle, and in Logicians and Metaphysicists, from which a volume can be formed, and a catalogue of Authors can be made, which would occupy a lot of paper.

Expositors of Porphyry divide what he discussed about Species as a Universal into eight contexts. Here it can be recognized that this is a homonymous term, because it admits different meanings, since the word Species, taken from Latin, is used in Spanish for a form that is species-like, which is equivalent to Perfection, along with other meanings noted by Ambrosius Calepinus and Passeratius.

Dialecticians and logicians define this term as that species which is placed under an assigned Genus. This definition is consistent with that of Porphyry, who said: Species is that which is included under the Genus, which is predicated of them. And more commonly by the same Porphyry: Species is that which is predicated of many differences in number. And more descriptively: Species is that which, under the same genus (upon which it does not transcend another), is placed at the lowest level, such that no other species is given under it. From all this it follows that the Genus and the Species are relatives, and they mutually define each other, because the knowledge of one depends on the other due to their relationship.

Porphyry places the Species immediately after the Genus because it commits to it, as in this science, where Wound is the highest Genus, above which no other ascends, and its immediate Species is Cut, etc., and its mediated in number, Slash, Backslash, etc. From these principles another definition is formed, saying: Species is that which is predicated of the different in number. By this definition, one inquires what the entity being sought is, like Slash, if it is Diagonal or Vertical, etc., Thrust, if it is of Quarter Circle, etc., searching for the lowest species through the different in number.

The understanding of the Species is divided into intermediate and lowest, because an intermediate one is, being a Species with respect to another Genus, it can be a Genus with respect to another Species; and such are all intermediates between the highest Genus and the lowest Species; in this consideration, those that refer to the lower ones are Genera: e.g., from the Wound in highest genus, its intermediate Species will be Cut, or Thrust, which with respect to the supreme Genus Wound, are Species, Cut, Thrust; and with respect to a lower Species, the Cut is a Genus, and the Thrust is a Genus, as can be demonstrably shown, forming a category from the highest Genus to the lowest Species, which does not admit another after it. This is essential in this Science, in which many questions debated in schools are omitted.

The term Difference is placed as the third word, or Universal term among the Predicables of Porphyry (which in Greek is pronounced Diaphora, a term that is ambiguous and signifies divide, cut, arrange, distance, differ, differentiate, all of which are meanings that result from the verb Differ.

Porphyry understands the term or word Difference in three ways, which are: common, proper, and most proper.

The common Difference (according to Porphyry himself and his Expositors) is that which, by accident, denotes separation from the subject or subjects, demonstrating, for example, how one thing differs from another, or in the same, slow or violent, these are differences by accidents in a subject, to wait or to attack, which are also admitted in combat in different subjects when they fight: and these differences, which are perceived by the physical act in the operation, are physical differences, like metaphysical ones those that are perceived in the understanding by speculation; and because both types are caused by accidents, they are called Differences in common.

According to Porphyry, Proper Difference is the inseparable accident with which one thing or subject differs from another, such as proceeding by cut the Cut, and by point the Thrust, which are inseparable accidents that manifest a proper Difference.

The most proper Difference (according to Porphyry and Saint Thomas) is that which shows the distinction and difference according to essence or species; e.g. man and lion; Cut and Thrust, which in essence and species differ most properly, even though they are included in the Genus; since animal includes man and lion; and wound includes Cut, and Thrust; and they are distinguished and recognized in essence and species by the difference.

The other five distinct definitions noted by Porphyry are deliberately omitted. Logicians and Metaphysicians elaborate on these in various questions. The curious can see these extensively in works by Porphyry, St. Thomas, Scotus, etc.

The term Proper (according to the opinion of Porphyry and his expositors) is the fourth Predicable in order of nature, because it approaches the very nature of the Species, as a property that is considered in it in four ways.

The first, according to some accident, applies to every individual of some species, like wounding by moving a sword diagonally, or vertically, etc. This is an accident that applies to the individuality of the species of the cutting wound, whether it is a slash or backhand, etc.

The second way is when some accident applies only to the individuals of some species, like Skilled, not Skilled, which, although they apply to man, the subject of this science, and those who learn, use, or profess it, not for that reason are all in it skilled, nor all not skilled.

The third way is when some accident applies to every individual of some species; but, nevertheless, it does not always apply, like Thrust of the Quarter Circle, which is an accident that applies to the individuality of such a Thrust; but not always to the individual of the point wound, which can be in another lowest species.

The fourth way is when some accident always applies to every individual of a species, according to aptitude, but not according to necessity, as happens to man in all passions, in which he has a permanent aptitude in potential, but not in continuous action, such as moving, and moving the instrument with which he works, in which he is permanently potential, but not in continuous action.

From here, it is noted that the second and third modes are understood by the act, not by the natural potential, but by the acquired one; and in the natural, it pertains to the fourth mode.

This term, or fourth Predicable, is essentially defined as follows; Proper is that which applies to every subject, only, and always, and reciprocates with that thing, or subject, of which it is proper.

However, it does not belong to the internal essence because the Proper is partially distinguished from the Genus by the Difference, which pertains to the Species in the internal essential part, with which it reciprocates.

Proper is distinguished from common Accident in that the latter does not reciprocate with that which is a common accident, but the Proper does reciprocate with that of which it is proper. From this, it is inferred that the Proper results in a certain way flowing to the nature, and essence, of which it is proper. For this reason, the Proper separates from the common Accident because the Accident does not belong to the pure essence of the thing, of which it is an accident; but the Proper proceeds from the same essence, as from the essential principles of the thing, or subject, of which it is proper.

These conclusions are the most appropriate for this science, so other species and questions that pertain more to Philosophy, Physics, and Metaphysics are omitted here. In these disciplines, it is debated in what way the Proper is generic, or infimum, or interjected, or transcendent: as those curious can see in the Expositors of Porphyry.

Accident. This fifth universal was defined by Porphyry in three ways. The first said, Accident is that which can exist or not exist without the corruption of the subject.

This definition is subdivided into separable or inseparable accident from the subject: That is an accident which can exist in a subject; in being, and in not being of the same subject. And by negation it is defined: That is an accident which is neither Genre, nor Species, nor Difference, nor Proper, although it is always in some subject.

Metaphysicians and Logicians expand on this Universal term, explaining the definitions of Porphyry, raising various questions, from which what most applies to this Science is selected, where in terms of movement, it is considered as a common Accident, which can exist, and not exist in the subject of the Skilled, or the non-Skilled without corruption of the same subject, because the operation is according to the differences of the movement’s accident. And separable and inseparable accidents from the subject are also considered; because some are inherent in it, and these are not separable; and others, which are not inherent in the same subject, are separable, as the Expositors of the first and second Definition extensively explain.

However, there are accidents that, in intellectual cogitation, transform into other accidents that are produced by operation, in respect to the accidental nature; for example, in the case of a cutting wound (which is a Slash) and in the case of a puncture wound (which is a Thrust), the Physical agent considers them in relation to their inseparable accidents, which are inherent in the very species of the wound, which the Right-handed determines by first intention; but in the course of combat, such a foreign accident occurs on the part of the opponent, that the Right-handed in intellectual cogitation transforms the cutting wound, which he decided to commit, into a puncture wound, which he executed by second intention, the cutting wound being accidentally transformed into a puncture wound, just as he could also transform the puncture wound of first intention before executing it, into a cutting wound, executed by second intention. Everything will be demonstrated in its proper places, resulting from all this, that in the perfect act by Common Accident, the Accident is neither Genus, nor Species, nor Difference, nor Property, but another fifth Predicable term, which is divided, and diverse from the Predicamental Accident, because the Predicamental Accident looks at what is not Substance, and the Predicamental is the opposite, because it is considered in the substance, dividing into the nine Accidents, which admit categories by the partition of being: it should be considered here, that the Predicable Accident, and the Predicamental Accident differ in various ways, because one is considered A parte rei, (which is according to its real being) and the other (according to its objective being) which is said, and diverse from the same substance, untransformable from accident to accident, in respect to intellectual cogitation; and this alone is Predicable, and Universal term, and the other categorical A parte rei, included in the partition of being, which is dealt with in the Categories of the Philosopher, in which more light is entered, having knowledge of the Predicables of Porphyry, which has been discussed in this Discourse, as useful, and necessary for this Science of understanding, and exercise of the Sword, choosing what is necessary, and excluding what most properly applies to Physics, and Metaphysics, as is disputed in the Schools.

SEVENTH DISCOURSE.

PREDICAMENTS, OR CATEGORIES: of the Metaphysics of this science

In this science, as in all, understanding and the precepts of the Predicaments, which Aristotle named Categories, or series, in which Philosophers, Logicians, and Metaphysicians make a partition of being, is unavoidable: order is common in all sciences, and specific in that of the Sword, where most of its foundations rely on essence, existence, potential and act, substance, and accidents (which are also considered in the understanding and practice of the science, which the common people call ‘Skill’, whose subject and object is man, known in his entirety and in his parts) to which Scotus’ conclusion refers: Potential by itself is ordered to act, and the subject is in the potential for the accident, as matter for the form, because the accident has no other matter, but that in which it is according to its potential.

From this results, by this true doctrine, that in the science of the Sword, the subject’s potential by itself is ordered for the act, and in the same subject (which is man) the potential is for the accident, like matter for the form, because the accident, and accidents, which result from the operation in this science, have for their subject matter that in which the accidents subsist, which result from the work: for this it is necessary to know what substance and accidents are in this science, according to the partition of being into the ten Predicaments, or Categories, without getting entangled with Metaphysicians, on whether they can be more, or are less than those posed by Aristotle, whom we follow, looking only at what is necessary for our purpose. In this science, the Categories are very useful (as in others), because to define, it is necessary to inquire into the true Genus, and this cannot be achieved except by the formation of the Predicament, ascending from the lowest Species to the highest Genus, or forming a concept, or being of the highest Genus nearest or remote, to come to knowledge of the defined Species with the utilities that are experienced in all sciences, and will be demonstrated in this one, seeing how the matter is produced for the argument and the demonstration.

The meanings of the Greek term Categories are diverse, because Orators have it for Accusation; but philosophers choose words, or terms, to facilitate their understanding of the difficult, and they are allowed to draw to the use of sciences, terms, or words, invented of old, or forming them anew, to explain themselves with them, and by them, as Ciceron did; and it is seen in Aristotle, that the term Category uses it in three meanings: The first, Attribution: The second, Predicaments, or Highest Genres of Substance, and Accidents: And the third, Series of Genera of Forms, and of Individuals. For this science we will use the term Category in the second and third meaning; including all the essential principles of this Science.

Some people doubt what is disputed in the Categories, or Predicaments; because some carry, that of entities; others, that of voices; others, that of notions; and most have, that of everything, voices, notions, and realities. In this consideration, we agree, as most suitable for our intention, explaining what is Reality, what is Voice, and what is Notion; and thus, we define that entity in subject, or in species, is that which (according to its essential and proper attributes) is signified, and understood: like the man, who is an animal participant of reason; and thus corporeal substance, animated, sensible, etc. Voice is that term, or word, with which we name some subject, or species, like man, to signify the rational nature: Peter, John, etc. to explain their individuals. Notion is that apprehension, perceived by the understanding, which gives it intelligence, in a formal concept of something, by which it comes into its knowledge; and this definition, although descriptive, is proper to the Notion: and the apprehension perceived by concept in the understanding, is divided into first, and second Notion.

The first one is that naked apprehension in the understanding, which is made, without attention to what the sense perceives, as when man is considered in the most essential essence, or any other subject, or Treta, or Wound, etc. according to its essential essence, without respect to the perception of the senses. The second Notion is that apprehension, or consideration, that is caused in the understanding from what the senses perceive. From here come the First and Second intentions in the science of the Sword, which are correlative, to the notions: and also results the formation of the Categories, or Predicaments.

Avoiding the hassle of the questions, if the Categories are six, as Plato wanted; or are ten, as Aristotle wanted, whom I follow, I put the ten of the Philosopher, which are, Substance, Quantity, Relation, Quality, Action, Passion, Where, When, Position, and Habit.

Entities can be placed in Categories in three ways, either by themselves, or by others, relatively. What is placed in the Categories are Genera, Species, Individuals, because the Category is the order of the Genera, of the Forms, and of the Individuals.

Individuals are placed because they are the foundations of the second substances, such as Genus, and Species, therefore it is said to be placed in the Categories that which is not only by itself, but by the reason of its whole, and therefore physical and natural parts are also placed, like matter, form, soul, and integral parts, such as in man, head, hands, feet, etc. as parts of his whole, just as in Fencing, Movement, Compasses, Tricks, Wounds, etc.

Material principles such as point, unity, number, time, movement, term, and quantity are also placed, and it is usually referred to as an increase in the Category of quantity, as in the science of the Sword distance, movement, and species of continuous and discrete quantity are increased.

Negations and defects are placed reductively in the Categories, such as not man, not Pedro, etc. blind, deaf, mute, etc. that is admitted in the Category of Substance, and Accidents, and in that of the Sword, not Cut, not deviation, etc. It should be noted that the entity of reason is understood in two ways, because, either it fits to real essence, or it does not fit to perfect reality, but forms Chimera, or Hypocentaur: and these entities of reason, without real object, are not properly admitted in the Categories. But there are other entities of reason, which are adequate to such forms, that can be admitted in the Categories, which is all explained by the Logicians with the voices of the entity of reason, with or without foundation; effect of reasoning reason, or reasoned.

The questions of the entities of reason of the first and second mode touch in their speculation to the Metaphysicians, and to our intent only the partition of the real entity, which is more proper of the Science of the Sword, where most times the entities of reason are instructive, with respect to the practicing part, to which intelligence looks: this, teaching by the formation of real entities; and that, by the exercise, which produces the right operation, resulting from both the rules and precepts that form the Art, and from everything the perfection with experience.

In this Predicament the subject, and object of this science is demonstrated, which is the man, armed with such an instrument, like the Sword, which is chosen for defense and offense against another man with the same precaution, reduced to combat, which admits the term Duel, which comes from Duorum bellum, which without restraint, is said by the Latins, Duellum, which is, to battle; and so, to Belona Varron called her Duellona, as can be seen in the Authors of the margin. In the vulgar it is improperly received the term Duel for challenge in genre, or species, or be it of two, or more number, and in this part it is to be abhorred: in the proper signification all Rights permit it, because it only looks to the defense and offense lawful of two singulars, with equal Swords, to get agile, and to exercise the lawful defense, and offense.

The Entity (As has been pointed out) is divided into ten supreme Genera, which is the first the Substance, whose dignity precedes that of the other accidental Predicaments, in which is the partition of the entity; because the Substance in first signification is taken by the essence, and with such a term it is placed in the Categories, with respect to the Accidents, as superior to them. In second meaning the term Substance is taken for everything that is not accident. In third meaning it is received by finite, perfect, and lowest substance, that which is not part of another, such as, Genera, Species, and Individuals, which are not parts of others.

Aristotle divided substances into two, some he called first, and others second, defining them thus: First substance is, that which is not in subject, neither is said, nor predicated of subject. It is not in subject, because substance is by itself; and it is not said, or predicated of subject, because it is first individual substance. Second substances are Genus, and Species, in which the first are contained, according to essence, like Animal in man, who individualizes according to his essence, and is contained in the Genus, or the Species: from which it follows, that the Substance in essence, does not admit definition by Genus, and Difference, because the supreme Genus does not admit over itself another Genus.

Aristotle noted six properties in Substance: the first, not to be in subject, this property belongs to the first Substances, insofar as they are not in subject, nor are they said of subject: and to the second, insofar as they are defined by the first, because they participate in them, not as in subject, but are said to be in the first substances, because they contain their nature.

The second property applies to Differences. and to universal Substances. It is so proper of Substances to agree in name and difference with the first individual Substance, from which they derive; such as Man, which is said by name and difference, Peter, John; because in one way and another, animal participating of reason is produced.

The third property is of the first Substances, to signify something: this is, by nature, certain, and defined, existing by itself.

The fourth property is, that it does not admit contrary; this is, that in that Substance there is no contradiction of another Substance or Accident, because two contraries in substance are proper accidents; and so, they cannot be Substance. And if the Elements are said to be contraries, like water, and fire, such contrariety is not because of the Substance, but because of the qualities, from which the contrary Elements are so called, not because of the elemental substance itself, but because of the qualities, which are contrary.

The fifth property of Substance is, not to admit more, nor less; this is, when the Substance is said of its inferiors, it is not said more, nor less: e.g. when it is said of Peter, John, etc. In the Science of the Sword it is the same in Substance; e.g. Wound as to individual: such as to say by Cut, or by Reverse, or by Thrust, or by Half Cut, or by Half Reverse, which is not said (as to individual) more wound, nor less, than the specific, which is terminated from its individual term.

The sixth property of Substance is to subsist the same in number, although it admits contrary affections, like Peter sitting, Peter walks, is hot, or is cold, or is sick, healthy, etc. And in this Science, Natural Movement, Slow, or Violent, or Mixed Movement, although they admit contrary affections of their mutation, they subsist in their number, substance, and movement.

In the rest that is arguable, I refer the curious to the Metaphysicists, Logicians, and Dialecticians, in which various opinions and subtle sharpness are found, most of which are foreign to this Science, and so I omit them. In this Category, I demonstrate from the supreme Genre, which in the created does not admit another above itself, signifying it with the term Substance, discussing until the lowest individual, subject, and object of this Science (which is man), giving him to know in his whole, and in his parts, so that his regulation is also known, as this Science supposes, from where the art is produced, which with experience is perfected, and all together is what is called Skill.

For supreme Genre, created, the term Substance is placed: this is divided into corporeal, and incorporeal. The incorporeal subdivides into Angel, Demon, Soul separated from body, or in it, vivifying it: the corporeal produces body, which is placed in the straight line: Body is divided into mixed, and simple. Mixed produces Mixed in the straight line: simple body subdivides into ethereal, and elemental. Ethereal subdivides into Heavens, and Stars; elemental into the four Elements, Earth, Water, Air, and Fire. The Mixed in the straight line is divided into animated, and inanimate. Inanimate subdivides into perfect mixtures, and imperfect ones. Perfect ones, into stones, metals, etc. imperfect ones, into meteorological impressions, rain, snow, hail, clouds, lightnings, thunderbolts, comets, etc. Body animated produces in the straight line Living: Living is divided into sensible, and insensible: insensible vegetable subdivides into plants, into fruitful trees, or fruitless trees, herbs, some fruitful, others fruitless, etc. The sensitive, or sensible produces in the straight line Animal. Animal is divided into participates of reason, and lackin reason. Lacking reason are in multitude of species, birds, terrestrial brutes, aquatic, amphibians, etc. Animal participates of reason produces in the straight line Man in perfect form. The term man includes both sexes, male and female, from which individuals, Peter, John, etc., propagate, as everything is demonstrated in the series, or Category, which here, goes by demonstration.

Stamp 1

This category results in the man (according to his whole) being a created, animated, corporeal, mixed, living, sensitive substance, an animal participating in reason, and all the composite rational man: for human procreation, male and female, who as far as the body produce by generation, individuals, Pedro, Juan, etc. like they are.

In wanting to show the perfections of man, one could form a volume, and volumes, discussing his efficient, material, formal, and final causes: His states, happiness, lapse, and penalty, which theologians consider: in the first innocence, and grace, with what infused knowledge? with what supreme, dignity? in the second state of guilt, how naked, delinquent, and condemned. Let the pondering of David suffice, saying to the Creator: I will see the Heavens, the work of your fingers, the Moon, and Stars, that you founded. What is man, that you remember him? or the son of man why do you visit him? You made him little less than the Angels, crowned him with honor, and glory, and constituted him over the works of your hands. You subjected everything to his feet, the sheep, the ox, the universal species, who graze the fields: the birds of Heaven, the fish of the Sea, which breaking the waters, make a path through their waves, etc.

The Great Basil eloquently said, embracing the extremes: What is man, in respect to his Artificer God? And what is man, in respect to the dust from which he was formed? He is, with all that, an epitome of all things, a small world, a particle divided into parts, being united. Horace called man, An image of all superior gifts. Pedro Gregio (by the authority of Hesiod, who spoke under the name of Pandora) said: God breathed an immortal soul into man, with which he participates, and understands with the Angels, feels with the animals, vegetates with the plants, lives common to all, and has being with the others.

The Philosopher, giving a reason for the upright stature of man, said: Only man is erect, and elevated, because his nature, and substance is divine, and his Office Divine, to understand, and know that it would not be appropriate if the composition of the body became heavy, because the weight would make the mind, and common sense slow: for this reason to the heavy disposition, grave, oppressive in the bodies, working urgently, they need to lower themselves to the earth, as seen in irrational brutes. Cicero recognized that God constituted men as exalted, and raised above the earth, so that they would contemplate Heaven. By this doctrine, Macrobius (it seems) said that the Mind of man has to be common with the Stars. Protagoras said that man is the measure of all things by his proportion, and measures: as is demonstrated in Architecture, as seen in Vitruvius, and Pomponius Gaurico.

The man was called Ab humo, which is earth, from where he was formed; thus Plato confessed, and not as Marco Varron was persuaded, that the term Humus came from Homo. The Hebrews explain the man with the name, or term Adam, because his corporeal matter is the earth, which in Hebrew is pronounced Adama. The Greeks signified them by the term Andras Epictonions, which is the same as terrestrial man. Man is, in short, a rational animal (as Pedro Gregorio says) consisting of soul, and body, conveniently constituted (according to the Hebrews) of a double nature; one part incorporeal immortal, which is the image, and likeness of God: not as the Gentiles wrongly thought, made by chance, or fortune, but by God himself created, to praise, and recognize the Divine Majesty: the lower terrestrial, and corporeal part, is also the work of God, who formed it from earth, to return to earth, as Eusebius Pamphilius wrote, with whom St. Ambrose, St. Bernard, St. Basil, St. Athanasius, and other very grave Authors concur, where curiosity can be satisfied, and widely in the work of Father Pereyra, with which we excuse the many that erudition offers us, without dwelling on the various opinions of Philosophers, and Pagan Poets. As for the fabric of man, consisting of soul, and body, I only say, that in it fits the speculative, and practical science, reduced in the speculative to the ratiocination; and in the practical to art, and work, and everything together is in the Science of the Sword, from whose understanding, and exercise results the consummate Skill; whose subject, and object is man known in the Predicate of the Substance; with which one can proceed to its knowledge by its parts, according to what pertains to this Science, without the anatomy, which is more proper to the physical sciences.

Understood that man, in his entirety, is an animal participating in reason, derived, according to his Predicament, from created, animated, corporeal substance, etc., acquires knowledge that he is capable of speculative and practical science: and being so, as it is, and is pointed out; it is also essential to know the three requirements that are necessary for the Science of the Sword in man.

In the first one, it is necessary to investigate, what kind of Science is the Sword? If it is practical, or if it is speculative? Or if it admits both species? Demonstrating how it works as science, in what we broadly call Dexterity. In the second, it is necessary to declare what essence and existence are, and if they are distinct. In the third, it is considered and recognized in man what is potential and act for this Science. And if armed with the Sword, and other weapons with which he adorns himself, do the warlike instruments provide potential or act, by intention or extension. These principles (perhaps not pleasing to everyone, nor for everyone, because they require other not common ones for those who have some scientific light, or want to take it from the one that is given in this Book) are so precise, and compelling, that without them, the deficiency that will result will be great, leaving diminished in essence so much work, as it costs to understand, and make this Science understood, as Science; but whoever does not wish to enter through the true doors, we do not force him to get entangled in more; since he may be content with the common precepts of art and experience, seeking a scientific voice that explains and exercises him in the speculative and practical aspects of the Tricks, which are achieved by science, with which he can take advantage; but he will not be able to say that he knows the Science of the Sword as Science, because it consists of method and precepts of Science, just as in Philosophy, and Metaphysics, and the others that are sciences, cannot be entered or known as such, if their method and principles are not studied, which are acquired through Definitions, Divisions, Predicables, and Predicaments, causes, arguments, and demonstrations.

It is assumed out of necessity the Logic and Dialectics for the acquisition of all Sciences, as taught by Boethius and explained by St. Thomas; by whose doctrines, Ancient and Modern establish this principle as maximum, with which it is inexcusable not to follow such precepts, to understand and make this Science of the Sword understood; and more compelling, when its species is investigated, being the object, and subject the man, forewarned, prepared, disposed, and according to pure Castilian, ready for the operation of soul, and body, which all these synonyms signify the term Parasceue in Greek, as can be gathered from Ancient and Modern Dictionaries, and Pedro Gregorio, with which we can discuss in our commitment, and question.

Aristotle says as a maxim, or rule, that that of which is predicated, as of subject, and predicate, is reduced to the subject; and he gives the example in man, who is the essential subject of this Science, considered in his entirety and in his parts, is capable of the Science of that common instrument, dedicated to offense, and defense. It is therefore necessary to know how man perceives it. This question can be shown with various arguments, whose subtlety is not for all temperaments, nor for all tastes, so I will try to omit what is excusable and limit myself to the most compelling.

Science in common, is a Term, or Voice, which broadly taken, signifies the knowledge of any proposition; but this is not perfect science in the definition given by the Philosopher, saying: Science is certain and evident knowledge of a necessary thing through its causes. It follows that this knowledge by causes is discursive, from which arises discursive or speculative science. This (as Dr. Torrejon puts it) is that which, by force of rational discourse, knows some proposition, and in this respect it applies to the Science of the Sword, which, as a real entity, by force of discourse, knows the truth of the proposition of the Trick, which the scientist premeditates, and perfects in the understanding, either by means of syllogisms or by other discursive means, which compels reason to the knowledge of truth by premises, optimal dispositions, from which originate the two terms Opinion, and Arrogance.

Opinion is caused by probable premises, although these have fallacy, as is experienced in what they call vulgar Dexterity, whose major foundations are opinion, either already received by many, or assented to by those who are guided by it.

Arrogance, is that which is deduced by certain and evident principles, and this is properly called Science, because the discourse investigates and inquires the truth deduced by its causes, arguing it by syllogism and demonstration; and in this part there is no doubt that the Science of the Sword is speculative; and as such, it assumes the logical and dialectical principles, for being, as they are, forceful, and necessary to all sciences, as has been demonstrated in its place, and it is conclusively concluded by Cardinal Toledo, and many others.

Another type of Science is what they call experimental, or practical in common terms: this is acquired through the senses, according to their operation, whose knowledge can be without discourse due to principles already posited in the understanding, which they call axioms, or common notions: for example, that The whole is greater than the part: that Two and two make four: that From equal parts, if equal parts are taken away, equal parts remain, etc. From these common notions, or pronouncements, without other discourse, with the terms accepted as evident, knowledge is judged; and of this kind are the Mathematical disciplines in their operative and experimental aspect, and this also applies to the Science of the Sword, insofar as it is a habit acquired by demonstration, to which cause the mathematical disciplines serve as subalterns: in the practical or experimental Science of the Sword. Noting that in the way of knowing, or acquiring Science by habits learned in understanding, a habit will be that which has left certain knowledge of that thing that comes to be known easily, and promptly to be exercised, both in understanding and in operation, just as in this Science, as far as experimental practice, that facility is acquired which is called habit, as Torrejon aptly defined, saying that thus in understanding by comparison habits are given, by whose means, with their frequency, the same understanding is facilitated.

The same Author, convinced by reason, admits that it comes from the memory of past events, which quicken understanding and operation, because what is already known about the same Science facilitates knowledge; because what is already known of one proposition, making the antecedent, one passes to another, and the consequence is acquired.

But this mode, which is the experimental in the intelligence and exercise of the Sword, is more properly called habit than science, because it results from repeated natural acts, which pass to the understanding more by memory than by rational discourse: and in this part, what is written and taught is what is most exercised with the Sword; but that is not therefore the pure science of it, which is not acquired without Logic and Dialectics, which are the common doors through which all Sciences are entered: from which it is concluded for our purpose, that man acquires true science, when he speculatively discursively knows the true Skill scientifically, perfecting it in practical experimental, not by Opinion, but by Arrogance; and this is to be the man subject, and object of this Science, as an animal participant of reason, ascending to the highest Genus by the straight line of the Predicament of Substance, leaving, by all the above, the proposed question understood.

Man is not well known in his formality, which comes from the soul, a physical and organic instrument, which informs the living individual, and gives him aptitude to wield the Sword in his defense, and in the offense of his contrary object, unless it is investigated, what is in man Essence, and Existence, and where does the power, and act in this Science come from?

Understood, then, that being is divided into its inferiors, which the Philosopher called Categories, the same as Predicaments, we enter into this question, omitting the many that Logicians and Metaphysicians move, and we follow Saint Thomas, Cardinal Cayetano, current of the Thomists, and Boethius, who says: That in creatures, being is one thing, and what it is, is another, because they have a participated being, and in this it is impossible for the participating and what is participated to be the same. It is proved by the reason of the essential compared with existence, which is like the power for the act, because the essential in the creature, by itself alone, does not have being, but truly exists by existence; and thus it is like its actuality: then the essence and existence in man are really distinguished, because a true act and potency cannot be understood without real distinction, as also in the essential and existence a real distinction is admitted: this affirmative conclusion is taken by Saint Thomas, and the Authors cited here, and it is to our intent.

Upon this foundation of Boethius, and opinion received from Saint Thomas, a multitude of arguments are formed that conclude the real distinction of essence and existence: just as also in potency and act; although the Masters, Durand, Enriquez, Gregory, Gabriel, and others, choose other theses, or hypotheses to prove by other means the distinction that is given between essence and existence, power, and act.

It is confirmed: from the essence flow and result all the passions of the same living compound; and thus also the mode of existence, if it is formally distinct, flows and is derived from the essence; because what is real comes from and flows from a real being; and in the same way, first it is supposed (according to nature) the essence antecedent to existence.

This metaphysical conclusion is proven with many arguments, some of which Father Oña compiled. For the curious, I direct them to him and to the other authors cited in this part. For my purpose, in the Science of the Sword, it must be considered that in man there are two apprehensions in understanding, both being primitive. One is in the essence of understanding itself, ingrained in the soul by the very essence of rationality; and this is a certain being that in essence precedes the first concepts, and from this flows the second apprehension, which, although also intellectual, moves to become existence in rational understanding. For this doctrine, one can refer to Aristotle, Saint Thomas, and the disciples of both.

From here also comes what is known in schools as ‘being of reason’, and ‘real being’ by first and second intention. The first attention in the understanding of man is for things, or concepts, that are put forth, as the first objects in the intellectual essence of man; and this is properly the first intention in the essence of understanding, signifying things or concepts according to their entities, and this is pure ‘being of reason’.

In existence, the intellectual term will be the one that truly declares the affections of things that are shared with the knowing understanding, and this is the ‘real being’, or second intention; which, although it flows from the first, is distinct from it, as are essence and existence, to which potentiality and actuality have analogy; and in such terms it is first perceived in the Science of the Sword: and whoever does not accumulate such knowledge, will poorly presume that they are skilled by Science.

Aristotle treats ‘potentiality and actuality’ ex professo in Metaphysics, where his expositors extensively dispute what is in man Potentiality, and Act, whose affections are divided into active and passive: and these, not only are considered in animate species, but in inanimate ones; in which also their powers are found by principles of operation, or action, like the heat in fire, the cold in water, the virtues in stones, in metals, etc. In animate species, if one considers the vegetal ones, trees, plants, etc. or sensibles, like beasts, birds, fish, etc. one finds in ones and others powers, and natural acts, proper to the same animate species: and in all there is a certain ordering to their own defense, and to the offense of their adversaries, as we touched on, treating of offense, and defense in general.

To this end: in man (as noted by Pedro Gregio) active and passive powers are considered, which we will discuss in the Predicament of Action and Passion, where it is their proper place, as from here, that Act and Potentiality have a relationship in such a way, That the act is that which is not in potentiality: and potentiality is that which is not in the act.

These definitions are essential, from which it follows that nature is reduced to act through potentiality; but if the potentiality is remote, it occurs after many intermediate transformations; e.g. the earth in remote potentiality is a tree, is a plant, is grass, is a flower, is fruit; but before the earthly potentiality is reduced to act, it requires a multitude of means. Likewise in man, the food that in potentiality is blood, is flesh, is bones; before it is reduced from remote potentiality to act, it passes through a multitude of means, as also in Fencing, the Cut, Thrust, etc., before it is reduced from remote potentiality to act, it requires a multitude of means, positions, compasses, movements, etc.

From here it follows (as noted by the same Pedro Gregorio) that what is worked in another by remote potentiality does not have the name of that which is acted upon, because the matter is remote: and on the contrary, passing from close potentiality, it comes to the act; e.g. the Trick in the understanding and knowledge of the Fencer is in potentiality, either remote or near; if remote, it does not have the name of that which is in the understanding by rational entity, or by real entity until it is acted upon, requiring a multitude of means to reduce it to act in operation, where it receives the name, which it lacked in remote potentiality, due to the remoteness of the matter; on the contrary, if the potentiality is close, and is immediately reduced to act, due to the immediacy, it acquires the name due to the immediacy of the matter and operation. From here it is understood what is first intention, and what is second essence, and existence by rational entity, or by real entity, that in the Science of the Sword, as far as understanding is concerned, the potentiality is always first for reason, and knowledge, and this is properly called active potentiality. But in the passive (as noted by the same Pedro Gregorio) the act can be first or subsequent: first, in terms of number: subsequent, in terms of species; because passive potentiality in one way or another can be considered in relation to the act, because the being of some act in species necessarily precedes what is in potentiality to be reduced to act.

From here stems the use of the terms ‘First Intention’ and ‘Second Intention’ in this science when applying it to actual infliction of wounds, considering the passive potentiality by number or species: When it acts by number, it refers to that wound which the fencer executes by immediate potentiality to the act; that is, without admitting or depending on the opponent’s movement: so the act, as a primitive numerical immediate to the potentiality, acquires the name of ‘first intention’ wound; and the potentiality, as a numerical impulsive cause, takes precedence over the act in any kind of wound. When it goes to the species from the remote potentiality, converting the wound into a type, such as a Vertical Cut, or a Diagonal Reverse, or a Fourth Circle Thrust, etc., as the species has consideration or relation to the opponent’s movements, they are called ‘second intention’ wounds, and from passive potentiality, which can be prior and subsequent to the act, according to its accidents and way of acting.

For this reason, it is considered that the active potentiality can be innate, and can be acquired: innate, by understanding and feeling; acquired, by pure practice; both of which concur in the Science of the Sword, which is composed of intelligence and practice, where the active potentiality can be innate in understanding with respect to intelligence, and this produces ‘first intention’ wounds, as it follows from the preceding principles, which can be applied to the senses. The reason is that, being acquired from one of the powers of the soul, the potentiality can be innate active; and so, before the act, as it comes from innate potentiality, with respect to understanding, which perceives with the senses; and in such ways, the active potentiality acts in this science, with the potentiality preceding the act, e.g., the fencer, through the means of innate active potentiality, scientifically anticipates the reduction to the act, reasoning from Universals to the lowest intimate species, defining, and distinguishing by topical arguments the truth of the Tricks, to pass them from potentiality to act: also through the senses (supplying the powers of the soul with the scientific species of the Tricks the active potentiality) can reduce them to the act by appropriate means, according to the proximity or distance, mediate or immediate, according to the potentiality is with the operation.

Active or passive potentiality, acquired by exercise, can be considered subsequent to the act (as taught by Pedro Gregorio) because in the acquired, the frequented acts are generative of potentiality, and then it will not be said to be innate, but born from frequented acts; e.g., the practiced organist, the keys; and other musicians of instruments, harp, lyre, vihuela, etc., by the frequent practiced acts, generate the potentiality to know how to play the organ, harp, lyre, vihuela, etc., making the effect a cause.

In this Science, the Fencer can generate potentiality acquired by exercise, and this will be subsequent to the act, because the frequented acts are generative of the potentiality acquired by pure practicing habits; and the cause comes before the effect: then the act comes before the potentiality in this mode of consideration.

But note from the doctrine of the same Pedro Gregorio, that the Organist, the instrumental Musician of the harp, lyre, etc., and the same in Fencing: through exercises and frequent habits, those who practice can be called Fencers in terms of the art, but not scientists, because the acts remain imperfect without the Science, and are not due to innate potentiality, but causative to the potentiality acquired by exercise; being so strictly speaking, it paves the way for the potentiality acquired in the Fencer, which in this way will be due to frequent acts, but not due to science: he will have acquired art through precepts and rules, frequenting acts, which converted into habits, pave the way for the potentiality; and in this way it is seen that there are acts that precede the potentiality, and that this can be subsequent, thus being understood by the preceding in this Category, that it is the man as a whole, for what he does to this Science of the Sword, with which it is better given to know in its parts for the same purpose.

The anatomy of man is not of this endeavor, according to his interior composition, which is more suited to Medicine and Surgery than to the Science of the Sword, which, in terms of the parts of man, considers the external ones, as it suits to the Dexterity acquired by science and art, with which it proceeds by discourse and demonstration, avoiding as much as possible, the arguable, referring the curious to Andrés Laurencio, regarding the parts of man, which the Philosopher and his Commentators also discussed.

The Greeks called man Antropos, which means an inverted tree, or upside-down, because he has his head with hair, like roots: his arms and legs, like branches: the rest of the body, almost a trunk, elevated on two feet upright, for two reasons, given by the Wise; one in the natural sense, another in the moral: the natural reason is that in other animals the head abounds with earthly matter, which depresses them, lacking the erecting or elevating heat, which is the opposite in man.

For the moral reason, man consists of an upright stature, so that the body testifies to the uprightness of the mind, raised high, so that it contemplates the celestial perfections, to which it should adhere, considering that accidents of the soul are transmuted to the body, from where Avicena said that imagination makes things happen; so much so that he who vehemently fears leprosy becomes a leper. On the contrary, the passions of the body overflow into the soul, considering man as a small world, whose parts have proportion and correspondence to the larger World; the distance from the tips of the largest fingers of the hands, with the arms extended at right angles to the body, is as much as the length from the top of the head to the soles of the feet: as also in the larger World, the distance from the Zenith to the Nadir, points considered with respect to man, by correspondence to his head and feet, is as much as the distance to two other opposite points, one in the East, and one in the West. Also considering in man the circle when the arms are raised and the legs extended, in such a way, that if a compass foot is placed where nature marked the center, and with the other describing a circle, it will touch the Periphery at the ends of the feet and hands.

The human body is composed of four elements, just like the greater World, being earthly in the bones and flesh; and in the humors blood, phlegm, bile, and melancholy, including the four qualities.

Air is contained in the lungs, which is always in continuous movement, serving as the bellows of the heart, so that excessive heat does not dissolve it; because fire is contained in the heart, and throughout in the form of flame. Water is the blood that is diffused through channels, which they call veins.

There are three main organs in the human body: they are called radicals, which are the liver, heart, and brain, where the being of the individual is mainly placed, because in them resides the natural, vital, and animal spirit; others are servile organs, such as veins, arteries, hands, feet, and those in which agile movements are exercised, and all those that move, are called officials, like the hands, the feet, and those in which agile movements are exercised; and all those that have movements, are called artificial, because they mutually help each other, and some resort to others, the lower ones serving the superior ones, by whom they are governed, as demonstrated in the eyes, tongue, fingers, etc., and the rest, that make up the brief human world: supporting, sustaining, and moving the machinery of man are the feet, like the base, the legs, like columns, the shoulders, like architraves, the arms and hands dedicated to the execution of actions; and especially to the defense of the whole individual, and to the offense, and repulsion of its opposites, all respecting each other with reciprocal action, some parts sympathizing with others, as participants of pain, and delight, contributing to the preservation of their entire integrity, because of the connection and coalescence that some have depending on others, for which reason they supplement correlating defects, as can be elaborated in long discourses.

In humans, science, providence, and senses are placed in the head: the eyes apt and active for seeing, the ears and hearing for listening, the mouth for tasting, the nose for smelling, the whole body for touch: all senses serving the soul species, which are perceived, according to the sensitive organs admit them; some that have external objects, such as sight in objects, which through visual rays, perceives the forms, representing them to the soul with different perspectives; by whose arrangement in proportional distances they appear larger or smaller, with lights and shadows, distinguished by the lights, from which art learned painting, derived from perspective science in terms of speculation and practice.

The ear perceives the sense, and the formation of voices, and articles, by which means the word, the prayer, the concept, and the reason are ministered to the soul: when perceived, it is distinguished, and from all together agreeing, and reprobating, science results in opinion, and arrogance. These two senses, which are the noblest, are the organs through which the Science of the Sword is acquired, as far as it is speculative; and as far as practice, it is exercised by the parts of the body, and as main ones, arms, hands, legs, and feet, serving the lower to the superior of the other senses, such as touch, which not only spreads intensively in the human body, but is extended extensively to the Sword, in which strength and weakness are admitted, recognized by the extension of touch, communicated by the arm, and hand to the armed instrument, which in power is ruled by the understanding, and in act by the operation, subjecting everything to free will, which as the first mover, carries after it all the other lower movements.

The parts of the human body are the radical measures, from which art and experience took and measured for human operations, composing from four grains of barley the common width of a finger, and four fingers what the common people call a palm, and from four palms a foot is composed, which they call Geometric, which differs in nations as to the larger or smaller; just as the visual span, received by distance, or extension, from the ends of the first and last fingers, from where the Spanish visual span is a quarter of the Toledan rod, and the foot is a third, and the cubit sesquipedal: the Mathematic step is five feet, and the common vulgar considers it to be two and a half, in which there are disputes. One hundred and twenty-five Mathematic steps make a stadium, omitting the other measures, because they are not of this Science, but the first ones, which result from palms, feet, and visual steps. And anyone who wants to see more, consult Philippe of Burgundy, Pomponio, Gaurico, Vitruvius, and others, and of our Spaniards, Juan Perez de Moya.

As for the proportional parts, which correspond to each other in the human body, a multitude of authors deal with them, from whose proportions those of Architecture are drawn, as can be seen in Vitruvius, Viñola, and others, in which the curious will find an expanded field. Contenting ourselves here with what is most precise to this Science, reserving for the second Book the lines, sections, planes, and angles, in which man is considered divided, for the understanding, and exercise of what the common people call Skill.

EIGHTH DISCOURSE.

SECOND PREDICATE,

Quantity, or How much

As for the proportional parts, which correspond to each other in the human body, a multitude of authors deal with them, from whose proportions those of Architecture are drawn, as can be seen in Vitruvius, Viñola, and others, in which the curious will find an expanded field. Contenting ourselves here with what is most precise to this Science, reserving for the second Book the lines, sections, planes, and angles, in which man is considered divided, for the understanding, and exercise of what the common people call Skill.

Having explained the first Predicate Substance, which produces man (the subject of the Science of the Sword) by a straight line, we properly move on to the second category, the first accidental part, where the division of the real being is admitted, according to the common doctrine of Philosophers and commentators of Aristotle, Ancient and Modern: although there are those among these who, by specifying the term, want it to be considered, not the real being, but the knowable being, because this admits more latitude, intending to apply to the being of reason, with certain circumstances, that are not so common to Logicians, who understood the division of the real being, according to the ten Predicaments, in which the Philosopher distributes it, whom we follow in the most received, and most of our intention.

Quantity, or How much, is placed, as Aristotle taught, in the second place, or Category, where it is admitted as a supreme Genus, for two reasons: the first, because Quantity (whose term we use as more common) is the most proper and similar to the substance, as it does not admit contraries, nor more, nor less in its species: the second, because Quantity is the subject of other accidents, as they cannot subsist without it, because it is first, that there is an interceding or middle subject, so that other accidents subsist in the substance, or in the same accidents: these, as the Metaphysicists and Theologians debate, can be without the same essential substance, but not without Quantity, which is the interceding subject for the substance, with respect to other accidents.

We define, then, Quantity, or How much, saying: It is that which is divided into parts of Succession, Extension, and Description: in parts of Succession, like time, which is divided into parts that are causes of continuous movement, or are causes of discrete movement. Of continuous movement, like the cause in past, present, and future time: of discrete movement, as we will explain in its place, following the Philosopher: As far as the same time is considered successive, although it is divided by the past, present, and future, it does not cease to continue in the succession, because its parts are conjunctive, and what is conjunctive is successive: then, time is successive, and a proper species of continuous Quantity, which is understood to mean, that they are parts of the succession.

In parts of Extension, it is understood, as in the line, which admits extension in conjunctive lines, produced by the first petition of Mathematicians; since, although the line lacks breadth, which is not given in it, because it lacks wide (or width, as the common people say) extension, at least extension is given in the production of length without breadth.

As with the line A.B., which is considered to be 4 and produced to 8, it will be extended by another 4, and its common extreme terms will be points that end at 8, and consequently the conjunction of 4 on the line extended by another 4, if given movement, will be in the extension of 8, as shown in Figure 1, which is in the Diagram of Quantity, or How much.

Thus, a man with a sword in his hand, whose arm is considered as two units in conjunction with the sword, considered as 4 units, will have an extension of 6 units. Consequently, he will be able to perform an extended length motion or movement of 6 units. In this consideration, the Quantity will extend from 2 to 6 units because the arm is considered as 2 units and the sword as 4 units, and the entire movement of the arm and sword has an extension of 6 units. This is demonstrated in Figure 2 of the said Diagram.

En Deſcripcion conſideraſe la Quantidad, como numeral, donde el Todo ſe divide en partes diſcretas, y diſiuntas, como el binario en dos vnidades, el quaternario en dos binarios, &c. eſto baſte quanto à la primera difinicion. Otros, coligiendola de las palabras del Philoſopho, dizen: Quantidad es aquello, que mira à la coſa en quanto; para cuya explicacion, los Modernos ſe valen, ſuponiendo, que qualquiera corporea entidad, padece en sì afecciones, que no miran à la miſma inmediata entidad, ni ſe producen de ſu effencia.

The common opinion of logicians and metaphysicists asserts that all bodies have accidents of some coeval of the primary matter, although really distinct, yet so considered that all affections arise from it, and this accident is called Quantity.

Aristotle explicitly defines it as follows: How much is divisible in that in which it subsists. According to this definition, which is relevant to our intention, it can be said that How much, or Quantity, is that which admits division into parts, of which it is composed, in such a way that any of them can persist on its own and be a something, or How much, whose division is considered in potentiality in terms of continuous Quantity, and in act in terms of the discrete.

Hence results the most common opinion, which grants, Quantity is a certain accident of actual extension of formal measurability, from which its affections arise, not by essence, but by effects that declare, that assign the essence in the mode that they can.

From everything, following the Philosopher, it can be deduced that Quantity is the numerosity of parts of the same substance, from which arises (in terms of the physical) diverse extension in the position of the subject, such as in the impenetrable figure, hardness; in the light one, lightness; in the linear, length without breadth; in the surface, width without depth; and in the Body, all dimensions combined, etc. All these attributes are attributed to Quantity.

Everyone admits Quantity as the supreme Genre in its Category, although it can be challenging to understand how essence applies to our intent; thus, we grant the most general Genre, Quantity, in its Predicament. And it will be said that in the distribution into predicates; since these, being Species of the supreme Genre, will be genres of those species that are its predicates. For example: Line is a species of the supreme Genre Quantity, and is the Genre of its predicates, like straight, curved, spiral, etc.

Thus, we notice that the Philosopher in this Predicament does not define Quantity by explicit words, but How Much, and he divides this into: A part that is continuous, and a part that is discrete.

From the aforementioned, it can be understood for this Science, what the predicates of this Category are; to whose demonstration it could be said:
Quantity is the supreme Genre, to which entities compete for the reason of measurability, from whose affections, or passions, the predicates that are species result, according to the knowledge with which we investigate the affections of the same things, which we call accidents.

This description can be a thesis of this Predicament, whose terms in abstract are measurability in potentiality; and in concrete, it is measurable in act; because just as the essence, if perceived quidditatively, in it questions are resolved by the term What: so too in this Predicament, questions made by Quantity, or How Much, are satisfied by measurability, or measurable, divided into continuous, and discrete, as Aristotle taught, and from the affection of these terms results the equality, the inequality, the majority, the minority, etc. and for our intent we consider, That Quantity is nothing else but the number of parts understood by extension, to perceive their measures and ranges by continuous Quantity, or by discrete Quantity, in which following the Philosopher, the Category, or Schema, is formed as it is at the end of the explanation of discrete Quantity. Thus, without a doubt, it will be recognized by the table, or Schema, that the term Quantity, or How Much; is the supreme Genre in this Predicament, and is distributed into continuous and discrete Quantity.

Five main species belong to the continuous, which are, Line, Surface, Body, Place, and Time: and these are considered as Genres of their lowest Species: the Number, and the Speech belong to the discrete Quantity, which are also considered Genera, in relation to their Species, up to the most inferior, as will be explained, and reduced to the most proper of the Science of the Sword. The principles for the demonstration in all Sciences are definitions, distinctions, and immediate propositions, these in Science, as in Mathematics (which it uses as subalterns) are reduced to problems, or theorems: those that demonstrate on a given principle, that can be formed: and these, which investigate and recognize the qualities, and passions of the proposition already formed.

From the immediate propositions, other proper principles result in this Science, as in others, which as Bradwardine noted, can be called Maxims. From these and other principles, the common ones are produced, which the Philosophers call Suppositions, and the Mathematicians Petitions, to whom Bradwardine gave the name of Complex Principles, and we need all of these in this Predicament, because it includes the species of continuous and discrete Quantity.

The geometric terms that serve this Science, are either practical or speculative: if practical, they define the Species by Genus and Difference, which looks at the demonstration, as is seen in Euclid’s Elements, thus it will be said: Point is that which has no parts, line, length without width, etc.

If in the speculative, Bradwardine notes well, that the Definitions are not so much by Genus and Difference, but in another way, that looks primarily at the essence, like I assume Genus; e.g. The Point is the beginning of magnitude, or Quantity; the Line is the trace that limits the clear and obscure, constituting a single dimension. Surface is that which admits two dimensions; Body is that which admits three.

In this Science, in terms of definitions, sometimes they are formed as speculative, other times as practical, always trying to ensure they are essential, as noted in their proper place, where we discussed the precepts, with which we enter more clearly into the explanation of this Predicament, whose first species of continuous Quantity is the Line, considered as the Genus of its Species.

Understood that the Point lacks parts, and that without them, although it is the beginning of Quantity, it does not constitute it (from which it follows that it is the end of that species, which can be terminated in points, as will be any dimension, or Quantity, that does not admit width), we will come to know the first dimension, and this is commonly called Line, which we consider with Mathematicians As length, which does not have width, whose ends are points, leaving to Philosophers the dispute, whether the line is composed of points and parts; and how does it consist, or can it consist of indivisibles? and the other questions in which they are vigilant.

We carry, then, that the Line is caused, and understood by the trace of the movement of some physical or metaphysical point, ending in points, and this dimension is the one that is considered as the first species of continuous quantity, and is Genus of its species, which are relevant to this Science are the Straight, the Curve, the Circular, and the Sinuous, and the others, that will be noted in their proper places. Note that because in the following Book we put all the geometric definitions that pertain to this Science, with the application that is made of them for the practicality of Dexterity, we omit here to demonstrate the figures of this continuous Quantity.

A straight line is the shortest extension between two points at which it ends. A curved line is one that forms an arc, terminating at two points, not following the shortest extension, but rather a more deviated one; thus it can be more or less curved, depending on how much it expands in the deviation of its ends.

A circular line is one that, equidistant to a central point, is considered to be caused by the regular movement of a point, which, if it ends at another point before returning to the same one, is called a portion of a circle; if it ends halfway through its course, it will be half a circle; if it ends at the quarter point, it will be said to be a quarter circle, from which, without cutting off the end, there are wounds that are called quarter circle, half circle, or a larger portion of a circle, according to how they are considered by the movement described with some point, like the tip of the Sword, etc.

The spiral line is that which, in increase or decrease, is composed, forming a coil or spiral, a term used for the movement described by the center of the Sun in the sphere, relative to its course, with which it deviates, declines, and retreats from one Tropic to another, its maximum increase being at the Equinox, and its maximum decrease at the Tropic; and for our purpose, a spiral line will be considered on the central point, and in a spiral it will increase to another external point; and conversely, in decrease, starting from the external point, and ending at the central or interior point: this line is very typical in the Science of the Sword, due to the movements of its tip in the execution of some wounds, or Tricks, as will be demonstrated in their proper places, where it will be noted in what modes, and species it is of continuous Quantity.

A wavy line is one that is caused by a point moving to another, not by the shortest extension, as in the straight line, nor with regularity, as in the circle or spiral, but wavering, or snaking, like a river, or a snake.

A perpendicular or vertical line is considered to be one that, with respect to the opposite, or above another straight line from a point of elevation, falls directly onto the plane of the horizon, or onto a parallel to the same plane, in which it will form a right angle if it ends on the parallel, or the horizontal plane; and similar lines are named Vertical lines after the term Vertex, point of elevation, above the vertex of the opposite, and from this principle the terms Vertical Cut, etc. arise, as will be noted in their proper places.

A diagonal line is that transverse one, relative to the plane of the horizontal, caused by the point that moves along a transverse course, with respect to some Parallel, which is imagined Parallel to the Horizontal, from which the terms Diagonal Cut, etc. are produced. And these Horizontals, and Diagonals, and their close and distant species, are typical of the movement that in this Science is called Reduction, or Retreat, as far as the Horizontals, and in the Transverse, Diagonal; as will be demonstrated in their places, when it comes to action, and passion, and movement, and stillness.

I omit many other types of lines, because they do not belong to this Science, but to Geometry, where all their differences, like the Quadratrix, the Conchulis, etc. are recognized. Those lines that are very relevant to our purpose, we pointed out in the Book of Art, adapting them to the understanding of the Art of Fencing. Concluding, parallel lines are those that are equidistant from each other.

A surface, with respect to the Supreme Genre of this Predicate, is the second species of continuous Quantity, which is a proximate Genre to the Surface; and this is an immediate Genre to its proximate Species, as noted in the Predicables, in the voices, Genre, and Species.

A surface is that, whose boundaries are lines in the Plane, and circles in the Spheres; and so, according to their forms, concave or convex, considering latitude without depth: all surfaces admit the properties of continuous Quantity, insofar as they are potentially divisible; and of the discrete, insofar as they are actually divisible.

For its dignity, and capacity, the Circular is placed first, which consists of a line equidistant in all its parts from a point, which is called the Center; and Periphery, the container, which includes the Circular Surface, without ending in points, but in itself. And so, from any Point, or Center, and with any interval, the Periphery of the Circle is described, which includes the flat Circular Surface at the same distance, with respect to the center, from which, any straight lines drawn to the termination of the Surface, will all be equal among themselves, by the definition of the circle, and the terminating line will include itself, without giving other points that terminate it: from this consideration, the Surface is caused, which causes the Ellipse, which is that Line, which moving a point, until its beginning ends, is not regular in its equidistance of all its parts to its central point, but rather it describes a quasi oval.

Surfaces, in their lowest species, are recognized by their shapes, caused by their boundaries; thus, Euclid defined: A figure is that which is enclosed by one or some boundaries.

This definition encompasses not only the figure but also the Surface, which is contained by its boundaries, in respect to its latitude, not in respect to depth, which does not pertain to the Surface, hence Clavius pointed out that not because every Quantity has boundaries, it will be a figure, but rather that, whose common boundaries coupled, include the figure or Surface they end; and from here it follows, that that Surface, which is enclosed, and ended by its common boundaries, or coupled among themselves, will be a figure, and consequently a species of continuous Quantity; and if it is not composed of these parts, it will neither comprehend nor form a figure, nor a Surface of the species of continuous Quantity, but of the discrete, whose division will necessarily be in act, more than in potential.

Understood thus, figures, and Surfaces are divided into various species, and from these are proximate Genres their immediate ones, as a Plane figure is a Genre of its species, which all are Planes; Solid of the Solids, Concave of the Concaves, Convex of the Convexes, and in all it does not go beyond latitude without depth, investigating their Superficial forms by their figures.

A Plane figure is ended by lines that include it, and consequently the Surface: so it will be the same to say figure, as Surface, and so we will use one of the two terms. Superficial Concave, or Convex figures are divided, in respect to interior, or exterior: the interior is named Concave, because it does not go on to be a Solid figure: Convex is named the outer part of the supreme Surface. Some say that Concave is the one that has the body outward, and Convex the one that has it inward.

Figures without angles are those that are enclosed by a Surface, or Line, such as the Circle, the Ellipse, the Lenticular, and their like. Angular, or Polygonal figures, are those that ended by lines, consist of angles. Planar Rectilinear figures take their names from the sides, or angles, or by both, as taught by Euclid, and his Commentators.

Those that end in three lines, or sides in their immediate genus, by the name Triangle, or Trilateral figures, are diverse species by their forms, and terms. Equilateral are those that consist of equal sides.

Isosceles is the one that consists of two equal sides, whose base is larger or smaller than its sides. Scalene is the one with the three unequal sides.

Trilateral figures are subdivided into different species by the quality, and value of the angles. In the Right, or Rectangular Triangle (whatever the species may be) its three angles do not admit more or less value than two right ones; the cause touches speculative Geometry, because the two Acute angles are equivalent to the Right one, and the Right triangle can have the quality of Isosceles or Scalene, but not of other species, which it does not admit. Obtuse is that triangle, which consists of an angle greater than the right, and can also be Isosceles, and Scalene. Acute is that triangle, which is constituted of all three acute angles, which are less than right angles.

Triangles are subdivided into other species, whose names they take from the quality, and affection of the lines, of which they are composed, and formed. Rectilinear are those that are enclosed by straight lines, Curvilinear those that by Curved lines. Spherical are those that by portions of circles, which admit location in the Spherical Surface. Mixed are those that are not of one species of lines, but different, are composed, and in all qualities and names are considered, which results from them by the value of angles, and sides, and every Triangle is of the continuous Quantity, because it is included by the coupled terms.

Likewise, those with three sides are named Trilaterals, thus those with four are named by the number of their terms, or sides, Quadrilaterals: admitting this Genus different Species, which commonly are reduced to five, which are principal; the four regular, and the fifth subdivides into other smallest Species, which are included in its terms.

Perfect Square (as Euclid defined it) is a Rectangular, Equilateral Quadrilateral, the first regular Species of its immediate Genus. Rectangle is the second regular species with four sides, the opposite ones are parallel and equal, the two larger and the two smaller, and all its angles are right.

Rhombus is the third regular quadrilateral species, consists of all its equal angles, not right ones; although the opposite ones are similar, because two are obtuse, and the other two are acute. Rhomboid is the fourth regular quadrilateral figure, it does not admit right angles, nor are its sides all Equilateral, although the opposite ones are, as they are similar to each other. And so, from these species are the Rhombic and the Similar, that to the others pronounce them Rhombic and Similar Rhombic.

All the other Quadrilateral figures, which are constituted of different unequal sides, and unequal angles, generically are named Trapezoids, and although they are multilateral, are unequal sides, and unequal angles.

Parallelogram properly is a Quadrilateral figure, whose opposite sides are Parallel; and consequently it results from the Rhombus, or Rhomboid: a Diameter is constituted in such a figure, naming it as such that Line, which is drawn from one angle to another, the most distant.

Pentagon is a figure, that is constituted of five sides, that if they couple at five points, where forming angles, if the sides are equal, will be equal and the figure will be a Regular Pentagon. If the sides are unequal, and the angles, it will be irregular, and consequently a Trapezoid. Hexagon consists of six sides, and equal angles, being regular, and the contrary. So for more sides, like the Heptagon, Octagon, etc. which Euclid widely demonstrates.

Rectilinear figures are divided into simple and compound: the simple ones, Triangle, Quadrangle, Pentagon, etc., and they are so because they do not admit more than the angles, at which their sides end, simply caused by the passion of their convergence.

Compound figures (calls Thomas Bradwardine) are those that are composed of ingressive and egressive angles, as will be demonstrated. Generically simple figures are all those that constitute simple Polygons. Of these, some are regular, and others irregular; of the regular ones, some fill place, and others do not; the irregular ones do not fill place. The regular ones consist of sides, and equal ingressive angles, and for that reason they are named Equilateral and Equiangular.

To fill, or fill a place (as Bradwardine himself points out) is to occupy the space surrounding a given point in a plane: only three regular figures are considered to be capable of this quality, which are, the Triangle, the Square, and the Hexagon. None of the others admit such a circumstance: the speculative reason is, because it is found in the regular Triangle, in the Square, and in the Hexagon, such order, and disposition, that coupled, they fill the place surrounding the given point in a plane.

The affirmative part is proven, because it results from the number and position of the value of its right angles: Bradwardine himself demonstrates this, saying: If four similar squares are coupled at one point, they occupy the surrounding place, because they compose a square, whose central point will be placed in its circumference. In the Triangle, when six are coupled to the given point, they also fill the circumference; and the reason is, because the Triangle is worth two right angles, and the Square four, which is double the Triangle.

The case for the Hexagon is proven because the six angles of it are equal to eight right angles, according to the common demonstration (repeated by Bradwardine). It is known that in any regular figure, given one central interior point, if lines are drawn from it to the angles of the Polygon, doubling them, and subtracting four from the product, the value of right angles remains: therefore, if three Hexagons are coupled at the given point, they fill the surrounding place, because in the Hexagon there are eight right angles, and three are worth four right angles.

And so from the Equilateral Triangle results a similar consequence, because the angle of the Hexagon is double that of the regular Triangle; and it is demonstrated, because three angles of the Hexagon are worth double the Triangle, whose three angles are worth two right angles: then their double four right angles: and by the final demonstrable consequence, in such a double, six Triangles are required for the filling of the place, which the Hexagon fills; and so it turns out, that three Hexagons fill the surrounding place to the given point in a plane, and six Triangles also. It is also confirmed, because the three angles of the Triangle are worth two right angles: then six are worth four, and so they fill the surrounding place to the given point.

The conclusion, or lemma, is therefore rightly said, that fill the surrounding place six Triangles, four Tetragons, and three regular Hexagons. All can be demonstrated by different problems. In a given point in a plane, its circumference is occupied, and filled, drawing a straight line, on whose basis four Tetragons are formed, which coupled, occupy, and fill the circumference of the given point at the distance of the Line. And not making a delineation of this figure, and others, here, is, to not increase the volume, and that for skilled Mathematicians, it is a prolix matter.

Chosen as the center the given point in a plane, coupled six Equilateral Triangles, their bases will form a regular Hexagon, as facilitated in the common problem to any compass opening on the point, or center, forms a whole Periphery, and with the same compass opening it is divided into six arcs, or points, and from one to another straight lines are drawn, the chords of such arcs, and from the angles to the center; the straight lines, or semidiameters, result in six coupled Triangles, that occupy, and fill the surrounding place to the given point.

If three regular hexagons are joined at a point, they fill and occupy the surrounding space around the given point. When these three hexagons are further extended by joining three more, as seen in the problems resulting from this theorem, they form connected hexagons. It is easy for anyone with a non-vulgar understanding of speculative geometry and continuous quantity to acknowledge that these connected hexagons fill the space around the common point of connection. As demonstrated, all these figures and speculations are of continuous quantity in relation to their entirety.

It’s proven that only three shapes, the Triangle, Square, and Hexagon, can fill the space surrounding a point on a plane. However, it remains to be demonstrated the negative part, that no other regular shape is capable of filling space. This is shown (as demonstrated by Bradwardine himself) because each shape has larger angles than its predecessor, as is evident by the common proposition of the knowledge of right angles that each figure holds. Every subsequent figure adds, but doesn’t diminish, because no angle can be worth two right angles, as will be demonstrated in discrete quantity and in regular shapes such as those proposed. Every angle of the subsequent shape is larger than any angle of the preceding shape, a common principle in geometry. Therefore, it’s a clear conclusion that no figure, after the hexagon, is capable of filling the space surrounding a point on a plane. Because if three angles of the polygon, from the regular shape after the hexagon, are superfluous, and no two angles of them will fill space, just like two straight lines don’t fill a surface. No matter how large an angle is given, it’s worth two right angles: therefore, neither two angles can be worth four right angles by the definition of a plane angle. Thus, the heptagon is not capable of filling the surrounding space around a given point on a plane.

The same reasoning applies to the Pentagon, it also doesn’t fill space because its three angles are not worth four right angles, they are not equal to those of the Hexagon, and four angles of the Pentagon have the Square as their preceding figure in the order of regular shapes. Hence, the intent is demonstrated, which is necessary in the Science of the Sword, which always considers a given point on the plane of the combatants. From this point, the consideration passes to find which shapes are capable of filling surrounding space to understand distances and form stratagems based on proportionate means, which often result from the knowledge of geometric regular shapes that, when connected without leaving a void, fill the surrounding space around a given point on a plane. This consideration belongs to the realm of continuous quantity.

Compound figures are those which, while regular, are not only composed of the inherent angles that make up the figure or polygon, but whose sides, when extended, form another figure with outgoing angles; that is, angles that emerge from the basic figure.

This speculation has been explored by few, for only Campanus (among the many commentators on Euclid, who needed the Pentagon) pondered on the extension of its sides. Consequently, he found the Pentagonal figure, composed of outgoing angles, created in regular proportion by extending the sides to their point of convergence, which generates a continuous straight line, dividing into five, forming five outgoing angles, opposite to the inherent sides.

From this principle, Thomas Bradwardine advanced the speculation in the following three conclusions, reducing the composition of such figures to three orders, which we repeat, as it is one of the most significant principles in the Science of the Sword. This is due to the speculation of the outgoing angles, which, with respect to figures, can provide understanding through continuous quantity. By extending the sides of regular figures, not only is the knowledge of the inherent angles that they are composed of in their formal root obtained, but also of the outgoing ones. This is where the proportions of the extensions are provided, a concept that motivated Thomas Bradwardine (whom I follow), as he was the first and only person to expressly speculate on figures that, through the extension of their sides, accept outgoing angles.

The first of these types of figures is the Pentagon. It is demonstrated that the Triangle is not a figure capable of such quality and order with respect to the extension of its sides, even though it is, with respect to the compound combination of Triangle to Triangle. But simply extending its sides, they not only do not converge at a common angular point, but the extended lines deviate, forming external angles over the internal ones. Therefore, the Triangle is not a figure of this type.

Nor is the Tetragon such a figure, because its opposite sides are parallel lines. Parallel lines are always equidistant from each other, as demonstrated by Euclid, so their extension will never form an angle. Therefore, the Tetragon is incapable of producing a figure with outgoing angles. It is thus evident that neither the Triangle nor the Tetragon, the figures preceding the Pentagon, are capable of simply forming, through the extension of their sides, a figure of outgoing angles, which is the proposition at hand.

The Pentagon is the first figure which, simply by the extension of its sides, can form a figure of outgoing angles. This is demonstrated and exemplified clearly, as its extended sides will converge at a given point, forming an outgoing angle. Thus, the other sides will converge with each other, forming outgoing angles, and consequently, a single movement to different endpoints creates the entire figure. For, from one endpoint to another, a figure of outgoing angles opposite to the incoming angles is formed by continuous quantity. With this, this conclusion is demonstrated, upon which we could expand with various speculations that serve our purpose, leaving an open field for the discourses typical of this Science; and generally, we refer to Bradwardine. Here, for more clarity, we will recognize different orders in figures of outgoing angles, both those that are capable of being produced from continuous quantity, as well as those that have their composition from discrete quantity. This refers to which figures (when their sides are extended) form outgoing angles, as in the proposed Pentagon; and which figures require two or more regular figures to produce a composite one, which is formed of outgoing angles. An example would be the Hexagon, which is not capable of forming a figure of outgoing angles by extending its sides, because it has opposite sides consisting of parallel lines; and therefore, no matter how much they are extended, they will always be parallel by their very definition. With this, it is demonstrated by the preceding, that the Triangle, the Tetragon, and the Hexagon are not capable figures of outgoing angles, and consequently the Pentagon is the first simple figure of such quality, and for this reason it is referred to as a first order figure in continuous quantity.

In summarizing this topic of figures capable of outgoing angles, by extending their sides to points of convergence, it is demonstrated that the Pentagon is considered in the first order, because it is the first regular figure that admits such qualities in itself, without any preceding or subsequent figure that can have them. Consequently, the regular figures of the second order, capable of outgoing angles by extending their sides, are recognized to be the Heptagon, the Octagon, and the Nonagon, because in the second order they admit the qualities of outgoing angles by the extension of their sides in the formality of continuous quantity, like the Pentagon, as demonstrated in the following theorems.

In figures with more sides, continuity is not admitted in their forms, unlike the three proposed, which by continuous movement of lines ending at equidistant points, without lifting the pen, the figure is formed, as demonstrated in the Heptagon, where from the given point the straight line can run from point to point, and in its convergence, they will be outgoing angles.

In the same way in the Octagon, by extending the sides of the interior, the outgoing angles result by continuous quantity, drawing the line from point to point, and as they are produced, the Octagonal figure is formed with outgoing angles.

In the Nonagon, it is demonstrated in the same order, because by extending its lines until they end at the given point, the outgoing angles result over the interior Nonagon, with its sides extended to the referred points of its angular convergence. And for the purpose of the Science of the Sword, the interior positions are recognized in such figures, from whose sides the reaches and angles that the Sword can form are produced, governed by the movements of the arm, feet, and body of the mover; and consequently, in the operations of the opponent. Although accidents in execution vary the regular positions, this does not prevent the knowledgeable and experienced practitioner from recognizing the positions in which they place themselves, and having perceived in the mind the figures of outgoing angles, they make use of them on occasions, as they can avail themselves.

These considerations and demonstrations on the surfaces speculated by continuous quantity seem sufficient, without going into the extensive offer of Geometry, because this discipline is assumed to be subordinate in the Science of the Sword. Thus, as a warning, we will try to stick to the essential and compulsory, leaving the figures of outgoing angles of the third order for the discrete quantity. These result from some perfect regular figures placed in others of the same species, as will be demonstrated in its place.

The grandeur of Bradwardine’s discourse on these figures of outgoing angles is inescapable, leaving in the interior angles such perfect regular figures, like the Pentagon, the Heptagon, the Octagon, and the Nonagon; and that he had not foreseen the strength of reason, and grandeur, that assist these figures. Indeed, in the internal parts of the ingoing angles, they leave these figures formed. I also point out that the same figures are found in the outgoing and exterior angles of said figures that are found in the interiors, as by drawing chords from the ingoing angle to one of the points, and continuing from one to the other, the same interior Pentagon will be found formed in the exterior, and thus the other referred figures of this order, these exterior chords of great consequence for the Science of the Sword, since through them the fencer will give his compasses, serving him as routes, or paths to occupy good places in the outgoing angles, as will be demonstrated in its place.

Euclid gives a generic definition, saying: A solid figure is one that has length, width, depth, or thickness, these are the three dimensions that every body consists of. And for the formation, he adds: The boundary of every solid is the surface or surfaces, made up of the planes or convex bodies, which include the solid figures, according to their species. There are straight and sloping planes, which are considered according to their forms, oppositions, with which they compose different solid figures.

The inclination of one plane to another plane is considered by the acute angle, constituted by inclining straight lines. Plane to plane, similarly inclined (that is, of equal inclination) are those whose angles are equal: that is, of one value. Parallel planes are those which in their entirety are equidistant, without inclining, nor declining with respect to one another. Similar solid figures are those contained by similar planes, equal in their number.

Peleteario, Tartalla, and Clavio understand by similar solid figures, those that consist of an equal number of angles, and planes, proportional to each other. It results thus, that equal, or similar solid figures, are those that are contained by equal, or similar planes in their size, and number. For understanding, it is necessary to know, what solid angles are, noting, that in general they are caused by the concurrence of planar angles, or curved, or mixed. It is thus defined: A solid angle is that, which besides two angular planes, not consisting in a plane, but converging at a point, contain and constitute a solid angle.

This definition is clearer, and no less essential, than that which Euclid places, formed by inclination, and concurrence of lines, terminated in angles, and all is one, from where the solid figures result, Conics, Prisms, etc.

If it is a simple Conic solid figure, it is caused, in Euclid’s consideration, by the movement of a right triangle, the perpendicular being the resting line, or in another inclination, placed in very short extension of the Cone to the base, and the Diagonal, or Hypotenuse is considered the movable of the triangle, whose revolution with its trace, leaves formed a solid figure circumfluent conoidal, caused by entire movement, that consists of two planes; one circular by the line of the base of the triangle; and another from the base to the pyramidal Cone, caused by the Hypotenuse.

It should be noted, with the same Euclid, Campano, Peleteario, Clavio, and other Expositors, that if the resting line, and the base were equal, the Cone will be Orthogon, because the perpendicular on the base, the Hypotenuse will form angles of 45 degrees, and in the revolution the angle, terminated at the point of the vertex, is double to that of the base; and so right if the line of the base (which is the one in the whole revolution results semidiameter of the circle, which describes the revolution) were greater than the resting perpendicular; the angle of the pyramid at its vertex will be Amblygon.

And conversely, if the resting line were larger than the revolving one of the base, the angle of the vertex in the pyramid will be Oxigon, the more acute, the more the resting line of the figure exceeds the mobile one of the base. According to the proposal, it can be defined that pyramid is a generic name, which includes all solid figures, which are composed of planes, continuing from the one that is the base to the Vertex point, or Cone, where they all converge.

The species is distinguished and is defined by the plane (figure of its base) as demonstrated by Euclid’s expositors, and noted by Bradwardine, because the base of the pyramid gives the name to the whole pyramidal body, hence, if it is a Triangle, it will be called triangular; if Quadrangular, quadrangular; if Pentagon, pentagonal; if Hexagon of the pyramid, they are necessarily all triangles, because they end in the common angle, which they call solid.

Prism is a solid figure, which is composed of planes, and of them, two are different from the others; although similar, equal, and parallel to each other, as the Pyramid is explained, and named for the terminating base, so the Prism by the number of its sides, which constitute the surface of its body, hence if that solid figure, whose two opposing planes, Parallel, equal, and similar, that constitute its plan, were triangles, they are named triangular Prism; if Quadrangular, quadrangular, etc. as in the pyramid.

Cube is the most regular solid figure, and is composed of six square surfaces, the four converging among themselves at right angles, and the other two ending in the cubic figure, or Hexahedron.

Tetrahedron is a solid figure, composed of four triangular surfaces, one is the base, and the other three end in a solid angle, and can be the triangles, that end on each surface, all equilateral, or the base diverse, or all different; and in the same way the following solid figures are considered. Octahedron is a solid figure, contained under eight triangles, or equal and equilateral triangular surfaces. Dodecahedron is a solid figure, contained under twelve equal equilateral and equiangular Pentagons. Icosahedron is a solid figure, contained under twenty equal, and equilateral triangles.

These five bodies are called regular, because all the planes, by which they are contained, can be Equiangular, and Equilateral, as is recognized in their definitions. Philosophers call these bodies Platonic, because the consideration of them, according to their doctrine, is for those five elements that constitute the Universe, Heaven, Fire, Air, Water, and Earth, whose speculations I omit here, as they are not of our intention. The curious should refer to the expositors of Aristotle. Ptolemy in his Great Construction, and those who deal with the division of the Sphere according to substance.

Geometers will find the construction of the five regular Bodies, defined in Euclid, and his expositors, who in various ways have sought to demonstrate the composition of the five regular Bodies, not easy on paper, and easy in wood, or in other material suitable for the formation of their structure, which as it is not of our concern; we could skip them, to exchange demonstrations; and for the same reason we do not engage in the solid Parallelepiped figures (which are those quadrilateral) that are contained by six, or by coupling the parallel surfaces, and forming a solid body, as demonstrated by Euclid. And even less are of this intent the solid figures, which are considered inscribed, and circumscribed one in another, although all the repeated (perfectly solid) ones are of the continuous Quantity.

Complex principles are those that embrace, or comprehend the concept, with such demonstration, that the understanding accepts them without repugnance, as felt by Thomas Bradwardine, dividing them into two genres; one to which is given the name of Petitions; another more common to all sciences, which are understood by Axioms, Pronounced, or common notions: and of both used Euclid, and we use in the Science of the Sword, and we place them in this place, not because they are of this Category, but because we need such principles for the understanding, and forced arguments of it, and the others.

Petitions in Geometry, and Science of the Sword, are some suppositions, that should be granted, both for their certainty, and for the infallible possibility, with which the understanding perceives them, and for our concern the following are proposed.

From any given point to any other point, a straight line can be produced; and without an intermediate obstacle, it can be physical: and having one, or not being visible, or actual, but imaginary, it will be metaphysical: and in both ways straight, for being the shortest extension from point to point.

Any given straight line can be produced in continuous augmentation, because in every line its ends are points, and from an ending point, a line can be produced and continued to an ending point, which is the ultimate end of the produced line: and we deny the production into infinity, because it is not human to comprehend, nor of this Science of the Sword.

Given any point as a center, a circle can be described at any interval, according to the chosen radius, or according to that point that ends the interval, to which it is described. This is proven because an end is that which is extreme of something, as Euclid defined, from where it follows, that on any point chosen as center, a circle can be described: in respect, or proportion of any quantity, or size, greater or smaller quantity, or magnitude can be given, whether considered in Line, Surface, or Body, or in number.

From such principles it results, that equal circles are those, whose diameters, and radii among themselves are equal, and consequently, those circles are unequal, which differ in their diameters, or radii. This is proven by common sense, because the circle is a figure contained by a regular circumference around a point, which is the center, from which all straight lines drawn to the Periphery, are among themselves equal; and consequently, the other figures, that do not consist of such circumstances, are not circular, but of other shapes. Thus all the curved lines, which are caused by the movements of the Sword, not being uniform to a given central point, will not be portions of circle, nor whole circle, but of other species, that can be caused by curved lines.

From such principles it results by petition, that From point to point given, not only a straight line can be given, due to the shortest extension, but also a Curve, Spiral, Flexuous, or Mixed, at the will of the governing or operating.

All right angles are equal to each other, because they consist of indivisible, unchangeable equality, for in any variation, they will either be larger or smaller than right angles.

If a straight line falls upon two straight lines, intersecting them, if the two converge at a point, forming an angle, the line falling upon the intersections will constitute figures and angles, which will be complementary to two right angles, upon the angle formed by the convergence of the two given lines.

Two straight lines do not include a surface, nor do they constitute a figure; therefore, the first figure is a triangle. These principles are specific to Geometry and the Science of the Sword: they are commonly named Petitions, or Assumptions, because they are accepted or admitted as complex principles of the first kind, without needing any other proof or demonstration, as they are self-evident, providing sufficient evidence.

Certain common principles are found in philosophers and mathematicians, which embrace the concept, and they name them with different synonymous terms, such as Axioms, Pronouncements, common notions, etc. They consider them as evidences, to which the understanding agrees, without more proof than the intelligible explanation, enough to give to understand the sentence that is pronounced. Here I could compile many of these principles, but I exclude those that are not proper to the intention, reducing the most essential to a small number.

  1. The whole is equal to its parts, because all parts together do not make up more than one whole.
  2. Any whole is greater than its parts; this is understood categorematically, but not without syncategorematically.
  3. Any of the mathematical or physical species, which consist of a perfect dimension equal among themselves, are equal.
  4. If, according to their constitution and formal terms, they are unequal among themselves, they will be unequal.
  5. If equal quantities are added to equal amounts in their entirety, they will be unequal.
  6. If equal amounts are added to unequal quantities, the totals result in unequal amounts.
  7. If equal quantities are subtracted from equal amounts, the residuals result in equal amounts, and vice versa.
  8. If portions or equal quantities are subtracted from unequal quantities, the residuals are unequal.
  9. If equal forces or powers or equal quantities are assumed, the results are equal, and vice versa.

If in forces, powers, or unequal quantities, supplements are applied by accident, science, or art in operation, which exceed the inequality, they will not only reach or terminate unequal terms, but the lesser force, power, or quantity, as much as it exceeds by accident, science, or art in operation, will result larger by the excessive supplement.

This question arises from those who believe, or hold the opinion, that there is a fourth type of continuous Mathematical Quantity, whether considered in abstract or concrete, while the correct understanding of Philosophers, Physicists, and Metaphysicists is that there are no more Mathematical species than Line, Surface, and Body, which properly belong to the Category, or Predicate of continuous Quantity.

Those who claim otherwise, deviate from the Philosophical doctrine, which truthfully only admits these species of Mathematical continuous Quantity, considering them as parts that comprise a whole, which is the Body, adding (regarding the physical consideration) two other species of permanent continuous Quantity, which are, Place, and Time, as taught by Aristotle.

Some Moderns, without considering the entity of the species, add Angle as the fourth, and deducing from their arguments (those that weigh with greater acuity) argue thus: Every Mathematical continuous Quantity is constituted of terms, the Angle is constituted of terms: therefore, the Angle is the fourth species of Mathematical, or Physical continuous Quantity.

Every continuous quantity is suitable for dimension, because it is the proper passion of continuous quantity. Therefore, the angle admits dimension by Quantity: therefore, the angle is the fourth species of continuous Quantity.

Every continuous quantity is suitable for dimension, because it is the proper passion of continuous quantity. Therefore, the angle admits dimension by Quantity: therefore, the angle is the fourth species of continuous Quantity.

Against this is Aristotle, and the whole current of Logicians, Physicists, and Metaphysicists: and the wise Mathematicians feel, and must feel, the same. This is proven because in two ways the species of continuous Quantity are understood in terms of Line, Surface, and Body. One is, considering the species, like pure Philosophers; another, like pure Mathematicians. Neither in one way nor in the other is the Angle the fourth species of continuous Quantity, and there are no more primary species in it than Line, Surface, and Body, without admitting the Angle as the fourth species, as Aristotle has, and his Expositors carry, without disagreement, admitting immediate fourth and fifth Species, Place, and Time, and everything else, that can concur as a species of continuous Quantity, the Philosopher wants it to be by accident.

For true understanding, it is necessary to suppose, with Aristotle, that Quantity, or Quantum, is in two genres: Continuous, and Discrete. If Continuous, its species are Line, Surface, Body, Place, and Time.

If Discrete, its generic species are Number, and Speech in terms of distinctions, derived from reason, because in the continuous Quantity the terms are common comprehensive; if in the discrete, they are distinct: from where by maximum received, Scotus said, speaking of Quantity: That being is a union of the extremes.

For this reason, Ancient and Modern Logicians, as Philosophers, admit as a conclusion that, speaking properly, the Line, Surface, and Body are not three species of permanent continuous Quantity, but rather, in a certain way of understanding, they are parts for the Whole, and can be called incomplete parts, since Length, Surface, and Depth (which are all dimensions of permanent continuous Quantity) all are found in the Whole, which is the Body, from where the concept can understand them as parts composing the Whole.

Mathematicians, who do not pay so much attention to the entity of things in themselves, as to the demonstration by Problem, or Theorem (without getting bogged down in the way of proving by syllogism, and reasoning, like Logicians, Physicists, and Metaphysicists) although they do not add more to the continuous Quantity than the three species, Line, Surface, and Body, they consider, at least, in each one, distinct passions or affections, as if in a perfect dimension others did not concur, distinguishing Lines from Surfaces and Bodies, although the Line, and the Surface precisely signify, and demonstrate the Length, and Latitude, which are found, as parts of the Whole with the Depth, constituting a finished, complex Body of its common terms, achieving the perfect being of continuous, permanent Quantity by the union of its extremes.

From the previous two conclusions, to which the discourses of true Philosophers and Mathematicians are reduced, a third conclusion is drawn, with which it is reconciled, and it is understood, what is continuous Quantity, and how it is reduced to the three main species, Line, Surface, and Body, without admitting the Angle as the fourth species of continuous Quantity, as it proceeds from reason, and is demonstrable, because although when they concur, forming the Body as perfect, like common united extremes, this does not prevent the Line, and Surface from being distinct species, when they terminate without the union of the Whole, ending from their common united extremes, thus the Line is a pure species of continuous Quantity, as Length, without admitting Latitude, including in its united extremes, which are points: and thus, the Surface is also a proper species of the continuous Quantity, when it is contained by its common extremes, which are Lines; and consequently, the Body is the third perfect species of the continuous Quantity, when its Depth, or thickness is contained by its common united extremes, which are Lines, and Surfaces. For example: The cube consists of the three dimensions, Length, Width, and Depth, constituted in its whole six copulated Surfaces, and each Surface of four lines, with which it receives its being from the union of its extremes, constituted of its common united terms.

More perfectly, the spherical Body, which without admitting an angle, receives a perfect being of a solid Body, and continuous Quantity, by the union of its common extremes; in whose composition Euclid wanted the three Species, Line, Surface, and Body, to concur, from which the Whole, or Spherical solid results; and so he defined it by the circular line in the Quantity of a semicircle, saying, the Sphere is the transit of the revolution of a half circle, &c. whose movement described, and formed the extreme Surface, which includes the depth. For these true fundamental demonstrations, the Angle is clearly excluded from the continuous Quantity; because in truth it is not, but passion, or affection of concurrent lines at a point, which produced by the first petition, must necessarily be cut, causing proportional Angles, equal to each other, to four right, being the lines two enough to form an Angle; and consequently, the Angle is not a species of the continuous Quantity, but of the discrete; for this reason it receives its essence, and quality from the numbering, which demonstrates its value by degrees, and minutes, or in other terms (which are more from other Predicaments, than from the continuous Quantity) because of the passions, and concurrences of some lines in others, inclining, and declining, the Angle is caused and as well as from the inclining, and declining planes, with respect to the concurrence in another plane, in which the reason, the discourse, and the mathematical demonstration widely finds an open field, as it will be noted in the proper place: and for more convention, the contrary arguments are demonstrably responded to.

To the first it is conceded the greater in as much as it admits that the continuous Quantity is constituted by united terms. The Angle, then, is not constituted by united terms, but by separate ones in the constitution of its being. Thus, the Angle is not the fourth species of continuous Quantity. This is proved, because this: can be in its parts, and in its whole, without constituting an Angle, and when it constitutes it by accident, the Angle will not be an essential species, but a passion of termination, and concurrence of lines, as they concur on the Surface.

The greater of this argument is proved by the sentence of Scotus, saying: That being is in the union of common extremes. The greater is notable, as proved by Thomas Bradwardine, and it is common that two lines do not constitute a Surface, nor is such admitted, being straight; and they can constitute an Angle, which is not of the continuous Quantity, like the Surface, or the Line alone; and if two curved portions can form two Angles, then copulated in the unity of common extremes, they are not considered by the Angle, but by the Surface, which they include, as complex terms, as noted in the other figures, that uniting in common terms, their extremes compose a Surface, which is the second species of the continuous Quantity; and consequently, the Angles are passions, or affections in the figure, being caused by the lines, which by uniting at the extremes, give being to the figure, as seen in all.

From here it results, that two produced lines (being straight) cause interior and exterior Angles, which are worth among all four right, proportioning themselves among themselves, according to the point of concurrence, by the section, and production of the two straight lines, causing the Angles, without union of extremes: then the Angle is not the fourth, nor another species of the continuous Quantity, but a passion of concurrent lines at a point.

To the second argument is conceded the greater, but explaining, that the continuous Quantity, and the discrete are distinguished as to their dimensions, and divisions, and differ; because the continuous Quantity in itself is apt for dimension, and division as to power; but the discrete Quantity is in act (as says the Philosopher) because the number 5. includes the 3. and the 3. is not 5. because its division in the discrete Quantity is in act, and in the continuous is in power.

The Angle, then, is numerated, and divided by the Number, which is a species of the discrete Quantity, just as the Angle of 5. degrees, although it includes the one of 3. the one of 3. is not the one of 5. but different, etc. then the Angle is not of the continuous Quantity, but of the discrete, because its being receives it from the numeration, caused by the concurrence of lines at a point, and not from the union of all its common extremes.

To the third argument it is answered, distinguishing the greater, and denying its absolute; since as it has been demonstrated, the Line by itself is nothing more than length without width, whose common terms are points; and in this part the greater of the contrary argument does not apply to the Angle, which is not caused by the length alone, but by the division of two lines, without termination of all its united extremes, with which they do not constitute Surface, nor Body, which are second, and third species of the continuous Quantity, that perfects the whole by the union of its common extremes: from where the Angle, although the lines that include it, end in points, they do not unite in all their extremes, nor can they constitute a species of continuous Quantity, but discrete numeration of its interval, caused by its greater or lesser deviation of the lines, which, being concurrent, form an Angle, and thus we achieve the intention.

With what has been referred to, we follow the doctrine of the Philosopher, placing as the fourth species of the continuous Quantity the Place, in which we will briefly gird ourselves, excusing the multitude of questions, and arguments, in which the Logicians, and the Physicists get entangled, from where the dispute is more proper, finding out what place is, and in what way it is considered, as to be given void in nature, it will occupy, or will not occupy place? The other discourses, and difficulties, that are disputed, I omit, for not being of the commitment of the Science of the Sword, in which I will try to choose the most forceful, and convenient.

We consider with the Philosopher that every body occupies a place (according to its capacity and form), hence Plato called the receptacle what is commonly named Place: and from this principle it is defined by description, saying: Place is that concave surface that surrounds and contains the body, in such a way that, without leaving a vacuum, it encircles it and unites with it, in such a way that Place and Body continue by the contiguity with which they join; e.g. the vessel, or the urn full of water, or another liquid, encircles and surrounds the concave surface of the vessel, or the convex of the liquid body, uniting without a vacuum the placing body with the placed body, not by pure continuation, but by unitive contiguity, which is reciprocal in the external surface of the body, and in the internal of the vessel that circumscribes it, excluding the vacuum, as the Philosopher amply proves, discussing our intention the causes that delay or facilitate the movement from place to place, because the lighter the natural placing body is, the more speed it admits in movement; and the denser it is, the more it impedes and slows it down. Take the example in water and air: both elements are apt to surround any moving body, either by itself, or by the impulse of another, touching the mobile body (as proposed) without giving a vacuum, as demonstrated by the Philosopher. Thus, due to the greater density of water, and the greater rarity of air, which makes it light, the mobile body has more aptitude to speed up in the air than in the water.

From here it follows how one Sword hinders another, moved by the impulses of the combatants, and because the arm and the Sword are located in the air, they are more apt to move more quickly than the feet, which move on a dense surface: that being located mostly in the air, in the end, is a dense part on which they rest, which is enough not to speed up as much as the hand and the Sword: from where it is noted, that the farther the feet are from the earth, the more ready is the aptitude with which they acquire speed: and the more united by contiguity, the more impeded and slow. From the same places in which the body, arm, and Sword move (which are in themselves heavy parts) and to where they move, also results in slowing down or speeding up in the aptitude and operation of movements, as will be more distinctly demonstrated in its place: this is proper to consider the rectitudes, in relation to the location of the bodies; for as Aristotle proves, every body occupies a place, and is occupied by its placer by contiguity, whether it is at rest, or in movement, with such consideration, that there are always its differences noted, in relation to the same body, and these are commonly called Rectitudes; but the Philosopher notes them as parts, and differences of location, reducing them to six, which are, Up, Down, to one side, and to another, forward, and backward.

Here, for more distinction and necessity in the Science of the Sword, we use the most common terms, and we name these parts and differences rectitudes, noting them in their six differences, or parts, which are straight to each body, Up, Down, to the right side, to the left, forward, backward; and this consideration is so forceful and necessary in this speculative and practical Science, that it is recognized as one of the greatest foundations of all Skill, because from such principles of place and rectitudes, comes the knowledge of the intelligence, and exercise of the Sword, as is seen demonstrated in this Category and Species, and in that of Time, and Movement, and Stillness, &c.

Noting here, that in the occupation of place, or places, the combatants have certain respects against each other, and each one in itself, according to the positions in which they find themselves place, or places, that they occupy, and they are occupying postures and modes, in which they are placed, and they are placed, and how they acquire, and lose the aptitude to movements, which are slow, which are fast, which are remiss, which impede, and which are impeded, in relation to places, bodies, and rectitudes, and the other circumstances, and considerations, that arise from knowing and understanding, what kind of continuous Quantity is the Place? What is Body placed by itself, and in relation to another? How by the distinction of places are advantages won, or lost? How are we to pass from one place to another? And in what way what in one gives disposition to execute outgoing angles, causing extension in the subject, in relation to his Sword, and local figure, where it is planted; in another it is the opposite due to the ingoing angles, that cause tension, and reduction in the reaches from place to place: because the Sword, is not only ruled by the arm, but by the position, and place, that the body occupies in its placement, in relation to the postures of the combatant subjects, which all this depends on the understanding of this species of continuous Quantity, as considered by Philosophers and Mathematicians: of how.

Aristotle and his expositors define as Vacuum that surface or space, not filled with located body, although apt to fill, in relation to the locator assuming that between one and another there could be a vacuum, which Philosophy does not admit.

Whether there is a Vacuum, or Void in the nature of things, is the matter in which a multitude of Ancient and even Modern Philosophers have been lost; although, the most learned denied and deny the vacuum in the nature of things, both in the composition of the Universe, and in the placement and movement of bodies in which it has been touched, and could have been discussed with Lucretius, Pythagoreans, Platonics, Xenocratics, and better with Aristotle, who proved demonstrably, there is no vacuum in nature, neither in relation to the filling of place, nor in relation to the movement of bodies, nor to the consistency and transmutation of Elements into each other, nor in the conjunction of one body, in relation to another body, nor in the same porous bodies, like wool, sponge, ash, &c. that admit tension, and extension by their separate rarity, or by the comprehension, because in the occupation of the air it fills, and without admitting a vacuum. The curious reader can see, among others, Plutarch, who compiles various opinions of Philosophers.

Pedro Gregorio wisely observed from the place in Genesis, that the earth, at the beginning of its creation, was void and without form, he said, that not absolutely, but in a certain way, the term Vacuum is probable, not looking at it by the rigor of the signification, but by the lack of something that completes, as the earth is natural, to express its operations, it is used by common terms, Left place empty: Did not occupy place entirely: Found empty, or occupied empty place, &c. and in such ways the signification is to understand the lack to the fullness, that is acquired, or the complement in what is worked.

In this way, and similar ones in Skill, the use of the terms Vacuum, Void is not absurd, because they do not look at the nature of things philosophically, but at the explanation of operations, with distinct consideration, to explain more briefly, and more intelligibly the proper meaning of actions, as also found in many classical authors, Cicero against Catilina: By the death of your first wife you left the house empty. In this way Passerasio noted that the common people call air-filled what is empty. The same was used by Virgil and Lucretius, and others, for the wide and spacious, as also used by Virgil, and the same Cicero called the idle mind empty, and from there came the proverb: Vacuos habere dies, to signify idleness, and Vacuus equus, the horse, which is not occupied by a person, as Livy said: Vacuus equus errans per urbem. And from vacuum come the common terms, Empty, Emptying, Emptied, &c.

With that, it is sufficiently excused in the Science of the Sword to use the terms Vacuum, and Void, in which erudition can be expanded, which is deliberately omitted here; with that we move on to the fifth species of continuous Quantity, which is Time, leaving for its place the understanding of Movement, and Stillness, which is so much of this Science.

The Philosopher placed in the second Predicament, or Category as the fifth species of continuous Quantity, Time: we leave for the Physicists the debatable, whether Time is contained, or caused by movement, and how they should be understood in their essential being, Movement, and Time, both by comprehension, as by substance, or accident in Quantity or Quantum.

Theologians investigate by other means the principles of Time in the creation of the Universe, and what was the first light that formed day and night? and when created? whether the first darkness was time? and other questions proper to the exposition of Genesis, where the curious can occur, for not being of our concern, in which excusing the long debatable, of the essential, which is found in Aristotle, we define time, saying: Being apart from a thing, a formal transitory duration, which the understanding perceives by permanent extension, divisible, and measurable, according to power, by the regulation of the natural movement of the first movable, with which it admits distinction of past, and future coupled in the point, which is given as present, and from where its measurable continuity in potential is known, teaching the Philosopher, That continuous movement is continuous time, and continuous quantity, concluding the similarity between Time, and Movement, and Movement, and Time.

These doctrines make it difficult to determine whether Movement is also another species of continuous Quantity, separate from Time, which Scotus touched on with his acuity, and after him other Moderns, saying: Movement is seen to be in the genus of Quantity, as is inferred from Aristotle, who said: Time is Quantity by movement: therefore Movement is Quantity. It is confirmed: Time, then, is a species of Quantity, because it is the fifth of continuous Quantity, according to Aristotle: then Movement is more a species of the continuous Quantity.

In response to our intent, Movement is not a species of continuous Quantity, because it does not have extension and measurability in potential embedded in its own concept, as in the opposite persistence of the agent it can be weakened, because against Movement a greater efficacy of the agent can occur. That which by itself is not consistent in all its parts is not by itself extensive and measurable in potential: therefore Movement is not a species of the genus of continuous Quantity.

The discussion about what types of Movement exist, and which are due to alteration, corruption, or transmutation, etc., is omitted because this is not very characteristic of the Science of the Sword, nor of this Category. But the essential will be treated when we talk about Movement and Stillness, following the Philosopher, who although included the matter, De Motu, etc. Quiete made a special discourse: not touching here more than to understand the five species of continuous Quantity, in which Logicians and Metaphysicians agree. One of them is Time, for being successive, measurable, and extensive, concluding with the Philosopher, that all other Species, which are intended to be applied to this Genus, are not truly Species of the continuous Quantity, but by accident: from which it follows, that in the Science of the Sword, the term Time is considered and used as a permanent, divisible, and potentially measurable extension; as by the regular movement of the first mobile, the other movements of Orbs and celestial Astros, we consider time as divided and measurable in instants, minutes, and hours, days, months, years, lustrums, ages, etc.

So, in this Science, through the movement and movements of the body and actions, Time is divided and measured in instants and operations, from where there are wounds that are named instantaneous, and others in other terms, using those of Time, and Times, taking the whole for the part, or the part for the whole, as is more appropriate for the explanation in the understanding, and practice of the Sword, demonstrating the Tricks, the Wounds, the Movements, and the rest, that in this Science constitutes the true Skill, remaining, as they remain, in this Category explained the five Species of the continuous Quantity, which are, Line, Surface, Body, Place, and Time. Agreeing with Euclid, Principle of Mathematicians, that Line is extended Quantity, Verſus longitudinem, coupled with indivisible points. The Surface, extended Quantity, Verſus latitudidem, coupled with indivisible lines. The Body, extended Quantity, Verſus profunditatem, coupled with indivisible surfaces. From which it is clear, that the Line only has one extension, which is the Length: the Surface has two extensions; that is, Width, and Length: saying, the first De formali, and the second De materiali, as the Philosophers note. The Body consists of three extensions, of which two, which are, Length, and Width, expresses them materially; and the other, which is the Depth, explains it formally. Which Aristotle confirms, saying: That the continuous magnitude Ad vnum, is Line, or Length; if at two, it is Surface, or Width; if at three, it is Body, or Depth, that all are Propriè, & per se, Species of the continuous Quantity, as can be seen broadly in the Metaphysicians.

Finally, it is established that Place is the measure of the located, per external: and Time is the number of Movement, according to what is before and after, adding in passing the definition of Movement for the understanding of Time, which is, Act of the entity in potency, insofar as it is in potency as defined by the Prince of Philosophers. We leave, then, to them, different disputes, and so we move on to the Genus, and Species of discrete Quantity, as our effort allows, placing its Schema in the middle of the two Species immediate to the Genus Quanto, so that the Reader’s contemplation can easily register it.

DISCRETE QUANTITY.

The second Genus, dependent on the Generalissimo, Quantity, or how much, is the part that includes discrete Quantity (which is the same as disjoint) because just as the continuous (according to the Philosopher) is defined by that which is complex of its common terms; so the discrete is that whose parts do not couple in common terms, and of these all those that are reduced to Number, and Speech, are species, as admitted by the Logicians according to the doctrine of Aristotle.

It is proven. The parts of the Number are distinguished in such a way that between one and another unity, which are extremes, there is no common thing that is similarly part of the first and second unity, as explained by Torrejon, and in the same likeness it is noted in the parts of Speech, in syllables, and words, which are constituted in such a way that between the first and second syllable, and between the first and second word, there is nothing that mediates, that is similarly something of the first and something of the second extreme, as is demonstrable; because if it were something similarly something of the first extreme, it would not differ from it, and the same in the second. Therefore, the Number, the syllable, and the word differ from their extremes: ergo, &c.

As for the principle of Number, the difficult part is, and has been, the distinction of units, which is natural, which is entitative, which is predicable, which is mathematical, in which Logicians and Metaphysicians elaborate, taking as their object philosophical reason, in which we get little entangled here, because the Science of the Sword only makes that unity, which of discrete Quantity is species in this Predicament.

In the light of this, it is noted that the philosophical unity, either is the one that in its entity competes with the spiritual, or with the material, or the transcendental: and the one that we consider in this Science, is that unity suitable to the corporeal, which is proper Quantity in the Predicament, because it consists in the integration of its material parts, and this is properly the one that in this Science we admit as Predicamental unity. Thus Euclid defined it (as a pure Mathematician) saying: Unity is that which is understood as one, where the number is the composition of units.

From this it follows that, since the Number is composed of units, it is all of parts, which are constituent ones: then the spiritual and transcendental unity in this Science are not proper to this Predicament, but those corporeal mathematical ones that form the Number, which is called composition of units.

From this principle it follows that any Number is a species of discrete Quantity, because this is nothing other than a precise concept, which includes measurability, resulting from the division of parts, as we consider in this Science, because any Number in its precise concept includes the division of its parts by measurability, both by unity and by another Number, from which true quantity proceeds, as we consider in the gradual numbering, both of the Sword, and of the value of the Angles, in which we find with measurable equality, and inequality between numbers, and extensions. Consequently, it is inferred that equality and inequality essentially presuppose measurability in the number, or the extension in this Science: any number, and any extension is measurable; e.g., the arm, and Sword in extension of 6. by numeration of 2. and 4. units, arm, and Sword is a species of Quantity in this Predicament, because we find a composition of parts in discrete Quantity, not as in transitory Time, but by the positioning of the parts, which have an order of themselves among themselves, in order to Place, and location, that their discrete terms are recognized, one anterior, and one posterior, with respect to their number, not in the permanence of continuous Quantity, which has different measurability than the species of discrete Quantity.

In this (as Celio Rodiginio noted) there are numbers, which being proper to the discrete Quantity, respect the continuous Quantity by their terms, and composition of units: thus linear are called those numbers of continuous progression 1.2.3.4.5.6. &c. or as 2.4.6.8.10. &c. or as 3.6.9.12. &c. others are called flat, or areal, that proceed from two numbers, which mutually multiply: one by the other; and the one they produce is named flat, or area, whose sides are those numbers, which cause from their multiplication the flat; e.g., 4. in 6. produce the flat 24. whose sides are 4. and the flat, or area 24. that refer to the right parallelogram: and for the same reason, when equal numbers mutually multiply one by another, they produce a perfect square, whose root is one of the causing numbers, as 5. in 5. square power 25. root 5. as it is demonstrated in the square, whose sides are 5. root of power 25. and not only in such powers of flats, but in many others different flats are produced, by the different positioning of the Numbers, which multiply one by another, as the 24. that is caused by 4. and 6. can be caused by 2. and 12. and by 3. and 8. and so for many others.

Solid numbers, and cubes are called those, which are produced from the multiplication of 3. numbers, as from 2. 3. 4. the solid is generated, which all composes 24. because 2. in 3. makes 6. and 6. in 4. form 24. in such solid: and consequently, in the cube, when a number, carried in three multiplications, generates a perfect solid, which on all its faces consists of equality, like 3. in 3. generates the square plane 9. and the 9. in the same 3. the solid 27.

Such numbers corresponding to the 3 species of continuous Quantity with measurability of discrete Quantity, lead us to the understanding of powers, and roots, and the other affections of Numbers, which the discipline of Arithmetic teaches, of which this Science makes use, as of a subordinate: thus we presuppose the understanding of the Elements of Euclid, considering for our purpose the Number in three ways: the first, as a numeral number: the second, as a numbered number: the third, as a counting number. Numeral Number is that which the understanding perceives by pure concept, which admits number; e.g., of the Stars the understanding perceives, that they are in themselves a numeral number, capable of number: the grains of wheat of any measure, also the understanding perceives, that it is a numeral number, as Archimedes perceived of the sand, &c. but not because the understanding perceives the numeral Number, it grants, and distinguishes it in its own distinct numeration, because that is of higher knowledge.

Numbered Number is that in which the number is distributed, and comprehended, according to its composition of units, like 4. which is composed of 2. and 2. or 1. and 3. or like 6. which is composed of its aliquot parts 1.2.3. that form 6. or like any aggregation of units, or individuals, or spirits, &c. of which our understanding perceives distinctly the numbered number, like 100. 1000. &c. 10. men, 10. lions, 10. coins, &c. 20. Angels, 20. demons, 20. Stars, 7. Planets, &c. from which results, not only the knowledge of the numeral number, but also the understanding perceives it in its distinct Predicamental units, a counter in certain numbers, composed of its units, with a term terminated in distinct, and certain numeration. In this Science we consider such the value of the angles, and everything else, that in it the understanding perceives by distinct, and certain numeration.

Counting Number is the instrument of the mind, that in order to perceive things (to our understanding) we consider them by numeration, like the line, the Sword, the division of the angles, according to their composition, degrees, and values, in which we number things, so that the understanding makes pure concept by numeration, according to discrete Quantity, besides this in the Numbers, some are considered certain, others uncertain.

The certain ones are those that the understanding perceives with clear distinction, and with it their numeric terms are reached; e.g. all those Numbers, which the Arithmeticians call rational, because reason, and understanding investigates them, and perceives them, are called certain Numbers, like root of 36. which the understanding comprehends that they are 6. or like root of 27. which is 3. because 27. is a cubic number, and not flat, and so its root is 3. and its power 27. &c. and so all the numbers, which generate rational roots, and rational powers, propositions, equalities, &c.

Uncertain Numbers are called those, that even though in their being, and essence by fractions, or other unfound means, are without being perceived by the understanding for certainty of numbered numbers, although in themselves they have numbered terms they are not perceived: they are called deaf, or irrational, or uncertain, respect, not of themselves, but of our fragile understanding: thus root of 28. (it is said that) is root of 28. but not precise rational, &c.

The types of specific numbers include all those commonly called principal, perceived by their composition of units through their collection, subtraction, multiplication, division, powers, roots, propositions, equalities, etc. Euclid and his expositors, Boethius, Campano, Peletarius, etc., extensively deal with this. For uncertain values, Algebra and Logarithms provide a path, and for the value of angles, tables and the subject of sines (or ‘senos’, as pronounced in our vernacular) are used. Since this Science greatly involves the understanding of angles, it’s necessary for us to delve into their explanation, which is inherent to this category.

An angle is that space, caused and encompassed by the intersection of two lines, which converge at a point from two terminal points of their deviation. This point is the limit, whether the lines are straight or curved, or a combination of both in the various oppositions perceived by the mind and executed in practice. The angles derive their names from the types of lines and the manner in which the existing and insistent lines are found.

A rectilinear angle is one whose uncomplicated terms are straight lines. A curvilinear angle is composed of curved lines, converging at a point on the concave or convex part: and thus they can converge, forming the angle on the curvilinear concave part; and on the convex to convex part, just as on the concave to the convex part. Mixed angles are those caused by different types of lines, such as curved and straight; and for the same consideration, there are mixed curvilinear angles when one leg or line consists of a perfect circular portion and the other is not so curved. As for their species, angles are distinguished by the greater or lesser deviation of the lines, according to how they insist or consist on each other, according to the positions of their disjointed ends and the point of their convergence. A right angle is called that whose lines that cause it, converge perpendicularly at a point, without deviation or inclination, one with respect to the other, like the T.V.X. angle that the figure 1, Stamp 3 manifests.

All right angles are those that are caused by straight lines that, when extended, cut each other in a Square; that is, one falls perpendicularly onto the other, as Euclid demonstrates, and it is seen in the standing T.Y., existing Z.X., that they will cut each other at the point of the convergence V, and all its angles are right, and therefore equal, because there is no inclination of one line with respect to another.

From this, it follows that in any deviation or inclination of one line over another, a difference in angles is created. Such that the larger angle, known as the external, complements the smaller one, known as the internal; and vice versa, because between the two they total two right angles. The larger is called obtuse, and the smaller acute or sharp. This can be seen in the second figure, third stamp, as the straight line A.B., resting on the consistent straight line C.D., forms unequal angles at point B. The A.B.C. angle is obtuse or external, and the A.B.D. angle is acute or internal, inclining towards point D. The larger and smaller angles complement each other to two right angles, with the endpoints A.C.D. being uncompounded terms (that is, separate). The lines drawn to the point of convergence B, as in the ends of the deviation, do not admit coupling, do not include a figure, and so the angles they cause are not of continuous quantity, but discrete, as recognized by philosophers and Clavius, stating that there are three terms: Points that terminate the line, coupling in it, Lines of the Surface, Surfaces of the Body, and this last is not the end of another continuous quantity because there are no more than three dimensions, and every term surpasses its term by one dimension. It becomes evident that the angle is not of continuous quantity, but of the discrete, because it does not admit coupling of its terms, nor does it exceed in one dimension to its predecessor. From this follows the consideration that some angles are complementary to others, because if the existing line is perpendicular to another, it forms right angles, which are all equal, as demonstrated by Euclid and his expositors; and if the existing line is declining or inclining, the obtuse and acute angles that it causes (without one complementing the other) will equate to two right angles.

From these principles, and the others that have been touched upon, it also follows that two straight lines do not enclose space; although by their convergence at one point, drawn from different extremes, they form an angle, whose value is known, and qualified by the gradual number, and not by the figure, because (as has been said) two straight lines are not capable of enclosing space between their ends. Right angles are problematically formed by setting a straight line perpendicular to another.

From this it follows that two lines, extended and intersecting at one point, drawn straight to their ends, constitute equal angles at the vertex, as can be seen by figure 3, Plate 3. For example, the two straight lines A.B-C.D intersect at point E. It is said that the angles at the vertex are equal to each other because the angle A.E.D, and B.E.C (which are at the vertex) are equal to each other, because the straight line D.E. extended to C. insists on the straight line A.B. at E. And the angles at the vertex A.E.D and C.E.B are equal, and A.E.D and D.E.B are worth two rights, as well as A.F.C and C.E.B and all equal to four rights, being each other’s complements, and the angles A.E.D and C.E.B of the vertex are equal acute angles, and consequently F.F are obtuse, as Euclid demonstrates, and Proclus and others prove, drawing various corollaries.

From these principles, not only the formation of angles is investigated, but also their differences, their equalities, and inequalities, knowledge of which is essential in the Science of the Sword, and for its operations, in which it is necessary to know the value in which they are graduated; otherwise, one will proceed with a confused concept, making the understanding by numeral number, and not by numbered number, nor numerating number.

For this reason, the great Mathematicians, and Philosophers found that in the gradual and numeral value of the angles the Periphery is a competent measure, which shows the distance of the deviation of the lines from which they are caused, converging on each other. For this they chose a certain gradual numeration in which the circle is distributed, whether it is larger or smaller, with the understanding that the numeration should be one, and the parts proportional to their whole, as in the Sphere larger circles are placed, which are those that divide it into two equal parts: and in smaller circles, which are the more so, the closer they are to their Poles, being Parallel to the circle; for example, the circle, which is named Equinoctial, is a larger circle because it divides the Sphere into equal parts: those which are called Tropics, are smaller, and the closer they are to the Parallel Poles, the smaller they are; so also in a plane the circle, which includes the others that are Parallel to it, is the one that approaches the center, they are smaller; and therefore, dividing, as all are divided into a gradual numeration of parts, those degrees, or parts of the larger circles, will be larger, and in the smaller circles smaller, as is common; and this division of numbered number, which we number, for more convenient was done in 360. degrees, or parts, considering that the sixties are the most capable for operations, because they are composed of the two numbers, called perfect, both Mathematicians and Philosophers, the one of the Mathematicians is 6. because its aliquot parts 1.2.3 joined together form 6. without excess or lack. The one of the Philosophers is 10, considering it by the fingers, which are 10, and so these are named numbers digits. Having found these principles, they took the number 6. in itself, and it gave its power 36. these taken by 10. produce the numbered number, which we number, for the graduation, and division in parts of every circle, which are 360. From here it went on to make fractions of integral numbers, and each degree was divided into 60. minutes, each minute into 60. seconds, and so on to tenths, to which rarely is arrived, and these are called Astronomical fractions, unlike the Mathematical ones, which divide the Predicamental unit into smaller ones, as is suitable to the ultimate fraction (as the Arithmetic part teaches) which they call squares.

Through these and other principles, we proceeded to investigate the proportion of parts of a curved, circular line to the straight line, considering how the circle and its diameter relate to each other. This has challenged many ingenious minds, and until now (as everyone admits), a demonstrable proportion has not been found, leaving us with the laborious task of the Quadrature of the circle, on which many have written, to which we refer, acknowledging that the most widely accepted and closest to certainty is what Archimedes called the Spiral, which is the circle with its diameter, as 7 is to 22, which is a triple sexquiseptima proportion, sufficient for what is intended in the Science of the Sword, as well as for the investigation of the value of angles, and how they relate to the circular portions that number them, and these with the right sines, and the complement tangents, and secants, arcs, chords, and arrows: this Science uses tables of sines, or sines, for whose light figure 4 is proposed, of stamp 3, assuming that the total sine (which is the semidiameter) some divide it into 100000, and others into 10000000, and some into more, and into less, of which the most practicable is chosen, following Ptolemy from the Ancients, and Pitiscus and others from the Moderns, who all admit the distribution of every circle into 360 degrees, or parts, and each one into minutes and seconds, giving a numbered value of 90 degrees for the right angle, which is a quadrant, and to the proportion the oblique, obtuse, and acute angles.

The regular proportion between the curved and straight line (as mentioned before) is up until now a numeral number, but not a numbered number; thus, the common opinion received and put into use is followed, through which the tables of right sines, and complementary tangents, and secants, have been created, in which the following definitions are accepted: 1. Curved lines for straight lines are reduced by definition of the Quantity that straight lines have when applied to the circle, with respect to the radius: 2. Straight lines, applied to the circle, are subtense, sines, tangents, and secants: 3. Subtense is the straight line inscribed in the circle, which divides it into two parts, and when they are equal, it is called the Subtense diameter: 4. Line subtense is maximum, and not maximum: 5. Maximum Subtense is the diametric, like the straight line G.C. 6. Non-maximum Subtense is the straight line, which divides the circle into two unequal parts, one subtending for the larger portion; and the other, for the lesser, like I.B. that the lesser part of the Periphery subtends the arc, less than the semicircle, like I.F.B. and the other greater, than the semicircle G.C. because it is the arc I.H.B. 7. Sine, or sine, is either right or versed. 8. Right sine is that which is included in a smaller arc than the quadrant, like B.C., known by the straight line B.E which is the right sine of the arc B.C., and perpendicular falls on the semi-diameter A.C. at point E. 9. Versed sine is the one of the arc greater than the quadrant on the subtense diameter, or maximum, like B.G., and is considered by the same straight line B.E. produced in D., and similarly for subtending to the arcs B.C. and B.G. this is by half the straight line B.E.D. that similarly subtends to the arc B.C.D. or to the arc B.G.D.

10. Consequently, the right sine to the quadrant arc of the larger and smaller, up to the semicircle, is the same, as the right sine of the arc B.C. and the arc B.G. is the same line B.E. because being half of the straight line B.E.D., it is as much subtended to the arc B.C.D. as to the arc B.G.D. 11. Therefore, the right sine of the complement, in any way it is understood as the sine, complement to the arc of the smaller quadrant, like the sine of the complement of the arc. B.C. by the arc B.F. is the line B.K. and conversely reciprocal sine of the complement of the arc B.F. is the line B.E. 12. Tangent is the line, which ends in the secant, and at the end of the diameter perpendicularly, as of the arc B.C. is tangent the L.C. 13. Secant is the line, which produced from the center to the convergence of the tangent, cuts the arc of the quadrant, like the line A.L. that cuts the arc at B. and converges with the tangent at L. and so the similar ones.

14. Definition of the Quantity, that the lines have, applied for the circle, is the construction of the tables of sines, tangents, and secants, which are formed by the computation of right sines, and not of the versed ones. The reason is, because to the lesser versed sine, as to the right sine of complement, is equal the radius; e.g. lesser versed sine E.C. as to the right sine of complement A.E. is equal to the radius, or whole sine A.C. then if subtract the right sine of complement A.E. from the radius A.C. remains the versed sine, or sagitta E.C. and also in the greater versed sine is equal the radius, as is considered together the excess to the right sine, as the greater versed sine G.E. is equal the radius G.A. together with the excess: then if for the radius G.A. the excess A.E. is added, the versed sine for the arc G.F.B. will be obtained. And so, in the tables, work is not done on the versed sines, because the right sines are half of the sub-tenses. From where it follows, that if the maximum sine is found by the maximum subtense, also the non-maximum sine can be found by the non-maximum subtense, because the reason that there is from the whole for the whole, can be from the half for the half, just as the reason that there is from 10. for 6. is the same as there is from 5. for 3.

By such principles, one easily comes to how the foundation of the value, and formation of the angles, as numbered by the portions of the arcs, by whom they are measured: for whose understanding, the fifth figure of the third Stamp is proposed.

The entire larger or smaller circle (as has been said) is divided, and numbered into 360 parts, or degrees, which are proportioned, according to their diameters, in which we accept the received ratio of 7 to 22. From this it follows that the degrees, or parts of one circle, in relation to another, are similar, but not equal, not being of the same diameters, and radii, because the parts, or degrees, are larger as the circles are larger; and smaller, as the circles are; e.g. the circle E.D.F.G. its parts are larger than those of the circle L.P.J. even though the arc 45. degrees, number B.D. is similar to the arc O.P. 45. degrees, also as the quadrant D.E. is 90. degrees, as also as the quadrant D.E. is 90. degrees, as also the quadrant P.L. and as D.E.G. 180 degrees, so P.L.K 180. degrees, proportionally similar, in relation to each other, larger in the larger circle, smaller in the smaller: the angles, for the same reason are measured, and their value is qualified by discrete Quantity, according to the arc, which is cut by the lines; from whose convergence to a point the angles are created; e.g. the lines E.A.D. converging at the point A. because their interval is the arc E.D. 90. degrees; the angle they form is a right angle, and therefore, extending the lines E.A. in F. and D.A. in G. all the four angles they form are right angles, because the lines do not deviate or incline with respect to others, because all right angles are equal, and in the same regulation they are found, with respect to the smaller interior circle, as demonstrated by Pitiscus, by the doctrine of Euclid: the same reason of value, and measure, is recognized by the arcs in the formation of all the other Angles (which as has been noted) either are Right, or are Oblique: if Right, all are equal, because they are regulated by the quadrant, which is worth 90. degrees: if Oblique, some are larger than Right, others smaller, explained by the terms, Obtuse the larger than Right, Acute, the smaller than Right; e.g. the Angle G.A.B. is Oblique Obtuse, its value 135. degrees, the excess to 90. 45. and so the same the Angle K.A.O. and therefore Acute the Angle B.A.D. 45. degrees, like the O.A.P.

Complements of the Angles are considered by the arcs, because the Angles caused by the affection, and convergence of any lines one in another, Simul sumpta, are equal to two right ones, like the Angles E.A.D.-E.A.B.-E.A.G. where the lines converge at point A. on the straight line G.D are equal to two right angles G.A.E and E.A.D. by their own structure. Consequently, in the triangle A.B.C. right in C. the angle A.B.C. of the acute ones, the other one is equal to the angle B.A.E. because the angle E.A.B. is the complement of the angle B.A.C. by its structure: then the angle A.B.C is the complement of the angle B.A.C and so it can be reasoned in the other complements. With such information, one comes to understand the reason, because the angles caused on the circumference are half of those caused at the center, and it is manifested by the figure 6. of the Stamp 3.

The angle A.B.C proposed for its demonstration in the circle, whose center E. is the diameter, the straight line B.E.D excited from the angular point B. caused at the vertex of the circumference by the center E. dividing the circle A.B.C.D diametrically draw the radii E.A and E.C. it will be said, that the partial angles A.B.D-D.B.C are subduplicates for the partial angles A.E.D and D.E.C taken together: then it follows, that the angle A.E.D. for the angle A.B.D. is double, because the parts of the angle A.E.C for all A.B.C. is double: and consequently, the angle A.B.C is the measure, and graduation of the A.E.C caused at the center E. and although it is also the value of the angle A.B.C caused on the circumference at the point B. the value is diverse, because the angles A. and C. are equal to the partial A.B.D and D.B.C and the entire angle A.B.C. is half of the A.E.C as has been demonstrated, and proved by Pitiscus.

That the angle is divided into 2, into 4, into 8, into 16, into 32, and is common, by the common rule of Euclid, demonstrated in the 9th of the first, and the 3 following, which we summarize, as a common principle, for the understanding of the other divisions of the angle.

Given a straight angle, cut it into two equal parts, as seen in figure 7, of Stamp 3. This bifurcated section is achieved, given the angle: and let it be B.A.C. on the straight line A.B. at the chosen distance, take the point D. and on the straight line A.C. the corresponding E. couple the points D.E. with the straight line, of which they are extremes on D.E. constitute an equilateral triangle, which is D.F.E draw the straight line A.F. which divides the given angle B.A.F into the partial B.A.F and F.A.C follows that they are equal, because the sides D.A-A.F. of the triangle D.A.F are equal to the sides E.A.-A.F. of the triangle E.A.F. corresponding to each other, because D.A. is as E.A. which by its construction are equal, and therefore the triangle D.F.E. is equilateral by its construction: then the angle D.A.F. and the angle E.A.F. are equal partials, from which it follows, that the given angle is bifurcated into two equals.

From this demonstration common Practitioners derive a difficulty, which Euclid did not teach, nor is found; that is to know, the division of the angle into odd angles, because the bifurcated division only generates pairs, as Clavius noted; and so the angle is divided into 2, into 4, into 8, into 16, &c. but not into 3, into 5, into 7, &c.

Clavius himself responded to this deceptive doubt and formulated a demonstration by dividing the curve, or the Periphery, understanding the 27th Proposition of the 3rd of Euclid: and here by the same, and its consequences, recognizing by the doctrines of sines, their arcs, and subtenses, that the value of the angles is found, with which the veils are run to the difficulty, which is easily overcome, speculating the propositions of Euclid, where he taught, that in the circles in equal segments, the angles are equal to each other (as has been demonstrated) in which the Expositors of the Geometric Elements expand: to further demonstration, we admit here as thesis two theorems, repeated by Euclid, on whose principles we will base the hypothesis of our argument, and demonstration, as essential for the Science of the Sword, and proper to this Category in the Genre of discrete Quantity.

Thus, we say that in equal circles, equal angles insist, and in equal Peripheries, whether they are constituted insistent to the center, or to the circumference, and the same occurs in unequal circles, if the Elements are similar.

In equal circles, as in figures 8 and 9, Stamp 3, A.B.C-D.E.F. are the centers G.H. If equal angles A.G.C-D.H.E are constituted for the center, it will be said that the Peripheries A.B.C-D.E.F. two points at the vertex, which will be B.E. where the straight lines A.B C.B-D.E-F.E are derived. Draw the straight lines A.C-D.F. and because the angles B. and E. are medians for A.B-C.B-D.E-F.E will be the bases the straight lines A.C-D.F. because the angles B. and E. are subduplicates of the equal angles G. and H. and so they are equal to each other, because the segments A.B.C-D.E.F. are equal, and similar; and because the sides A.G-C.G. of the triangle A.G.C are equal to the sides D.H-F.H. of the triangle D.H.F because of the equality of the circles, and the equality of the angles, which contain G.H. by equal hypothesis, will be equal the bases A.C-D.F. and as the similar segments A.B.C-D.E.F are on equal lines A.C-D.F. they will be equal to each other, because if equal segments are removed from equal circles, the segments A.C-D.F. remaining are equal to each other, which is what is proposed.

Therefore, let the two equal angles B. and E. be constituted for the Peripheries, it will be said that the Peripheries A.C-D.F. on which they ascended, are equal. Also, as before, let the segments A.B.C, and D.E.F. be similar: it follows that they will be on the equal lines A.C-D.E. and as the angles G.H. are equal, because they are doubles of the equal angles B.E. they will be as before the straight lines A.C-D.F. equal: then the equal and unequal circles, similar in the segments, make equal angles, which is what is proposed.

The theorem implies that the angles in the center and on the circumference are gradually numbered by the propositions of the Periphery, which include between them the lines that cause the angle, with such notice that in equal or similar segments, the angle of the circumference is subduplicated from the one caused in the center, and the one in the center is double the one caused in the circumference, from which comes the knowledge of the value of the angles, by the portions of Periphery, that is included in the interval of the lines, causes of the angle.

In equal circles, the angles that insist on equal Peripheries, are equal to each other, or insist constituted for the centers, or for the circumferences, as seen in figures 10 and 11 of Stamp 3.

To understand this proposition, as demonstrated in the antecedent in the equal circles A.B.C-D.E.F. whose centers G.H. insist angles in the center A.G.C-D.H.F of equal Peripheries A.C-D.F then the angles A.G.C. and D.H.F. will be equal and not being equal, angle G. will be smaller, because it is caused by A.G.I. that should be equal to angle H. by the Periphery D.F. for the Peripheries A.I.D.F to be equal to each other (which is absurd) because they would be part, and all equal to each other: then for certain are equal A.G.C-D.H.F. and if they also insist on the same equal Peripheries A.C.D.F. the angles B. and E. it turns out to say that the angles in the Peripheries are equal, because otherwise, as A.B.C is larger, angle E. will be made equal to angle A.B.I. and they would give the Peripheries A.I-D.F. equal, because as first they were given in the Peripheries A.I-A.C. equal parts, and all: then the angles A.B.C and D.E.F. are equal, because in equal circles, equal angles insist on equal Peripheries, which is the intention of this demonstration.

Every angle, not only is divisible into equal even parts, but also into odd ones: therefore, it is divided into 3, etc.

Let the angle of figure 12, Stamp 3, B.A.C., be 45 degrees, either assumed or measured: if measured, it will be by the portion of arcs B.C-D.E, which are similar, because the common center is A. Thus, from any of the arcs B.C-D.E., 15 degrees will be B.H-I.C., and the intermediate arc H.I. will also be 15 degrees and consequently, similar proportions in arc D.E., 45 degrees will be 15 D.F. and 30 D.G. in equal divisions: then, angles of 15 degrees each D.A.F-F.A.G-G.A.E. result, as are also B.A.H-H.A.I-I.A.C of arc B.C measured, and thus the angles M.N.O. are also equal, because the angle B.A.C is the same as the angle D.A.E., since arcs D.E. and B.C. are similar by Bartolomè Pitiſco’s first (as we have demonstrated), and by proposition 9 of Euclid, the line A.F.H. extended to L. is perpendicular to the very short extension B.I., dividing the angle B.A.I., which is the same as D.A.G., into two equal angles; and similarly, line A.F.H. extended to L. is perpendicular to the very short extension B.I., dividing the angle B.A.I., which is the same as D.A.G., into two equal angles; and in the same way, A.I is perpendicular to the very short extension H.C., and F.E. divides the angle H.A.C., which is the same as F.A.E., bifurcating. Then, the three angles B.A.H-H.A.I-I.A.C are equal to D.A.F-F.A.G-G.A.E. because they insist on equal Peripheries; thus, the given angle B.A.C. is divided into three equal parts, which is what was proposed, and demonstrated by Euclid’s 26.27.p.1, Pitiſco’s first 53, and Clavio’s second Scholio in 9.p.1., and consequently, the angle is divided into odd parts 5.7.9.11.&c by the same principles.

As Father Clavio rightly warns, no one should be amazed that the division of the angle into 3.5. &c can be exhibited in practice, because the demonstrations depend on previous propositions; as he said in definition 10 of the 1st, what is relevant to the purpose is deduced from its own places, where the division is sought: straight lines, whatever they may be, are divided into equal parts, as Euclid taught, giving precepts for dividing the angle and the line into equal parts, demonstrating how to divide the line and angle bifurcating, because precise demonstrations are not always required in practice, but rather the effect of what is intended is correctly proven; and whoever is not content with bare practice, giving the demonstration that is required, can resort to investigating the demonstration by the necessary principles, speculating, because not all propositions that are relevant to the purpose are always cited, and in this Clavio himself is content with Euclid’s 27. Prop 1., which (well understood with the adjacent ones) removes the veils to what has been ignored: a cause that has reasonably moved and required to demonstrate that angles are not of continuous quantity, but of discrete one; and consequently, divisible into pairs and odd numbers, like 2. 4. 8. &c and like 3. 5. &c., because the understanding perceives it this way and can perceive it in the Science of the Sword, which does not submit to the absurdity that angular divisions are by bifurcation, but by gradual numbering, as it is convenient for this Science for its understanding and exercise, and for more teaching, and b

The angle, whose interval includes an arc in the quadrant, or semicircle, is divisible into even or odd angles, according to the gradual number that admits division: and the right and complementary sines will be proportional to each other, according to the degrees and minutes, which the secants consist of on the Periphery, because all sines are constituted from perpendicular lines that fall on the semi-diameter, being Parallel among themselves, like the subtendents, or subtenses, proportioning the tangent sines, and secants, according to the graduation of the arcs; and consequently, the cords, or subtenses Parallel to the diameter, the closer they are to it, the larger they are; and the farther apart they are, the smaller they are; and drawing, and constituting in a number of equal degrees, as distances cause, the closer they are to the diameter, the more separated they are; and the farther they are from it, the closer they are to each other: and extended the diameter, and drawn Parallel Diagonals from end to end of the cords, they will end in the extended diameter; in such a way, that the terminations will be equal to the cords, from whose ends they are produced, passing through the ends of their predecessors, as all is demonstrated by figure 13 of Stamp 3.

In the circle A.B.C.D. of this figure, whose center E. the quadrant D.A. 90. degrees from 9 to 9. its half the arc N.D. 45. degrees: the angle N.E.D. wants to be divided into 5, and it is achieved with the secants E.O-E.P-E.Q-E.R-E.S because each interval D.S-S.R-R.Q-Q.P-P.O. are terms in the tangent D.O. of the secants, which runs the arc D.N. the S. in 9. degrees, the R. in 18. Q. in 27. P. in 36. O. in 45. which are 5. equal divisions of the angle N.E.D each one includes 9. degrees of the arc V.N. 45. degrees: then it follows from the 26th and 27th of the 3rd of Euclid, that the arcs are equal, in which they are cut by the secants; and consequently, the S. is perpendicular to the very short extension between D. and the last term of degree 18. at the point, which is cut by the straight line E.S. and so it results by the 9th of the 1st and in the same way E.R. secant is perpendicular, and bifarious, it cuts the arc by the degree 9. to the 27. in which it is perpendicular by the 9th and 10th Prop. of the 1st of Euclid; and so, it can be demonstrated in the divisions, being the ones demonstrable proofs of the others: then the intention of dividing any given angle, in equal parts, even, or odd, is achieved, being demonstrated by those cited in the previous Theorems; and consequently, the perpendiculars on the semi-diameter E.D. from the points of arc, at which the grades 9. 18. 27. 36. 45. are terminated are right sines, which are found in the tables, according to the computation of the radii, or total sine with the tangents, and secants, which correspond to them (which is not from here its theory, nor its practice) with which we refer to the common tables, the more adjusted, the more number is made the computation, or following that of Pitis (which is one of the most modern) the right sine of 9. degrees is 17364. 82. and the tangent 17632. 70. and the secant 1010542. 661. and to the proportion the complements, equaling the right sine, and of complement in degree 45. to which corresponds 70710. 68. and the tangent, as the radius, or total sine, or semi-diameter, computed in 100000000. whose secant 141421. 36. with which we have demonstrated, that the angles are divisible, not only in even parts, but in equal odds, like 4. 8. 16. &c. pairs, and 3. 5. 7. 9. &c. odds.

Also, the second part of the proposition results in the proposed theorem, taken from our intention by Juan Bautista Benedicto, who took it from Cardano, and both from Clavio, explaining the 27. p. 3. of Euclid.

Therefore, in the proposed circle A.B.C.D with the diameters A.C-B.D intersecting at right angles at the center E. draw parallels H.F, which is the subtense of the arc H.B.F, 30 degrees away from the diameter A.C., and likewise the parallel I.G., 30 degrees of arc away from the H.F. It follows that the diameter A.C. is greater than H.F. and H.F. is greater than I.G. by Prop. 8.3, explained by Tartalla, and Campano. It also follows that the parallels to the diameter, the farther away they are from it, the closer they become to each other, as Ptolemy broadly proves in the Almagest, demonstrating the diversity of artificial days, and to our purpose for this science of the sword, extend the diameter A.C. to K, which is enough distance for the parallels to terminate, which are drawn from extreme points to the extremes of the parallels to the diameter, which are subtenses of 30 by 30 degrees, like H.C.I.F-B.G. When produced to terminate on the diameter, they will be at the points C.L.K., whose distances are equal to the lines, through whose extremes they pass to terminate on the diameter A.C. produced by the first petition of the first of Euclid. It follows that H.C., which terminates at C., includes the same diameter A.C., because the cause of its termination is the extreme C., and therefore, being parallel to H.C., the straight line I.F. does not terminate on the diameter, produced at the point F. passes to terminate at the point L., and because the extreme of its causation is F., a point of H.F. from the term C. to the term L. is equal C.L. to H.F., therefore, Parallelogram H.F.L.C. has equal opposite sides H.F. to C.L. and H.C. to F.L. and by the same structure the extreme G. of the I.G. drawn parallel B.G. to I.F. passes to terminate at the point K. of the diameter A.C. produced at L. and from L. to K., point of the termination of B.G.K., and therefore, as C.L. is equal to H.F., L.K. is equal to I.G., whose extreme G. was the point of its causation, passing to terminate at point K. Likewise, Parallelogram I.G.K.L. has equal opposite sides, recognizing to which terminating points the tip of the sword can be directed, and at what distances it will reach more or less, depending on the locations and movements, and what angles are formed in the different positions, and the other consequences that this theorem produces in this science.

It is concluded, therefore, how numbers are understood, what are numerals, what are numbered, and what are numerating, what we number, what are certain, what are uncertain, and for what reasons; how the angle is not a fourth kind of continuous quantity, but is included in the discrete, how the value of angles is recognized and graded, and their composition of right and oblique angles, how they are divisible, and how in equal parts, not only even (as practical geometers concede) but also odd, as the speculative ones have found, reaching the mysteriousness of different propositions of Euclid, and especially the repeated ones in this predicament, and what is the unit predicament in this science of the sword, etc. with which it only remains in this predicament to hint at what is the other kind of discrete quantity, which the philosopher called Speech, which, as it is not proper to this science, but to Rhetoric, Poetry, and Music, we will only say that Speech (according to philosophers) is considered in the composition of syllables, periods, sentences, verse, and song, which is all of discrete quantity, because the means are not similar parts of the extremes, but differences between them, with which harmony is composed, whether by voices or by numbers, finding the reason and cause of consonance, and dissonance, which, as it is not of our concern, is omitted, referring the curious to the professors of Oratory, Poetry, and Music.

NINTH DISCOUSE.

THIRD PREDICAMENT, Relation or Analogy, which Logicians explain that which pertains to something else

SOME get entangled in discussing whether the Philosopher observed the order of nature in placing this Category immediate to that of Quantity, because Quality seems to be closer to it: others find correctness, in that Relation follows Quantity, because the condition is taken from the dependency of knowledge: and as the Metaphysicians say, where there is no Quantity, there is no condition of cognition, from which it follows, that immediate to the Predicament of continuous and discrete Quantity, the one of Relation must be placed. Thus Aristotle included: It is necessary to know a relative by the defined knowledge of another. From where Oña summarized A defined relative cannot be known, if another is not known. This precept is specific to the Science of the Sword, because every Relative, or Analogy of Relation, has as its essential foundation knowing a defined one, to acquire knowledge of another.

The common doubt, which is offered among Logicians, and Metaphysicians, is, to investigate what Defined knowing in relatives is? To which Averroes, Albert the Great, and Saint Thomas respond, that Defined knowing is the one who knows the quidditative definition. The Moderns (with Boethius) carry with more clarity, that the specific determined knowing, must be in such a way, that it is not so much understood to be double, knowing that to subdouble, but that one must know, that double is 8. and subdouble 4. or that double is 12. and subdouble 6. or 20. to 10. because these terms are quidditatively defined. Cajetan also (by authority of Boethius) carries, that if a relative is known to exist, the other must be known to exist.

For such foundations, it is not enough in the Science of the Sword to know a defined relative of Wound, Feint, or Movement, if the other is not known, since from this it follows that this Science is of intelligence, and exercise, not only by objective concepts, but by real operations: because (as it was proved in its place) in this Science one does not attend so much to the being of reason, as to the real being, excluding as much as possible the pure being of reason, because it can be a chimera, thus it does not have a place here the subtlety of those who pretend, that Aristotle wanted In all the relations, that there were not true some real affections, really by the convenient things, according to the real being of themselves, but to be more intentional affections, that compete, according to the objective being. From where Torrejon concluded in his way, to be the relation according to the concept of the objectives: Because in the known things one looks at that, because they are known; and this has more respect to science by being of reason, than by real being.

And although in Metaphysics the understanding of Relations is debatable, through transcendental objective concepts; in the Science of the Sword, the concept is not considered for the mere sake of the concept itself, but for its reality, and thus as a real entity, and not as a rational entity. This true conclusion needs to form a question to test our intention by demonstrable means, in order not to open the door to doubts and difficulties that, once overcome, will lead us to proceed more securely in the speculative and practical aspects of this Science, which as it is, has been necessary to treat in its own terms.

It is a question of Schools, whether the Relation is a real entity or not? In opposition is Aureolus, quoted by Gregory, who says of the Ancients before Aristotle, attributing it to Zenon and Plato, who held that the Relation, or Id quod ad aliquid, is a comparison of two, and this can be by understanding: then by rational entity, and not by real entity; and the consequence is tested, because the Relation is not in itself, nor for another: then it is neither substance nor accident: Occa and others refer the Relation at times, because in things there is no order from one target to another: then it is only the notation of another end, when it signifies one, which is in voice, because every entity can understand another not understood, but not Relation: then it is only voice.

Durandus, Jabelus, and others argue that for the Predicamental Relation, a formality is not required, but to say one thing as another; and they give as reason that the resemblance is like two whitenesses, and this is only to conceive something as similar, noting the existence of another whiteness.

Torrejon, looking at the concept, says that the related Predicament, suits things according to their objective being, sometimes in their knowledge, in which we have respect for another, because we know them in this way. Hence in this Predicament there is nothing else to the Relation than accidents that are placed by themselves: because all things, which in their precise concept imbibe respect for others in the way, are either substances, quantities, or qualities; and he affirms that this resolution is of Boethius, Albert the Great, and Toledo: from where he concludes, that all Relations have being according to their voice, because there is no other thing than Relation, than the essence in itself absolute, known by respect for another entity, because no Relation of the thing is suitable according to the real being, and therefore intrinsically imbued in the objective concept of the conceived thing, which is called Related.

He adds with more force, that the difference lies between the transcendental relations, because there are some things that we cannot know except through others; and other things we know a priori: and the relation is so intrinsic that it is not worth stripping it bare, and it is said that the transcendental relation is that which is from the Science to the object. These are the ways of saying: against whose opinions, for our affirmative, the following conclusions are formed, proving that in the Science of intelligence, and exercise of the Sword the relations are analogous, or proportional, and their knowledge is by real entity, and not by intrinsic objective concept, or pure entity of reason.

The predicamental relation in this Science, and in others, is not just a denomination from the intrinsic, but from the extrinsic in that very thing to which it refers, as Santo Thomas and those who follow him argue, who all put the essence of the Predicaments, that say Relation, in being a subject in order to another: then it is in that for which it refers: in that to whom it refers is a real entity, and it is really in that to which it refers: then it is perceived as a real entity, and not just an objective concept, which is an entity of reason, subject to chimera. This conclusion is confirmed, because understanding is the most perfect act: then it is the most perfect real denomination: if it is the most perfect real denomination, then it is a real entity.

By the doctrines of Plato, and Aristotle, and all the other Philosophers, it is common, that the real Sciences, Geometry, and Arithmetic, etc. (which are subalterns to that of the Sword) consider proportions of figures, and numbers, which are always real Relations: then the relation of this Predicament in this Science is a real entity: and if this reason in Logic is not so urgent, because it also considers the entity of reason, it should be noted, that this evasion here has no place, because the Predicamental Relation in this Science of the Sword, is by partition of the real entity, although in the purely speculative it looks at the knowledge of the entity of reason; as it does not stop in it, but it passes to the formal reduction, which has for object the operation in defined acts. For this reason in this Science is formal, and not only objective the Predicament De his, quæ ad aliquid, and as such, it is divided: then it is a real entity.

In response to the first opinion of the contrary, it is said that the Relation in this Science is not a comparison, but order, convenience, and link of relatives, or extremes, or defined subjects: then it is a real entity, and not a pure objective concept.

To the second, that the Relation refers to voices, it is responded, that the knowledge of the relatives in this Science, is not by objective Metaphysical concepts, but that in their reality they admit quiditative physical definition, because there is no science without a precise object, nor form without matter: then it is a real entity.

To the opinion of Durando, and Jabelo it is responded, that the Predicamental Relation in this Science observes distinct defined ones, which are not only conceived as similar, but according to their analogy. And to the fourth opinion, that the Predicament related predicate agrees to things according to the objective being: it is responded, that in this Science the Relation by objective concepts has no place, but by real objects, because it does not consist of only intrinsic intelligence, but of intelligence, and exercise, where it cannot be absorbed in the only precise entity of reason, but it has to pass to the operating reality: then the relative absolute Predicamental essence in this Science cannot be known from an intrinsic entity in another entity of the same species, but in precise convenience, or numerical or geometric proportion: then it is a real entity.

And the difference that is found in transcendental relations is even less of an obstacle, because they are foreign to this Science, which (as has been said) consists of intelligence and exercise, like Mathematics, which considers them as subalterns: hence, the predicamental relation in which the real entity is divided, is not a being of reason, nor a transcendental relation; and so, Torrejon himself confessed: That the relation will be of the same kind as the thing known.

It is rightly concluded, that in this Science the predicamental relation is a real entity, De his, quæ ad aliquid, or perfect analogy from one to another defined.

Aristotle, and the rest of the Classic exponents, divide this predicament into three kinds of relations: the first, where their definitions are based on unity, or number: the second, by action, and passion: the third, by measure, and measurable. The one that is founded by unity, and number, is in the similarity of essence: the subject, or proportion in quantity, and quality; e.g., Peter and John, fighting subjects, where the relation by unity has its foundation in the similar essence, without the diversity there is from man to lion, but from one subject to another, composed the one, and the other of man, based on unity, and on number: just like an individual rational being against another of the similar composition, or a number against another number.

The second kind, philosophers call paternity, and filiation; the lord, and servant, etc., whose foundation is action, and passion; and this is not considered in this Science for the filial and paternal quality; ruler, and subject, etc., but by fighter against fighter, one strong, another weak; one fast, another slow; one skillful, another clumsy; one knowledgeable, another ignorant; one master, another disciple, etc. and in all, it is considered, Quis ad aliquem, by action, and passion, in which they are proportioned, or are disproportionate.

The third kind is by measure, and measurable: its foundation is deduced from the Science for the formal object, which in this Science corresponds to intelligence, and exercise: in all these three kinds, the commonly accepted opinion among Thomists works in this Science, based, by the authority of Saint Thomas, on the fact that the numerical relation is multiplied, or divided by the multiplicity of subjects, and actions; in such a way that the subjects, and actions have a Relation for the terms of their species, in which the relative foundation is considered; for as the Saint says: In the same subject there cannot be many forms of the same species, because in a relative alone there can be a unique species of Relation, which in one way to one, or in another to others is extended.

This doctrine is specific to this Science, where a single report is considered only for a unique species of Relation, or proportion, that in one way extends to some, and in another to others; e.g., two fighters are considered, one with respect to the other in a unique species of Relation, or proportion (as subjects) but in the relations that they are causing by what they perform and execute against each other; in one way they have a Relation, or proportion to one effect, and in another to others.

By virtue of this foundation (which is of the Philosopher) different relative, or analogous affections are inferred: the first, by the opposites: the second, by more, and less: the third, by conversion: the fourth, by similar nature. To these four species, some add as a fifth, similar knowledge: against this division of species, some Moderns oppose, that these accidents are not acquired by successive mode, as seen in the opposites: hence, they are not Predicamental Relations. It is answered, that the Philosopher, and the Ancients, who thus understand him, deal with the formal Predicamental Relation, and not the objective one, acquired by intrinsic concepts; and in this Science the entity is real, and the Formal Relations, with which the objection vanishes, which is of those who lean towards the Relations being an entity of reason, subject to chimera, and this is abhorred in all Science, which consists of intelligence, and exercise, like that of the Sword, in which they act as potency, and act; and as matter, and form.

Thus understood, we securely affirm, that in the Predicamental Relation in this Science, form, and paronymy are found: where the form is a relative proportion, and paronymy is the report, which is denominated from the same Relation, because (as has been said) the Relation is a comparison of one defined for another defined.

This maxim accepts (to our intention) other divisions: the first, according to its proper being, and this is defined, by saying: To be by itself knowledge of one extreme to another extreme; to which the first species, noted By opposites, is reduced.

The second is that habitude, which among themselves have proportionality, or comparison of more, and less; e.g., as 8 to 4, so 12 to 6, which is double, or as 9 to 3, so 15 to 5, triple, or as 3 to 2, so 4 to 6, which is sesquialtera, whose proportion, being similar in comparison, is more, and less in number; and to this division is reduced the second species By more, and less.

We consider the third division as that which varies the habits by accidents, such as right-handed, and left-handed, with respect to the column, or circular, or orbicular figure, in which we understand the Relation, with respect to the position in which we consider it, or arrange it, and this includes the species, which they call by conversion, e.g. the fighters, with respect to the dispositive habits in their movements, convert with respect to themselves, or with respect to the contrary the straightness up, down, forward, backward, right-handed, and left-handed, and in the wounds the Cut into the middle Cut, the Entire Reverse in the middle, the Slash into the Thrust, the Trick into the Trick, etc. because the corruption of one is the generation of the other, as is the maxim of the Philosopher.

The fourth division is what the Logicians call mutual, and not mutual, either because it is equal in the species, or in the similar knowledge of one defined for another defined, different, or similar, and of this division is the species By similar nature; e.g. as Science with respect to Science, or as Slash with respect to Slash, Thrust with respect to Thrust, Movement with respect to Movement, etc. which is all of similar nature, with Predicamental Relation among themselves: and it can also be not mutual, as man, and lion, which being mutual in the generic Relation Animal, are not mutual in the lowest species, because of the difference of their definitions: but the Relation of man, with the naked Sword in hand for another man, with the Sword like that, is mutual division, by the resemblance of subjects comprehended by the same quidditative definition, just like the lion for the lion by similar nature, and lowest species.

We also accept as a fifth relative division the Similar knowledge, e.g. as from right-handed to right-handed, from proportion to proportion, from number to number, from flat figure to flat figure, from Right angle to Right angle, from Obtuse to Obtuse, from Acute to Acute, from internal to internal, from external to external, in which the similar knowledge works; and as this in this Science observes proportions; necessarily a very brief notice is given of its terms, which is extensively dealt with in Arithmetic, Geometry, Sciences subaltern in the Science of the Sword.

Proportions are reduced to five, three are called simple, two are compound; generically they are defined thus: Proportion is the formal relative comparison, between two quantities of a similar, or nature, as Number to Number, Line to Line, etc. they are divided into equals, and unequals: equal proportion, or is Arithmetic, or is Geometry: Arithmetic, when two numbers are equal in species, and value, like 4 to 4, 6 to 6, etc. and the similar ones equal in value, species, and number. Geometry equal proportion considers that which is sesquialtera, with respect to sesquialtera, double with respect to double, triple with respect to triple, etc.

Unequal proportion is, when two quantities of one genre are compared, like 5 and 3, 15 and 4. This subdivides into greater, and lesser; the lesser is, with respect to the formal Relation, that there is from less to greater, comparing the lesser number, or quantity to another greater; e.g. as 2 to 5, 3 to 9, etc. The greater unequal proportion is, when the greater quantity is compared to the lesser, like 8 to 3, 9 to 4, etc. and just as in numbers Arithmeticly by discrete Quantity, so also in Lines, Surfaces, and Bodies Geometrically, and in both genres work the five terms, which are:

Multiple. This is thus defined in its genre, when the number, or greater quantity contains the lesser two, three, or more times; and so, however many times, they exactly give the term, like if two times, double; if three, triple; if four, quadruple, etc. e.g 8 to 4, which is known, dividing the greater number by the lesser; and finding that the inclusive admits in itself twice the included, the greater is double the lesser, in inclusive it comprises the included 3 times, and so triple. Hence it results, that the denomination is caused by the times that the lesser is included in the greater inclusive, and so double, triple, quadruple, etc.

The second genre, and denomination is Superparticular: it is considered, and it is known, when the quantity, or greater number contains in itself the lesser, its whole, and its half, and it is named sesquialtera proportion; and if the inclusive contains in itself the lesser, and its third part, it is named sesquitertia; and if the lesser whole, and its quarter part, sesquiquarta, etc. e.g. 3 to 2 is sesquialtera, 4 to 3 is sesquitertia, 5 to 4 is sesquiquarta, etc. and its knowledge is caused, defined from one term with respect to another, by the partition with the lesser number in the greater, like if 3 divides 4, the quotient is 1, lesser whole, surpassed by the greater in one particle, which is over the dividing number, and because it was 3, and the divided 4, the denomination is sesquitertia.

The third term is named Superpartiens, and it is when the larger number contains the smaller one an integral time, and some parts of the smaller number; e.g., if the larger number contains the smaller one once, and two-thirds, or one, and three-quarters, or one, and two-fifths, or four-fifths, etc. It would be said, making a partition of 5 by 3, that the result is one and two-thirds, which is one whole, and two parts of the smaller number in proportion to the larger one, and it is named Superbipartiens tertias, composing the denomination of three dictional particles over the Super, which is common to the second and third denomination; with such an understanding that if the quotient is one whole, and two-thirds (as has been demonstrated) the term will be Super, and with the Bipartiens tertias, because the overcoming of the whole was two-thirds, and if it were three-quarters, it would be said instead of the diction Bi, Tripartiens quartas, because the divisor was 4 and the overcoming three-quarters, so that one part of this genre is Super; the second is to add to the Super the remainder, that if it is 2, it is Bi; if three, Tri; if four, Quadri, etc. and the third diction will be as a result, which is Partiens, due to the partition, and divisor; and the fourth by the smaller number, like if you ask about 10 to 7, what proportion there is, dividing the 10 by the 7, and results in one and three-sevenths: and it will be responded, that it is proportion Supertripartiens septimas, because the 3 that are left are sevenths, being 7 the smaller number.

Multiplex superparticularis is the fourth genre, and denomination: it is composed of the first simple proportion, its term, Multiplex; and of the second simple, its term Superparticularis; and it is caused, when the larger number contains in itself the smaller number, more than once, and more one single part of the smaller number; e.g., as if one number comprehends another two and a half times, or three times, and a third, or if two and a quarter, etc. For example, from 15 to 6, inquire the proportion, as in the previous ones, dividing the larger number by the smaller one, and 2 result, and 3 are left, which placing the leftover on the divisor in the form of a fraction, they compose three-sixths, which abbreviated to the smallest denomination, is the same as half, and the dominating term of the proportion will be formed, saying, that it is double sesquialter, because the larger number includes the smaller one two and a half times, as seen in the proposed numbers 15 and 6. and if they were 10 and 3, the larger number will include the smaller one three, and a third, and it will be recognized, that it is triple sesquitercian, due to the composition of the two simple propositions: from which it is caused, that the Multiplex gives name to the first part, and the Superparticularis, that gives it to the second.

Multiplex superpartiens is the fifth genre of proportion, it is composed of the first simple, which is Multiplex, and of the third, which is Superpartiens, and it is caused; when the larger number includes in itself the smaller one, more than just once, and more than one part of the smaller number, For example: like if it was inquired, what proportion there is from 14 to 3. and dividing, as in the previous ones, the larger number by the smaller one, four result, and two-thirds, and it will be recognized in the whole integers, that the larger number comprehends the smaller one four times; and so it will be said by the first simple Quadruple; and by the third the fraction Superbipartiens tertias, and the whole denomination Quadruple Superbipartiens tertias. If you ask from 3 to 5, the given rule will be followed, dividing the larger number by the smaller one, and it will result in two, and three-fifths; and therefore it will be said, that the proportion is Multiplex superpartiens, and its denomination Double supertripartiens quintas: so that in this fifth genre, composed of the first, and the third, the denomination is caused by five dictions, or terms: the first, by the integral times that the larger number includes the smaller one, which is of the simple genre Multiplex: to which is added Super, as in the second, and third genre of the simple: and the last, by the result of the fraction Superpartiens, and all the dictions form the entire composed denomination; for example, for greater clarity from 23 to 6, the quotient results in three, and five-sixths, and it is recognized, that it is Multiplex, due to the integers; and Superpartiens, due to the fraction: and so, it will give in the term the dictions, which result from five-sixths, and it will be said, that the entire composition of the denomination is Triple superquinpartiens sextas.

It should be noted that in propositions, when the relative comparison is made by the lesser quantity, considered in the Quid ad aliquid with the greater, the term is not used as from the greater to the lesser, but rather the other way around, declaring it with the word: Sub, placed at the beginning; like Subdupla, subtripla, etc., and in the same way in the other terms Subsuperparticularis, subsuperpartiens, submultiplex superparticularis, submultiplexsuperpartiens.

Euclid and his commentators reduce all the common propositions to these five kinds, moving on to the harmonic ones, which are of another consideration, because it is not about finding the relation of a defined extreme to another defined extreme, but on the contrary between two extremes, or defined terms, finding a proportional harmonic middle (which we do not deal with here) as it is not proper of this science in this category, where the relations, or Quid ad aliquid the terms, that gives proper in skill, are the following: first, Middle of Proportion: second, Proportional Middle: third, Proportionality: fourth, Proportional distance. These terms all look at the relation of His, quæ ad aliquid, which exists from one combatant to another, from one attitude to another attitude, from one movement to another movement, and from one trick, and wound to another wound, and trick, as will be demonstrated by Schemas, understanding the four proposed genres, which in themselves contain four differences; that there is His, quæ ad aliquid.

The first, which is Middle of Proportion, is to measure the opponent’s sword, reaching with the tip of one’s own to the joint of the opposite wrist, from where arises the knowledge of equality, or inequality of the weapons, and in what proportion is the excess, or the lack; and how to choose the supplement of a defined term to another defined term.

The second, which is Proportional Middle, is that distance, and placement, which the skillful one seeks, or chooses, from where he strikes, and remains defended, either by gaining degrees to the profile, or subjecting the opposite Sword, applying degrees of greater power, and force to those of weakness, and frailty.

The third, which is Proportionality, is that relative knowledge, that the skillful one acquires, to outperform the opponent in the respective propositions, considering, and acquiring by intelligence, and exercise the positions of weapons, formations of angles, compasses, and movements, in which the combatants find themselves, and convert, that vary the Relations of His, quæ ad aliquid, according to the accidents that cause, or prevent proportionality:

From the above, came the nomination of the fourth term of relative analogy, which is named Proportional distance. This is that position, which supplements, or overcomes with the placement the inequality that there is from one combatant to another, both by the weapons, and by the dispositions with which the fight is ordered, because in it the most usually makes the distance; for when the opposite Sword is larger than the proper one, it is a general rule not to allow the tip of the contrary to pass the proper wrist; and this, and other reaches, which are achieved by the distances, gave the term Proportional distance. For a more demonstrable intelligence of this Predicament, the following Table, or Schema is formed.

SCHEMA OF THE RELATION.

  • Relation, or of His, quæ ad aliquid.
    • Either it is considered by defined extremes, which the Vulgar call Equivalences, or Differential proportions, such as
      • Similar ⸻ Dissimilar ⸻ And vice versa.
      • Equal ⸻ Unequal ⸻ And vice versa.
      • Strong ⸻ Against strong ⸻ And vice versa.
      • Weak ⸻ Against weak ⸻ And vice versa.
      • Skillful ⸻ Against skillful.
      • Skillful ⸻ Against unskilled.
      • Trick ⸻ Against trick.
      • Compass ⸻ Against compass.
      • Movement ⸻ Against movement.
      • Angle ⸻ Against angle.
      • Wound ⸻ Against wound.
    • Or by diverse extremes, due to the Relation to their terms, such as
      • Scientific.
      • Ignorant.
      • Agile.
      • Clumsy.
      • Master.
      • Disciple.
      • Theoretical.
      • Practical.
    • In these, as
      • Worthy, or unworthy, in relation to the diverse relation of one to another.

TENTH DISCOURSE.

FOURTH PREDICAMENT, Quality

The Philosopher defines this accident, saying: Quality is that, by which the subject is understood, and said to be such. In Metaphysics, expanding the description, he makes it in this substance: Quality is eaten by the difference, or substantial form, and by all accidental form, or by the special accident of this Predicament.

These definitions are understood by Alberto Magno, Boecio, and others, granting various divisions, according to those given by Aristotle, reducing the Generic Species to four, which are principal: first, Habit, and Disposition: second, Natural Power, or Impotence: third, Passion, and Passible: fourth, Figure, and Form.

To this distribution, the same Philosopher added three properties, which are so in this Science, and Predicament: first, to have contrary, or contrariness: second, more, and less; third, similar, and dissimilar. Applying various doctrines to the essential of this Science, in it this accident can be defined, saying: Quality is that term, by whose mode the accidental qualification in the subject is declared: then it is distinct from the relation, or De his, quæ ad aliquid. Giving thus light of the cause, which could move the Philosopher to precede the Relation to the Quantity, in terms of the categorical collocation.

The first species is Habit, and Disposition. Disposition is order of the parts of the subject, according to the place, or according to the power, or according to the species, in which habit fits. This is, possession, because the term holder in this Category is understood of the one who possesses science, faculty, or intelligence for the operation: and this is ordered according to place, power, or species, as the Philosopher taught. According to place, in this Science it is understood that order, which looks at the placement of the point, whose circumstance is occupied, according to the local disposition of each fighter, or with respect to both, which was touched on in the continuous Quantity, and more demonstrable will be noted in this Predicament, by the Geometric figures, which are capable of occupying, or filling surrounding place to the point given in a plane. According to power, it is understood that disposition in which the natural and acquired aptitude is ordered, by the force, agility, and ardor of the right-handed. According to the species, it is understood by that of each Tactic, of which demonstrations are made in their congruent parts.

All together, Place, Power, and Species, is what the Philosopher called Disposition, because it can be moved, and varied, from where the same Philosopher inferred, that the Habit can differ from the Disposition, because it consists of more permanence, and duration, and the Disposition of less; and he makes an example in the Science, which once acquired, is difficult to exclude, because it is obtained permanent in the subject, as long as it is not impeded by a most powerful accident, such as illness, forgetfulness, etc. and in this scientific acquisition (because not all are equal in perfection) according to the degrees of Science, which in them is considered, those who acquire more are called better disposed, and those who acquire less are worse disposed: in this consideration, Aristotle defined the Habit, saying: to be promptitude gathered by frequented acts, perceived in the mind, or in the body: e.g. in this Science, which is of intelligence, and exercise in which habits fit, that the understanding perceives, and habits, that with use the body perceives; and from one, and other results science, and this properly remains in the subject, acquired once; and the scientific is called right-handed, and habituated, and better disposed, the more perfectly he knows, and works, with which in the consummate right-handed is habit; and in the less scientific, and exercised, what he knows, and works, is disposition. By such principles it is recognized what is Habit, and what Disposition, and what consummate right-handed, and what not; and how they differ, or can differ the Disposition, and the Habit; and how they are understood, and regulated, according to their quality in this Predicament, and species, in which we treat of acquired habits, and not of the infused ones, that note the Theologians.

Power, or impotence is the second species; it applies to know, in this Science of the Sword: the strength, or natural weakness, is the second specific genus, which the Philosopher noted in the Predicament of Quality, where in terms of Power, or Impotence, he made the application to fight by struggle, or by another action of combat, in which it competes, with the aim of defense, and offense, where not only weakness and strength in the pure natural have a place, but the aptitude and agility acquired by intelligence and exercise in which science fits. So Power, and Impotence, are not so much qualified by natural strength, or weakness, as by aptitude, and order, which they receive in the action with skill in combat, achieving defense, and offense against the opponent.

Passion and passible is the third Species in this Predicament: here Passion, and Passible, is understood in a different way, than sweet, or bitter for the sense with honey, or absinthe, which cause passion in taste, or fire, which causes it in touch, with heat, or ardor, but the Passion, and the Passible as far as quality, the Philosopher qualifies them, recognizing them by the inner affections, from which the external effects result; and we say affections, and not effects, because in the effects there is no accidental quality proper of this Predicament, which looks at the passions inherent in the same subject, in which Passion, and Passible fit by quality of actions, which ones are permanent, and which transient, as in the Right-handed, that the inner affections are manifested by the external affects, which if they are permanent, cause quality in the same subject, that remains in it, by the operation consummated in the Trick, which causes in the inner affection; and goes to execute it, demonstrating the Passion, or the Passible in external affects: but if the affections were transient, they are imperfect qualities, as the same Philosopher felt, just as blushing, or discoloration, which are qualities, that do not remain, when they are caused by anger, or fear, as transient affections, which often happen in the course of the combat, manifesting in the fighters inner affections, that result in external affects of Passion, or Passible in pure quality.

Figure, and form. These terms are synonymous, because strictly speaking, Figure is the same as Form, and Form is the same as Figure, as the grammarians note with the specific differences in expressions, leaving aside the grammatical and rhetorical figures, which are not the intent here.

In this species, the term Figure, and Form, is taken for that figural and formative comprehension, which represents the figured species, according to the form disposed in its proper position, so it can be defined, saying: Figure, and form is a comprehension of terms, which include the extension of what is figured, and formed, like mathematically the circle, the triangle, the quadrilateral, etc. and the other mathematical figures, which by their composition are known, and signify, not only as to their forms, but as to their qualities, in which they are of this Predicament: so Saint Thomas noticed, that the Figure, and the Form do not differ in species, because the mathematical figure, and the form in natural being, are interchangeable, by their terms, although in mathematical being it is known, as Figure that very thing, that in the lined demonstration is named Form.

From these principles, we come to understand for this Science of the Sword, what qualities some figures and forms have, what others lack, which are useful for specific qualities, and which do not admit as much as others, about which if we were to discuss as extensively as this category of quality allows, in terms of Figure and Form, it would be enough to make a large volume of it; since it can comprehend everything most essential about Geometry, noting by Theorems the qualities of all those mathematical figures and forms, which this Science uses, as will be widely recognized in its proper places; and here, for very useful comprehension, it is compiled by essential which geometric figures and forms are capable of filling the circumstance to a given point on a plane, without admitting a vacuum; and which do not, choosing the common point with respect to both fighters, and the special point with respect to each one.

In the common one demonstrated, how all the figures can converge, which admit the quality of filling the circumstance to the given point, with respect to the fighters, and in the special one of each one, each species of figure, which has such a quality, and in which one has a greater or lesser perfection, adorning the whole of the demonstration with various Theorems of the most essential of all Geometry, in which the practitioner can elaborate, and speculatively wish to discourse.

For brevity, we excuse another second collective demonstration, to understand those geometric figures and forms, which admit the quality of producing outgoing angles by their sides, insinuating which ones do not, and what orders there are of them, with very special considerations, and how the proportions are found in the lines.

It is clearly demonstrated that in Geometry only the Triangle, when six equilateral triangles are joined together, fills the surrounding area of a given point on a plane. The Quadrilateral has the same quality, when four squares are joined. The Hexagon admits the same quality, when three Hexagons are joined

It is possible, and it is demonstrated, that with respect to the fighters, the Triangle, the Quadrilateral, and the Hexagon can converge at the given point on the plane, with the quality of filling the circumstance, adding the figure and form of concentric circles, lines of reach, essential theorems to the value, and division of angles; and especially those of greater speculation, both for this Science and for Trigonometry, as it is so proper to it.

In each special figure and form that has the quality of filling the circumstance at the given point on the plane, with respect to each fighter, it is demonstrated in which it is of better quality, and in which it is of less. For the whole, the following letters and notes are placed: A. center, and common point, whose circumstance is filled, with the convergence of the figures that admit such quality. B.A.C. Triangle, which when six are joined together, occupy without void the circumstance at the point A. given as common on the plane, with respect to the fighters. C.A.D. second Triangle. D.A.E. third Triangle. E.A.F. fourth Triangle. F.A.G. fifth Triangle. G.A.B. sixth Triangle, all of which are joined by their common sides. A.B. from the first and sixth Triangle. A.C. from the first and second. A.D. from the second and third. A.E. from the third and fourth. A.F. from the fourth and fifth. A.G. from the fifth and sixth. With this, it is demonstrated by Figure and Form, that six Triangles have the quality of occupying without void the circumstance at the point A. common to the fighters.

In the same way, the Quadrilateral is capable of the same quality with four Quadrilaterals, as demonstrated in the proposed Form and Figure, at the end of the Discussion, with respect to its entirety in the Quadrilateral B.I.E.H. where the four B.N.A.M.-M.A.L.H-L.A.K.E-K.A.I.N are joined by their common sides A.M-A.L-A.K-A.N, they fill the area around the common point A. without a void. The Hexagon is capable of the same quality, when three are joined together, as demonstrated in the proposed figure and form where the Hexagon A.G.Q.P.O.C. joins by its common side A.G. with the Hexagon A.E.V.X.Y.Z. also joining with the first hexagon by the common side A.C. All three fill the area around the common point A. given on the plane, with respect to the fighters. The inscribed and circumscribed circles are concentric to point A. and include the composed figure of the three, which have the quality of filling the area around point A. given on the common plane to the fighters, without a void. This allows the Fencer to recognize in what position he finds himself, both in the common jurisdiction, as well as in his own, and when he enters into the foreign one, as will be demonstrated in their proper places.

In addition to the proposed, we can see in the same figure the special points that each fighter occupies, whose place is occupied with special quality, because if the fighter stands straight; the given point, which in such position occupies, will be with four squares, as in the figures C. and F. And if he is not in a straight position, but as he falls in common, he will deviate the tips of his feet so far that if from the tip to the heel of each foot, straight lines are produced, they will end at the occupied point; and if from tip to tip of each foot another straight line is drawn, it will be the base of a Triangle, or Equilateral Triangle, that if six are joined together, they will fill the circumstance; and if the tips of the feet are further apart, the angle could be as n.m.t. and such position, although it occupies the point m. with three Hexagons, will not be of good quality for the fighter, because he will not have firmness or good position; noting that in each position the fighter has a different quality, in some good, or not so, or worse, from where the Fencer will come to know when his opponent is orderly, or disorderly, and when of good, or bad quality, with respect to his position, and figure in which he occupies his given point with respect to himself, and the side with respect to his opponent; from which result the three properties that converge in this Predicament, which will be discussed in it, where will be its proper place.

As the proposed figure looks at the differences in quality by Form and Figure, it includes the formal Triangle, which is the first figure that mathematicians consider linearly, and is found in the Triangle B.F.D., whose center is A. and the subtenses B.F., F.D., D.B. are chords of the arcs 120 degrees, and the lines of greater and lesser range, are those drawn from the point B. to the arc F.D., demonstrating the angles F.A.E. and E.A.D. which are equal, dividing each one into three ad libitum, the two of 19 degrees each, and the other greater of 22 degrees; and consequently, as has happened with the angles, caused in the circumference at the point B. which include various Theorems, which teach the possibility of dividing any given angle into even and odd parts, as demonstrated in the Discrete Quantity, and also demonstrates here the division of the right angle into three equal parts; since it cannot be denied that the subtense B.C. is the base of the angle B.A.C. which is worth 60 degrees: then the arc C.I. which is half of the subtense C.D. equal to C.B. is 30 degrees, and because B.A.I. is 90 degrees; a right angle its third part is C.I. and its two thirds parts C.B. and if by the 9. Prop. of the first of Euclid, were to divide the angle B.A.C. its division of each part, will be equal to the angle C.A.I. which is half of the angle B.A.C.

Then the rest E.A.I. is divided by demonstration into three equal parts, as C.A.I. so that in this figure it is demonstrated theoremetically, that any given angle, whether Right or Oblique, is divisible into three equal and unequal parts, as also recognized by Papus of Alexandria, Clavius, and other learned Geometricians; without being obscured, not having Euclid made Special demonstrations, being so, that he did not omit the Elements, as the Classical Authors explained; and here we could expand a lot, which is excused, for being enough the proposed, so that the Fencer understands, that all angles have division into equal and unequal parts; greater and lesser; even and odd.

This figure and form also includes the theoretical proposition 47 of the first book of Euclid, with all its qualities; since the sides H.B. and B.I. form a Right angle on the maximum subtense H.I. being a median proportional line B.A. and consequently, the squares, whose sides, or roots are H.B-B.I their powers are linked with the same one as that of the maximum subtense H.I. root of the square H.I.Z.Z. with the other qualities that result from the speculation.

And because the proportions and proportionate means are such important qualities in this Science, in this proposed figure and form enough light will be found for the understanding of the proportions, of which the Elements are largely in the fifth and sixth Book of Euclid, including in this figure many of its Theorems, which we do not explain specifically one by one, but enough for our endeavor, referring to the speculation of the wise Geometer what can be inferred in so many Theorems, which are virtually included in this maximum figure, which we propose; and here, by understanding, we will say with Pitiscus: That if many flat triangles are composed, and the Parallel lines are cut between the segments, there is proportionality, in which there is so much to infer, as will be specifically seen in its proper places, when we talk about the graduation of the Sword, and its points of strength and weakness, and how they are occupied and cut with various qualities; that if in this Predicament we had to refer to all, it would be enough to form a volume, entering into the precepts of the art, and in the explanation of many Theorems of Geometry, which one, and another is not proper here, but the Predicamental by Form, and Figure, in which the proposed is sufficient.

(Stamp 4)

ADMONITIONS

Despite avoiding, for the sake of brevity in this Work, the second collective demonstration, which includes those geometric figures and shapes that allow the production of outgoing angles by their sides, I will give a concise notice, albeit briefly, that suffices for their understanding.

In the Predicate of Quantity (by quantity), we touched on figures that, extending their sides, converge to end at such points that form angles, which are named outgoing because they go beyond the figure, whose polygon is composed of interior angles, called incoming.

It was also noted that Campano was the first to consider this, perhaps (as noted by Bravardino) once the sides of the Predicate are extended, it is not necessary to recognize which geometric figures admit such qualities, and which do not. In the occupation of filling the circumference without a void at a given point in a plane, we demonstrated in the comprehensive figure, that only the Trigon and Hexagon admit, and are capable of, the quality of filling the circumference at a given point in a plane; but in the qualities of outgoing angles, there is more latitude, and different orders are considered, as extensively demonstrated by Thomas Bravardino, advancing the speculation of Campano, by whose doctrines (for what this Science does) we put first order the Pentagon, the Heptagon, and the Nonagon: because from their Polygons in simple figures, extended their sides converge at points, forming outgoing angles on the simple figure, running the lines continuously, as in the Pentagon, which is in Geometry the first simple figure, that admits such quality, lacking the ability to fill circumstances, for if its sides are extended, it will leave formed on the sides of the Polygon as many outgoing angles, caused by the convergence of the extensions in first order.

The same quality can be seen in the Heptagon, which on the simple polygon of seven equal sides, that cause as many incoming angles, if each side is extended to the points of convergence, seven other outgoing angles are formed, with the quality of the linear continuation from point to point, with which this figure will be of the first order, and its simple polygon lacks the quality of filling a circumference, even at a given point in a plane.

The Nonagon is a simple figure of nine sides, which include as many incoming angles, and from the production of each side to the points of convergence, and by continuous movement, nine other outgoing angles are caused, which come out of the same simple polygon figure, as will be seen, exciting the lines from point to point, so this figure is also of the first order; and consequently, it does not have the quality to fill the circumstance of place. By this rule, speculation admits a lot of latitude, as great Geometers can recognize.

The second order results from the composition of two figures, which form another of outgoing angles, with such a quality, that in that number it could not be formed by the repeated first order; e.g. the Decagon, because its simple figure consists of even angles, it necessarily must have two opposite sides, that produced their lines, will be Parallel: but if it requires the formation of ten outgoing angles by the second order, two opposing Pentagons of outgoing angles will be placed, and they will form the figure of ten angles, opposing one Pentagon to another in placement, and in the interior the Decagon of ten incoming angles will remain.

The third order of figures with outgoing angles is in two ways, either simple or compound. Simple, of third order is, when from two simple figures, placed in position, as they allow, results another figure of outgoing angles, composing inside that one, which does not have the quality to constitute it by the production of its sides, nor also the simple figures, from which the composition is caused; e.g., the Triangle lacks the quality to cause outgoing angles by the production of its sides: but two Triangles, composed between them will form six outgoing angles, and an inner Hexagon, which also does not admit the quality to cause the production of its sides a figure of outgoing angles, because its opposite sides are parallel lines, and in this quality other figures can be formed, as speculation admits.

The third compound order is when from the composition of simple figures another figure of outgoing angles is caused, and results from the production of its sides; e.g., composed of two squares, as the Triangles, Shapes, simple Figures of third order, with the quality of eight outgoing angles, constituting inside an Octagon of incoming angles, which lacks the quality of filling the circumstance at a given point, having the square of its first composition; but from one, and the other is found, that produced the sides of the Octagon, results another figure of third order, with the quality of outgoing angles, as in the proposal, that composed two squares in opposition, formed a figure of third simple order; and produced the sides of the Octagon, the compound results from point to point.

The use of these figures in this Science has so many qualities, that their exposition, and demonstrations, are referred to their own places, which are of art, and precepts: because all figures, and forms have proportionality among them, the curious one can inquire the intelligence, and principles of the middle proportional lines Geometrically, finding the proportional mean between two proposals, as Clavius, Peletarius, and others demonstrate: thus given two straight lines, the proportional mean is found in Geometric proportionality; and given two straight lines, it is found in lesser extremity the one that is in Geometric proportionality: and given two straight lines in greater extremity, the third is found in Geometric proportionality.

In general rule, any lines are found in continuous proportion, giving the first ones, from whose reason the other proportionals come out: if it is well understood, and it is discussed, it will not be impossible to find between two given straight lines, two proportional means.

Neither will it be difficult, by the doctrine of Pappus of Alexandria, to find the fourth discrete proportional, understanding Euclid, with Tartaglia, and others, with which we excuse to extend the explanation of figures of proportional lines, both middle, and the others, that are necessary for the understanding and exercise of this Science of the Sword, demonstrating the qualities of angles, lines, and figures, that we have noted: with which the understanding, both as a natural being and as a mathematician, can perceive a real entity in this Science, and in the specialties, of this Predicament, in which its properties can be noted (according to the Philosopher) making use of the proposed figures in what they produce for the fourth generic species of Figure, and Form.

We also excuse, not to extend ourselves, to demonstrate how harmonic proportional middle lines are found, since given two straight lines, the proportional mean is found in harmonic proportionality: as well as given two straight lines, to find the harmonic proportional mean in the lesser extremity: and given two straight lines, finds the greater extremity in harmonic proportionality, in which laboriously Clavius, and Juan Bautista Benedicto are extended, to whom we refer the curious.

Drawing from the above in this part, it can be found that there is a harmonic proportion, which serves as a harmonic mean in the convergence of swords, one greater and the other lesser: that the Right-handed person must proportion his means with such harmony, that his knowledge results from what he will have of the excesses: and in the other proportions, he can also understand which are the extremes, and which are the means of proportion, noting as an essential point, that two middle proportional lines between two others (one being the antecedent, and the other the consequent) are possible: but it is not, according to natural being and mathematician, that there are two Proportioned Means, without only one, that acquires the perfection of such, because it would mean giving two Proportioned harmonic terms, which composed a single harmonic proportional mean, which is absurd, because from 4 to 4 there are no harmonic excesses, nor the power of two Proportioned Means, but of a Proportional Mean, that acquires power and perfection over the other proportional means, in continuous, or in discrete proportion: this, and other essential qualities in the proportions, will be explained in their places.

The Philosopher, for greater clarity of this Predicament, formed as a rule in it, to be those qualities, which are understood nominatively by themselves, or in another way, that manifest a proper quality in the subject, noting different examples, admitting among them combat and Military Art, in which the Science of the Sword is included, because it is intelligence and exercise, in which the three properties that the same Philosopher noticed are nominatively, which are, as was touched at the beginning of this Category.

Having an opponent, or opposition is the first property. The merely Philosophers, Natural or Moral, reduce all opposites to this species, such as white to black, light to darkness, heat to cold, etc. and in the moral, justice to injustice, virtue to vice, science to ignorance, etc.

In the subjects of the Sword, which are the fighters, one with respect to the other, ex contrario, or has opposition, either by the positions, or by the movement, or by another accident of quality, which is nominatively understood by itself, or in another way, that manifests its own quality in the subject: for example, in occupying a place surrounding a given point in the plane of combat: or common because it is with respect to both; or singular, because it is with respect to each fighter, as demonstrated in the comprehensive figure, that with only three lowest species of figures, the circumstance of the given point, or common, or singular is filled: as for the common, it is recognized, that it is not pure property of this first species for the common; and as for the singular yes, because one opponent with respect to the other, as far as itself, occupies the point of its circumstance in opposition of figure, like the square, that four fill the circumstance of this, when six Triangles, or three Hexagons the other; and so, noting the other oppositions by the positions of each one, as will be noted in their own places. There is also opposition in Movements, and in Tactics, etc.

More, and Less_ the Philosopher admits as a second qualitative property, such as white, more and less white; just, more, and less just; Right-handed, more, and less Right-handed, etc. With this, the qualitative property is understood in more, and less perfection, or in more, and less defect, not by pure Relation, but by its own Quality.

The third is Similar, and Dissimilar. The Philosopher explained this property, not by the contradictory opposition ex diametro, which touches the first species, but by the dissonance, or consonance; disparity, or parity, which is considered qualitatively in some species with respect to others, as in the square, the Quadrangle, the Parallelogram, the Rhombus, the Rhomboid, etc. that being all quadrilateral figures, they are similar and dissimilar in qualitative property: the same in Triangles, etc. Also in the fighters, who, either are similar, or are dissimilar: as if one, and the other, as for the point, and circumstance, that in singular they occupy, are similar by Triangles, or by Squares, or by Hexagons, or are dissimilar; this in Squares, that in Triangles; or this in Triangles, and that in Hexagons, etc. and in the wounds, like Thrust to Thrust, Cut to Cut, Backhand to Backhand, or the contrary, Movement to Movement, etc.

From all this it is concluded that qualities are not confined to a precise number, because they are subdivided into a multitude of lowest species; although most, or all admit the three repeated properties, of Contrariness, of More, and Less, of similarity, and dissimilarity, and Geometric, Arithmetic, or Harmonic proportionalities, Forms and Figures, etc. for whose comprehensive intelligence is proposed in Schema.

SCHEMA OF QUALITY

  • Quality
    • Disposition or Habit
      • Of the Soul
        • Through Understanding
          • Science
          • Art
        • Through Memory
          • Prudence
          • In Reminiscence
      • Of the Body
        • Through Will
          • Virtue, or Vice
          • Affections, or Actions
        • By Nature / By Habit
          • Strength, or Natural Weakness
          • Exercise
          • Dexterity
    • Power, or Impotence
      • By Nature
        • More or Less Apt in Operations
      • By Skill
        • For Arms
        • For the Sea
        • For Arts, and Labors
      • By Speed, or Cunning
        • In Applications
        • In Operation
    • Passion, or Passible
      • In the Soul
        • By Opposing Affections
        • Anger, Revenge, Disturbance
        • Fear, Bravery, etc
      • In the Body
        • By the Operation of the Senses
        • By the Cause of the Objects
        • By strange qualities, heat, cold, etc
    • Figure, and Form
      • Mathematical
      • Perceptible
      • Intelligible
      • Demonstrable
      • Natural
      • Visible, etc
  • Properties
    • Contrariness
      • In Opposed Subjects
      • In Dispositions, Postures, and Places
      • In Tactics, and in Executions
    • More, and Less
      • Strong, Weak, Skilled, Clumsy, &c.
      • In the Natural, Dense, Rare, Light, Rough, &c
    • Similar, and Dissimilar
      • By Form, by Figure, by Position
      • By Place, by Mode, by Proportion

ELEVENTH DISCOURSE

FIFTH PREDICAMENT, Action

The Philosopher briefly touched on the precepts of the six final Predicaments, complementing the ten, in which he partitioned being (which in this science is real) without admitting Metaphysical and Theological concepts, which go to a higher understanding. The Predicamental Action is defined (according to the Philosopher himself, saying) to be the influence and path of the agent in the object.

Aristotle. From the Predicates, Chapter 9.

Aristotle. Metaphysics, Book I.

 

In this science, this Action is considered successive, and thus united to successive movement, insofar as formal action will be produced, insofar as it ends in the effect, or a movement is corrupted, so that generation and formation of another may result, because often (according to the intelligence, and active will of the agent, who in this science is the man with a Sword) in the operation a wound begins by a slash; and before consuming the action by executing it in the opposed opposite. Due to a new accident, or for another reason, it corrupts the movement of the Slash, which it began, and from that corruption, it passes through influence and successive path, to form a Thrust, which it instigates, in whose termination it achieves the effect, which gives the final being to the Action.

In the same way, in other Tactics, actions are achieved by the influence and path of the working agent, which, generating some movements from the corruption of others, it proceeds through successive path to the ultimate effect, and with all, generated and corrupted, it consumes the Action, which could not have been otherwise; for this reason, the Action is distinguished in Immanent, and Transitory; the immanent, which subsists in the same subject; and the transitory, because it passes to another.

By Action, which subsists in the same subject, the Tactic, the Wound, which as a real entity subsists in the intelligence and power of the agent, can properly be understood: and by the transitory one, the one that through operative execution passes through the exercise, and the effect to the opposed subject. From this, this definition is made for this science: Action is movement, which emanates from the power of the agent, and passes to perfect itself in the termination of the act, either by movement, or by discourse.

Definition of the Action.

 

Assuming, then, that the Tactics, which are made with a Sword, are through action, and movement; those that are made, without preceding voluntary movements from the opponent, are correctly called of the agent’s first intention; and those that are formed preceding movement, or movements of the opponent, are called of second intention: and both emanate in their consumption from the potential action of the Fencer, which is directed to perfect them in the termination of the act by one movement, or by various, according to the nature of the Tactics.

From the above, it results to understand the imperfection, or inconvenience of those who have had, and have, that even if different movements are made, which belong to more than the Tactic, or wound, that is formed, they are not reputed for more, than one movement, which receives the name of the active termination of the wound. And although this seems so in terms of the effect, because it ends in Cut, Thrust, etc., however, in scientific rigor, it should be understood with distinction: as it is demonstrated in its proper place, any Tactic is formed of free cause, or subject, with special movements, according to the positions, in which the fighters with Swords are found, this does not remove the possibility that the Action can begin by one Tactic, and end in another: which forces the consideration of the different species of movements, which often precede, not being precisely necessary for the formation; and without this knowledge, one would proceed without distinction, and knowledge of the corruption of some movements, and of the generation of others; and of when the actions are continuous, or are disjointed, and therefore in Fencing the Action is distinguished into two species.

How are active movements understood, and what are the properties of the predicamental Action.

 

One, which by the last movement ends in the effect; another, when, according to the accidents, or real concepts of the agent, by course of various movements, Curved, and Straight, the action is the influx, and way of the agent, which through the generation, and corruption of various movements, according to intelligence, and exercise, is directed in the Fencer until he consumes the act, which he pretends where the two properties have a place, which the Philosopher noted in Action of Contrariness, and More, and Less. Of Contrariness in the contrary formations of Tactics, Wounds, and Movements: of More, and Less, for what they admit of formality, and the act.

SCHEMA OF ACTION

  • Action, or is
    • Of the Mind
      • Acquired by intelligence. By
        • Science,
        • Art,
        • Experience.
    • Or of the Body
      • Reduced to act by Exercise
        • By Movement
        • Operation,
        • Completed form.
  • Properties
    • Of Contrariness
    • Of More, and Less

TWELFTH DISCOURSE

SIXTH PREDICAMENT, Passion, y Passible.

As Passion in the Passive is the effect of Action, the Philosopher rightly placed this Category immediately after Action, defining: Passion is the reception in the one who suffers from the form that it receives in itself because of the agent.

Aristotle, in the mentioned place above.

 

For greater clarity in this Science (according to the opinion of serious Authors), it could be said: As Action is a passive disposition in the susceptible subject. From this definition it follows that, due to the effect of the operation executed by the agent, a certain form is introduced into the Passive; because the active power, although suffering in action, does not have a consummated effect until the act is perfected.

For this Science, it is understood between the skillful agent and his opponent, with four significant terms pertaining to the Action and Passion of both combatants involved in each maneuver: the first, the beginning of the Action; the second, the formation, which results from the entire Action; the third, the execution; the fourth, the specific form of the wound, in which the whole Action ends up in the susceptible subject: for example, the skillful agent forms a Slash and executes it on his opponent, so that all four terms are present in the maneuver: the first, when it began; the second, in the formation; the third, in the execution; the fourth, in the formal Cut that ended in the Passive.

Oña, and others, in the cited place.

 

These same considerations are found in all the other species of maneuvers, which according to their organization and scientifically by intelligence and exercise, the skillful agent can form, and the passive can receive.

Please note that if the passive subject suffers as a recipient, there is also passion in the active subject, with the distinction that its suffering is in its own active actions; but the Passive suffers the forms of the effects, of the maneuvers, and wounds, which are executed in it, sometimes due to ignorance of this Science, other times due to the various accidents that occur between the combatants.

How does the passive subject suffer, and how does the agent?

 

From which it follows that the production of the wound by maneuver, and execution is in the Agent; and the actual effect of the form is in the Passive, not by the interchange of the subjects, but because from the one part is the production, and from the other part is the reception; with this, the form perfected in the effect is achieved: and this does not make a univocal by itself, which is only found when the extremes are unifiable, as in Substance and Accident, between which inherence mediates: but the power, which admits passion in the skilled agent, as a Physical agent, is not passive, as in the recipient of the wound: with this, its formal being does not depend on the act of quality alone, as active power, but on the determined quantity, which is passive; because in truth, the reception of the wound is the finished form, which depended on a foreign active power.

From this it follows that extrinsically, reception is posterior to production. And being, as it is, posterior the finished form in the wound, than the production, which was anterior in its primitive being by a real entity, it is concluded that it is not univocal by itself, nor are its extremes univocally united, although in the whole a denomination is admitted by the consummated wound, Slash, Thrust, etc.

From the above, it is demonstrable that this Predicate is distinct from the previous one and requires a distinct Category. In this consideration, active exercise and the determined act are not univocal, due to the operative difference in the fighting subjects, with which Passion and Passive are distinct Predicates, in which a schema is formed.

SCHEMA OF PASSION, AND PASSIBLE

  • Passion, y Passible
    • In the Skilled Agent it is suffered
      • In the Mind
        • Understanding
        • Premeditated
        • Producing
      • In bodily exercise
        • Arranging
        • Directing
        • Forming and executing
    • In the Passive Recipient it is suffered
      • By the reception
      • By the finished Act
      • By the Form, and Species of the wound

THIRTEENTH DISCOURSE

SEVENTH PREDICAMENT. Ubi, or Where.

Regarding the last four accidents that admit category, the first is Ubi (Latin adverb) interrogating about place, or position in it, which corresponds in Castilian to the adverb Donde (Where), from which are derived Por donde (By where), and Adonde (To where), which are used in this Science.

Donde is defined as such: It is an accident that results from the acquired position in a certain place, and of the subject, or action, that is placed in it: e.g., how each of the fighters is placed, or is positioned, with respect to themselves, and with respect to their opponent, from which results a certain external accident to each one, or to one, and to the other; in such a way, that the term Donde is recognized, in whose meaning the main placement is explained, from which the other two adverbs Por donde, and Adonde are derived, and all three comprehend certain principle: mean, that guides; end, or final term: demonstrating the position, either as mean, or as end; and in all terms this accident is recognized as a real entity in this Science.

Against this conclusion, it is usually argued, saying: Ubi is a Predicament that ends local movement. This nomination, then, is not a real entity, but positive: therefore this Predicament Ubi is not for a real entity. To which it is answered: Every ended term, and its derivatives admit real entity: the term Ubi (the same as Donde) and its derivatives signify properly ended term: therefore the Ubi Predicamental, and its derivatives are perceived as real entity. The reason is, because the adverb Ubi categorically demonstrates the denomination by place, or position; in such a way, that it supposes reality of that which has a precise being really, either it is considered as principle, either as mean, or as end. Therefore, that which has a precise being, and not contingent, is a real entity: therefore the Predicament Ubi, and its derivatives, admit real entity, and not only positive.

For this reason, the ancient and modern dictionaries explain the word Ubi as an adverb of precise place, although with different punctuations, like Ubi? questioning: others, as relative, that means Por donde, and thus it is medial, as a precise and finished concept, and not as a contingent one: in others it is finite, and demonstrates term of conclusion in a determined place, and in all three modes it is real entity: and as such, it is admitted in this Science, and not as positive entity, nor as pure entity of reason, nor as objective concept; rather in the exercise it is perceived, forming a mathematical entity proceeding from the real entity. The reason why in this Science, and its operations, it is necessary, that they be regulated, and understood by this adverb, and its derivatives, is, because no action, or term, can be without occupying a place, according to the terms of this Predicament, because the Tactics, that are done governing the instrument Sword, it is necessary that they have a principle, De donde they begin, transit Por donde they guide, and determined end, Adonde they execute, disposing themselves by these terms to the perfection, that the common people call Dexterity, with which is achieved the own defense, and the offense in the opposite opponent, for whose intelligence a Schema is formed.

SCHEMA OF THE WHERE

  • Where
    • Where
      • Natural
        • By real placement
      • Accidental
        • By positions, which are produced from the first placement
        • Or because they are succeeding one another
    • Through where
      • Means between the extremes, which leads to the final term
    • To where
      • End, or conclusion of the action
      • By consummation of the act
      • Or by final existence

FOURTHEENTH DISCOURSE

EIGTH PREDICAMENT, When.

The definition of this Predicament (according to the doctrine of Saint Thomas) Quando is the same as being in time, and of existence in it. The a priori reason is that the movement of the first mover is uniform in its duration, for which reason the Philosophers call it primary time, also being a very certain measure of durations, which results in dividing them commensurably by days, by hours, by minutes, by instants, etc.

In all durations, one is considered and recognized predicatively as a real being, which is signified by the term When, which is the same as being in time; an accident, which originates from time itself, and existence in it, being included between two precise terms, which one is antecedent, and the other subsequent, to which are given the names Before, and After; and that duration included between these two precise terms, is precisely what is considered, and perceived by a real being in this Predicament, understood by reason, measurability, and recognized by primary time, which is the revolution of the First Mover, insofar as it is regulation of durations.

The subtlety of wits, to elucidate the truth further, seems to be able to argue to the contrary, saying that the commensurability, which is named When, is more in passive potential, than in commensuration: passive power is not of this predicament, but of those of Action, and Passion: then what is named When, is not predicative commensurability, but passive power; and as such; it has to be considered.

It is answered, that although commensurability in general, by the reduplication of its parts, seems to have a natural passive power, it is not for this reason that it has subordination, nor is it knowable insofar as duration, but by the uniform movement of the first mover, like the hour, the minute, etc. and that being in time, which is terminated by Before, and After, is what is properly named Predicative When. That commensurability, then, which in its own signification is being in time included between the anterior, and posterior, is not passive power, but measured duration, and recognized by a real being, which is the Predicament Quando: then it admits a special Predicament, which in this Science (which is of intelligence, and exercise) is accident, and action, and duration, which is born from the same primary time, and has existence in it.

In this Science, the Tactics, and Wounds are recognized by this Predicament: first, when they are of first intention: second, when of second intention: third, when before time: fourth, when in time: fifth, when after time. Wounds, or Tactics of First intention, as it has been repeated, are when no voluntary movement of the opposite party precedes until its execution. Of Second intention, when they are performed, intervening voluntary movements of the opposite party. Before time, when the Tactics are performed, without the opposite making a movement that motivates them. In time, when at the same time that the opposite makes some movement, it is hit. After time, when the Skilful one executes his Tactics after his opponent finishes any action, and the movements that belong to it.

With such distinctions, this Predicament is understood in this Science, from which a Schema is formed.

SCHEMA OF WHEN.

  • When
    • Past
      • The time to perform the action has passed
      • The action was performed
    • Present
      • What is being done in the current moment
      • What is in the present time to be done
    • Future
      • What is potential, that has not yet been reduced to action
      • What is premeditated in the understanding before being executed

FIFTEENTH DISCOURSE.

NINTH PREDICAMENT, Situs, or Position

Gilbert, in his extensive explanation of this Category, understood Position essentially as the bodily position, according to the whole, and parts of the subject, which in this Science is called Posture.

From this definition, we can recognize what kind of position or posture is chosen to achieve readiness for defense and offense against the adversary, whose kinds will be discussed in the second book. Logically considering here that this predicament is different from the previous ones, because although the operative power can be a quality, it is separate from that which is reduced to position or posture of the swordsman, or non-swordsman, with a sword to fight against his opposite. This position or situation in this Science is understood in two ways. One is in essence, which is considered in the whole and parts of the combatant, and in this mode the special attention is to the posture. In another way, the situation is not only with respect to the posture or postures, but also with respect to the places and forms in which he positions himself to achieve the operation more perfectly, which can be called bodily situational ordination to execute the Maneuvers.

This Predicament posturing is distinct from the adverb Where, and its derivatives, because it does not include Where, Through where, and To where, but is another kind of accident, that looks at the situation and position of the body, arm, and sword, to find oneself in the combat prepared, waiting, or attacking with the perfection that the swordsman must have, both in the postures, as in the formation of the perceived propositions by real being, and executed by mathematical being, until executing a wound, staying defended at the time he offends.

This Predicament is so comprehensive, that it embraces the most essential of this Science, both in the Theoretical and Logical, as in the Practical, from which demonstrations are formed in the second book, where it is taught in art by precepts and rules what is here reasoned by discourse and science, from which is derived the knowledge that must precede the operation, and Maneuvers, that include the postures of waiting, and attacking, with the means that must concur proportionally and proportioned, in order to the defense and offense, with the requisites and circumstances that must be observed in any posture, motion, and act, in which the swordsman will situate himself in the whole, and parts, with the perfections that he can acquire by nature and art, which is insinuated in the following Schema.

SCHEMA OF THE POSITION

  • Position
    • As for the Bodily Position
      • Standing upright, or in another form
      • In Defense, or in offense
      • Or complicated defending and offending.
    • As for the Exercise, and operations
      • Waiting
      • Attacking
      • Generating
      • Corrupting
      • Forming
      • Distracting
      • Executing

SIXTEENTH DISCOURSE.

TENTH PREDICAMENT, Habit, or External Ornament.

Habit in this science (as in others) according to the Philosopher, and his expositors, comes in terms of Latin language, from the verb Habeo, which means to have; this is understood in various ways and species: the one that makes this science is expressed by the Philosopher in this category, saying that Habere refers to the accident that results from the external to the body, such as weapons or clothing, stating it more precisely when he said in the same place that the term Habere signifies that adornment which is placed close to the body, as is the clothing, and Sword.

From this compound Man with the Sword in hand, which is the superior form that he acquires for perfect adornment, it results in an important question in this science, whether it admits a definition, like an accidental concrete, considered by substance and accident; or if the man is to be defined by himself, and the Sword instrument by itself.

This difficulty is not foreign to the Schools, nor to this science, as there are those who hold the opposite opinion, saying that substance and accident do not make one by themselves. They base this on their position that all concretes, in which the form is an accident of some determined subjects, are named before by accident as the Metaphysicians, Vazquez, Suarez, etc. have.

From this major premise, they derive the minor, and say: One by accident cannot be defined, according to the Philosopher: hence accidental concretes do not order a Predicament, because they do not admit genre, nor species, nor are definable, because they are not one, but many.

In such an apparatus, those who want the concrete, Man armed with Sword, do not admit a single definition, but distinct definitions, one of man and another of the instrument Sword, or the species of weapon with which it is adorned, understanding by distinct in the definitions the clothing, and Sword, as accidents of the concrete Armed Man.

To this difficulty it is responded that accidental concretes are defined, placing the subject in place of genus, and the accident in place of difference, as white man, black; naked, dressed; armed, unarmed, etc. The Philosopher and Saint Thomas do not disagree with this doctrine, teaching that in the accident, if it is taken concretely, the subject is defined in place of the genus, as Pedro with Sword, where Pedro is the genus, and the weapon Sword is the difference. If abstractly, it is defined, placing the accident in place of genus, and the subject in place of difference; e.g., armed with Sword is Pedro, where the weapon Sword is the genus, and Pedro, who is the subject, is the difference.

From here it will be correctly derived that the subject and the accidental form, although they do not compose one, like soul and body, do not therefore avoid that one definable results with respect to the union of the subject and form; e.g., man with Sword, although they are not one rational individual, at least is one, as subject and accidental form, with which it admits a definition: Likewise (although less perfect) the Kingdom, the Army, etc. composed of more diverse parts than man with Sword, where the doctrine of the Philosopher and Saint Thomas takes place, placing the subject for genus, and the accidental instrument for difference; or vice versa, according to whether it is defined concretely or abstractly.

In further agreement, that man with Sword in hand admits a quidative definition (like an accidental concrete) and that the Philosopher could understand it in this Predicament by one definition, and not by different ones; is the reasoning of Saint Thomas, expressing: That although the mode of signifying is not achieved by the mode of being of things; however, it is achieved, through the mode of understanding: e.g. the man with Sword in hand (which is the main subject of this Science) with respect to the immediate being of things, includes distinct parts, composing the accidental concrete of man and weapons: and yet, through the mode of understanding in operative union, it is achieved in this Science, that it is one definable.

It is more evident, because man and Sword, extensively, do not act by two impulses, but by a single impulse, to which this Science looks: then it admits a definition; if in concrete, in the subject in place of genus; and if abstract, by subject in place of difference, as has been demonstrated.

This consequence is deduced from reason: because abstract knowledge, although it is not immediately generated from the things themselves known that compose the accidental concrete Man and Sword; it is generated at least by the operations, or by the accidents of the same concrete, because the knowledge of the substance of some subject is acquired from the operation of the same subject; e.g., man with Sword results in being known by such species that are fundamental to the formation of real being: with which the compound Man with Sword is known as one in unique knowledge, as to the effect and operation it has, since they indivisibly come from man and Sword: then if the entity of reality is perceived by the knowledge of the operation and effect: that entity is known as one, in which the effect and operation is one by unique impulse, resulting in that in the one compound of Man and Sword (because by one way proceeding from one impulse, it has the operation and the effect) all the cause Man and Sword is defined as one in the way of one.

It does not hinder opposing that in the compound of Man and Sword, the cognoscibility comes from operations and accidents, which necessarily by objective concepts admit distinction, and as such are apprehended: then not as one are Man and Sword known, and thus they will be two definables, even if they are considered one by accident.

To solve this, we must understand that the essential whole, which includes operations and effects (as far as knowledge in this Science is concerned) comes from the same whole in the way of one, and it is conceived as a real being by a unique comprehensive knowledge, even though by the reason of diverse operations and effects it can be distinguished in various degrees; e.g., the compound of mortal body and immortal soul has those operations and effects that are called vital, animal, and rational; and these, with respect to the body and soul in the way of one, we know them as coming from a principle, and everything in the effective and operative way comprehensively as one, we know them as coming from a principle, with which a single real being is formed: then in this Science in the compound of Man of the instrument Sword (which corresponds to what is mortal, transient) by the rational soul (root of the impulse and movement of the whole compound) are produced those operations and vital effects, which are called movements, tricks, wounds, etc. these, as coming from a radical principle, are known in one way, which is called Whole operating): hence in this Science a single real being is formed, and the compound of Man and Sword is defined as one, resulting in this Science to be of understanding, and exercise, which is commonly named Skill, and the scientific subject Skillful, the object being the Sword scientifically ruled. So, the Philosopher rightly admits in this category as one Habere gladium.

These considerations produce perfect knowledge of the Skill by the operating union of man and Sword, accidental concrete, which in this Science, art, and experience is called Skillful, conforming to the most used term, and easier to understand, and to define, as one understood, according to its whole: with which properly all operations and effects are explained and understood, as of a defined one, and not as different ones, because extensively, as far as the acting is concerned, they are not different compounds, or subjects, man and Sword, but an accidental concrete, which composes one, and is understood, and known as one, and admits a unique definition in this category, as expressed by the Philosopher, saying, that Habere signifies in man to be adorned with clothing, and Sword.

It does not hinder this conclusion to say that in this Science, when the parts are distributed (to cause more clarity) the man is defined by himself, and the Sword, the Given, and the other weapons are also defined by themselves with unique definitions: then to man, and Sword does not embrace a definition by complex term, with which we return to the previous objections.

The response is that this and the other objections are easily dismissed; since the head, the arm, the foot, the movement, the compass, the posture, the trick, the wound, etc. are defined as parts of a whole, to understand their minute elements in operations and effects, not because the essential definition of the concrete does not include the parts, but because for the distinct understanding of a whole, the understanding of each of its parts is necessary. The parts defined distinctly all together do not exceed the whole, and are included in its singular definition, just as the matter and the form in a man have distinct definitions; and yet, the man is defined as one.

In the same way, the accidental concrete Man with Sword in hand, subject in this science, in itself, and in its single definition, includes all its parts, which do not exceed the whole, which is called Fencer, in whom any minutest species of weapons is included, as adjuncts, although they are defined and considered as parts of the whole, which is one, and one defined in operation and effect, as has been demonstrated: so this last objection has no place, nor is it foreign, but proper to define the whole as a whole, and the parts as parts, which according to their being have special definitions, without contradiction of the universal of the whole, which includes its parts, whether it is integral, or universal.

SCHEMA OF HABIT

  • Habit, Habere
    • Of the whole
      • Clothed
      • Armed
    • Of the parts
      • Hat, etc.
      • Sword, etc.

SEVENTEENTH DISCOURSE.

POSTPREDICAMENTS, of the Opposites.

The Philosopher (if well understood) added light to different issues, almost Predicamental, immediately after the referred ten Predicaments, referring to the preceding categories. The same necessity is done in this Science, following the method, and order of Aristotle, who first discussed the species of Opposites, reducing the main ones to four, in which Logicians, and Metaphysicians engage in subtle disputes, from which what is most proper for this Science will be selected, in which also the four species of Opposites, noted by Aristotle, and warned by Saint Thomas, also run in the Schools.

The first species of Opposites is that of Relatives, which was discussed in the third Predicament for its pure Predicamental nature. The second, of Contraries, or maximum extremes. The third, by Privation. The fourth, contradicting, or Contradictory. The generic definition is formed thus: Opposites are the extremes, which admit and have repugnance among themselves.

If they are Relatives, they are understood as strong to weak, Skilful to not Skilful, or the opposite, etc.

If they are Adverse in maximum extremes, they are understood as Those, which being of one genus, are maximally distant from each other: not with respect to place, like Earth to Sky; but with respect to the opposition in defending oneself, and offending the contrary, with the science of intelligence, and exercise in the strength of the instrument Sword, which art provided, use introduced, and necessity proved by science, and experience, and which are admitted, and valued by men in Political and Military Nations.

These opposites, which are of a genus and species; although distinct, they are considered in maximum distance contrary, not only by the placement of bodies, but by the position, and operation, which diametrically, is put in defense, and offense, both in the mode, and in the effect, with which they admit the term, and definition of extremes, maximally repugnant, not like man, and beast, that although they are contained in the genus Animal, and fight among themselves, it is with the difference of rational to irrational, which in that one can have science of intelligence, and exercise to wound, and kill the beast with hunting skill; and this one opposes no more, than with instinct, and forces, that it acquired in its own nature, without reasoning: so they are not diametrically opposed at maximum distance, nor are they comprehended under one species, nor are they opposed in maximum extremes. Then man and beast are not merely adverse, contrary, opposites in this Science, the man armed with Sword against another in the same form, in which there is a perfect opposition diametrically repugnant at maximum distance, and extremes by genus, and species.

By Privation it is understood, not only the maximum distance of opposites (which has been pondered) but also that operative opposition, caused in what having arrived, to have formality, it loses it by accident: like the one who was born with sight, and lost it due to illness, or other causes: the same is said in this Science, that combatants oppose each other by privation, because each one of them tries to cause it to his opponent; in such a way, that he does not get to achieve his Stratagems, depriving them at the time of their formation at the beginning, middle, or end, using the precepts of this Science, in which it is reduced to prevent the Skilful the actions of his opponent; in such a way, that he does not enter his jurisdiction, causing him privation in his operations, to always be superior to him, in the force of privation, and subjection to which he needs.

Noticing, both in the opposition by maximum distance, and by privation, that all the Stratagems that are chosen with knowledge, have their distances, and proportionate means (according to their species) and in the disposition, which is acquired with each one of the means, includes the privation, which is caused to the opposite contrary, so that it cannot offend at the time it is offended, that in this they are always, and must be maximally opposed, for being a precept, inviolable in this Science, and indispensable in it to deprive the contrary of being able to offend, when it is offended.

Contradictorily, or contradictory, is that reasoning, which by formal argument, disput.ing by contrary means, investigates the truth until convincing the opposite with the infallible demonstration, which is contrary to sophistical refutations. This is called contradictorily, or contradictory, as in this Science, not only are the actions contradicting, but the reasoning, and arguments, with which the infallible certainty is investigated by means of syllogism, and demonstration; since as the Philosopher teaches, the affirmation, and the denial, it is necessary that they are not simultaneously true, but that one is true, and the other false, as to the contradictory, or diametrically contrary, although in the relative the opposition is in another way, like double, with respect to half, etc., as Aristotle discusses at length, and Logicians dispute (where the curious will find what to employ their wits) recognizing, that the matter of Opposites, not only includes the Physical contraries, but the Metaphysical ones, it being appropriate for the Logician the reasoning of one, and the other, by contradicting, or contradictory: satisfying the Skilful with the sufficient understanding for this Science, in which contradicting, and contradictory are found

SCHEMA OF OPPOSITES

  • Opposites
    1. Relatives
    2. Contradictories, or Extreme opposites
    3. By privation
    4. Contradicting, or contradictory

PRIORITIES, OR FIRST MODES

After discussing the four species of Opposites, the Philosopher considered four other terms, which he called First Modes, conceding them as ancient, to which he added another, which he called Causality. The ancient ones are: 1. First in time: 2. First in consequence: 3. First in order of teaching, and speaking: 4. First in dignity: 5. First in causality. There is another Priority, not attained by Aristotle, nor by us, without the light of Faith, which is Priority of origin, which pertains to Theologians.

For understanding, each mode will be defined by itself. 1. First in time is that which, with respect to the same succession of time, had being in the term Before, to which the term After is posterior: e.g. in this Science those Stratagems, and wounds are considered first in time, which are acted from a free cause, and are executed first in time, which are acted from a free cause, and are executed on the contrary, when there is a disposition for them, without communicating his Sword, or by communication of it, without any preceding voluntary movement of his own; and these are called first in time, because they are in the term Before, from which they receive the denomination of First intention, as well as of Second, the Stratagems, and wounds, which are After movements of the contrary, with which it is understood what in this Science is first in time.

2 First in consequence is that which results consequent from some first principle, as in this Science, it is understood, when the contrary forms Stratagem, and the Skilful, taking advantage of his movements, forms another, in which he first achieves execution: and this is called First in consequence, because the other does not have it.

3 First in order is that which, according to disposition, is placed first. In this Science there are precepts in the formation of Stratagems, and wounds, in which the First intention precedes the Second, giving each one the place, and order that belongs to it, thus avoiding confusion, with which it is recognized what Stratagem, and wound is first in order.

4 First in dignity, it is understood that which, with respect to another, with which it is compared, is more worthy. In this Science, in force of this fourth mode, it is recognized that there are three dignities of Stratagems: the greatest is understood that which is by means of the movement of conclusion, because it deprives the contrary of his Sword: and if it is in all perfection, it can also deprive him of his life; and for such effects, this species is considered first in dignity.

The second ones are the four general Stratagems, which are named of second dignity, because they are immediate to the first, and each one has jurisdiction over other more particular ones, which are inferior to them.

The third dignity, or lowest, includes all the special Stratagems, which can be formed, according to ordered power, as with distinction, precepts, and demonstration, of each one is dealt with in their proper places.

5 First, by causality, is the fifth mode, which the Philosopher added to the four mentioned: And it is understood as that which, considered by causes, is first in respect to another, which although also considered by causes, is, or can be, later.

In this Science, the first in causality is understood as that Stratagem, which from its formation causes another, or others, to form, as has been demonstrated in the third Category, in the relation that some Stratagems have to others, from which it is recognized which are the first by Causality: with this we refer to the Category of Relation, concluding that this doctrine of Priority is essential in this Science, because of the application of these five modes, which give knowledge of what is first, and subsequent: with this, the understanding perceives what is first in time, in consequence, in order, in dignity, and in causality; and in this last one more detailed explanation will be seen in the Topics.

SCHEMA OF PRIORITY

  • Priorities
    • In time
    • In consequence
    • In order of teaching, etc.
    • In dignity
    • In causality

SIMILARS AND DISSIMILARS

The Philosopher considered Similarities, or Similes in two ways, either by Time or by Nature. By Time, those are considered similar that, in the same period of time, are similar in their causes and their effects; this mode of similarity is what is called by time, like the first-intention injuries, which are similar by time because they do not depend on the movement of the opponent but on the free agent, which is called a free cause because it is not dependent on another. In effect, they are similar because they occur without preceding movements or movements of the opponent on which they would be forcefully dependent.

Similars by nature are subdivided into two modes: the first, in those that receive reciprocation, even though the cause of one is not the cause of the other. Such are the Narratives that admit reciprocation in their origin, being distinct because the immediate cause of one is not the immediate cause of the other, as in natural filiations and productions, to which the movements and injuries in this Science allude, that can proceed from one another, receiving reciprocation in their principle; e.g., the Downward Cut and the Half Downward Cut, the Upward Cut and the Half Upward Cut, which receive reciprocation in their principle in such a way that although the cause of one is not the cause of the other, as every movement that proceeds from a primary causal action can be the cause of another, the Whole Downward Cut, Half Downward Cut, Upward Cut, and Half Upward Cut can receive reciprocation in their principle, considering the reciprocation they receive from their natural principle, which is the formation of a cutting injury, where the Half Downward Cut has a certain filiation from the whole, by production of its nature. To derive the lowest species, it is necessary that there is an original cause from which it derives, like the son from the father; and thus the Half Downward Cut from the Whole Downward Cut, noting that the lowest species receive reciprocation in those that are causal causes by nature, although they are distinct from each other.

In a second mode, similars by nature are also considered as being so with respect to the genre, although the species are dissimilar: e.g., the man and the beast are similar in genre by nature, and are dissimilar in species, as in this Science, the Downward Cut and the Upward Cut are similar in genre and are dissimilar in species, because the genre that encompasses all sharp injuries is slash. In species, being of the same genre of sharp injury, the Downward Cut and the Upward Cut are dissimilar in species because there is perfect distinction of similar in them; and in this way in the other injuries, genres and species are considered, recognizing in what they are similar, and in what they are dissimilar by nature and principle, and in what they admit reciprocation, or are not capable of it.

SCHEMA OF SIMILARS AND DISSIMILARS

  • Similars and Dissimilars
    • By Time
      • By First intention
      • By Second intention
    • By Nature
      • By reciprocation
      • Like the cutting wounds in their species
      • Or by genus, and species

EIGHTEENTH DISCOURSE

ON MOVEMENT AND STILLNESS

The material cause in this Science is the movement, to which stillness is the term, with which stillness, considered in itself, is opposed to movement, because just as the power that is not reduced to action is in vain, so too is the movement that is not reduced to the term in which it acquires stillness, perfecting the effect in defense and offense, which is the final cause to which all the perfection of Skill is directed, whose greatest foundation is in movements that end in execution, offending the opponent, or depriving him of the ability to offend, which both stem from terminated movements, because as long as they do not reach stillness, it cannot be said that Tactics and Wounds receive essentially consummated forms.

For such a subject, it is necessary to know what Movement is in its Genre and Species, as understood by philosophers, and how it is understood in this science? In philosophy, movement is understood in various ways, because some admit it as absolute, like Plato, others deny it, or ignore it at most, as noted by Galen. Democritus tried to reduce all movements to oblique or circular ones. Epicurus granted eternal movement to the eternal, and temporal movement to the temporal. From these and other philosophers, Plutarch compiled various opinions, which the curious can see.

Metaphysicists consider that nature itself is the principle of movement and stillness, with a permanent state in eternal things, and in temporal ones, with continuous or frequent movement in some subjects, and with an interval in others, and the aptitude to move and be still.

Plato assigns distinct metaphysical movements to the powers of the weapon, calling immanent action those that are in the agent itself, as in the subject, being the understanding of the intellectual power, the wanting of the appetitive or voluntary power, and the reminiscing of the memory. These potential movements look at intrinsic operations, and in this science, these very metaphysical movements are not considered, but rather those that can be perceived as real entities, or as physical and external.

Plato identified ten species of Movement: 1. Circular, or in a circle: 2. Local transit: 3. Condensation: 4. Rarefaction: 5. Increase: 6. Decrease: 7. Generation: 8. Corruption: 9. Mutual change from one to another: 10. Change in itself, and in another. Aristotle, in various places, noted various species of Movements: some spontaneous from nature, as in the Elements and the Heavens; others voluntary, or forced, as in animals, granting movement either inherently or accidentally, according to the causes and effects. Finally, he categorizes them into their specific genres, mostly agreeing with Plato: 1. of Generation: 2. of Corruption: 3. of Increase: 4. of Decrease: 5. of Alteration: 6. from Place to place. The same philosopher notes that all movements, in relation to each other according to their genres, are diverse and all contrary to termination or stillness, and can also be contrary to each other, as generation is contrary to corruption, increase is to decrease, etc. He observed in the species elevation and fall, and categorized alteration, mutation, movement, and stillness under the Predicament of Quality, acknowledging that alteration can be found without increase, and vice versa; and the mathematical increase can be without alteration, as in the square, or parallelogram, whose gnomon can grow and not be altered.

Celio Rodigino, following the teachings of Pythagoras and others, identified six species of Movements, by as many straight lines, which are: 1. High: 2. Lowest: 3. Right: 4. Left: 5. Forward: 6. Backward. And from these positions, he inferred, noting that every Movement, the more direct it is, the stronger it is; and the more oblique, the weaker.

From the preceding principles, as the most essential for this science, Movement is defined almost in its supreme genre, describing it thus: Movement is the aptitude of natural power, poured into the whole subject capable of moving, in which it causes its own or foreign impulse; if it’s own, in man it is produced by the rational soul, spread throughout, and in the parts of the subject, which results in movement in the whole and parts, not only in its individual, but extending the impulse to the instrument that moves or incites, as in the weapon that moves, or throws.

This descriptive definition embraces more latitude than the quidditative one in this Science, where the subject is reduced to the accidental concrete, composed of man and Sword, with which it could be cinched, saying: Movement (in this Science) is aptitude of natural power, caused in the whole, and in the parts of the subject by the rational soul, from whom, as a physical and organic instrument, the virtue and motive aptitude is produced, which by impulse, and extrinsic touch is communicated to the instrument Sword.

This definition, although also generic in terms of movement, is specific in the defined subject, which is one, and admits one definition, as was proved in the tenth Predicament, with which the division can be made in the species of simple and compound movements (as this Science admits), gleaning for this the most essential, excluding what is not so proprietary.

In consideration of the species, which have been noted in the cited Authors, and others, six simple species are chosen for this Science, and others mixed, which both, and others have their origin in the six rectitudes, which touched Celio Rodigino, by opinion of Pythagoras, whom Don Luis Pacheco de Narvaez seems to have followed.

The six species of movement, which are considered in the man, after having placed the arm in the plane, that corresponds to its principal center, as it comes out of the shoulder in rectitude, are 1. Down: 2. Up: 3. To his right side: 4. To the left: 5. Back: 6. Forward. The simple species of Movement, which originate from these rectitudes, are understood by their terms: 1. Natural movement, when the arm lowers: 2. Violent, when it rises: 3. Remiss, when it moves from the plane of its birth to its right side, and to the left: 4. of Reduction, when from the extremities of both, the two return to its plane: 5. Strange, when it retreats, preserving the same plane backwards: 6. Accidental, when through the same plane it returns to stand upright, as it comes out of the shoulder, without participating in the jurisdiction, which belongs to the other five species of movement.

Of these six simple species of movement, only the accident is not capable of mixing with the other movements, and the other five species are: and because these simple and compound movements, and those considered in some of the species (which take their denomination from their effects) are treated at length in the second Book, we refer to it, as its proper place is there.

Contrary to movement is what is understood by the word Stillness: and in this consideration, the Philosopher repeated, that just as there is movement contrary to another movement, so too the term that lacks movement absolutely opposes, and this is Stillness, also understood as effective deprivation of all movement, from where Plotinus said: Stillness opposes movement: then it is the opposite. Thus in temporal things he says deprivation, or change of all movement, what is named Stillness, because diametrically Stillness, and Movement are opposed.

From these certain principles, an essential definition results, saying: Stillness has its principle in the end of movement, either by suspension or by permanence. From this definition it is derived for this Science, that in the actual termination of all movement, either the beginning is given to stillness, or in the same instant that it is acquired, aptitude for new movement is obtained; and when this happens, there is no existing permanence, but instantaneous suspension. With such distinctions, what is Movement, and what is Stillness is understood in this Science, and in others, because it is always immediate to all the actions, and consummated acts of man, for the possibility of his whole, and parts in the operations of this Science.

NINETEENTH DISCOURSE.

ON DEMONSTRATION

In an attempt to avoid the commitment to discuss, while explaining the Philosopher in his books of Perhiermenias, Analyticos, Priores, and Posteriores, what is inescapable to this Science in the part that pertains to demonstration (which Aristotle extensively treated), the basis for Topical places emerges, recognizing that Definition serves as the basis, as a principle for Demonstration in every argument, with defining being the same as forming a summary of what is defined, the subject of what can be demonstrated, from which it can be said: Demonstration is an argument that produces in the rational intelligence perfection in knowledge by causes, because it is not perfect knowledge to know by effects, but the effects by the causes: according to this maxim, in this Science the Demonstration is an argument that produces in the Fencer the knowledge of the fundamentals of this Science, and of the Tactics, and wounds by their causes.

This knowledge is achieved by two means of investigating and proving, one Philosophical, and the other Mathematical. The Philosophical is by reasoning and entities, and it will be said with the Philosopher: Demonstration is a syllogism, which consists of true principles immediate to primitive knowledge, from whose causes the conclusion originates. The Mathematical is by evidence, which results from the arguments, Problem, and Theorem, as means of demonstration, as Clavius ​​proved.

These definitions are understood by Logicians and Mathematicians, both in the term Science, and in that of Demonstration: agreeing that there is a certain apparatus that precedes, to which the name of Prenotion is given, which is that antecedent knowledge of the parts of the Demonstration, considered before the distinct formality.

Prenotion is divided into that which exists in the nature of things, and that which is part of the Demonstration: and both are acquired by two means, which are acquired by real entity, or by Mathematical entity. In the first way, reasoning works by discourse, and syllogism, enthymeme, dilemma, etc., constituted in their figures, forming propositions, premises that Dialectics call Major and Minor, from which the consequence results. In the second, the demonstration of what is perceived by Mathematical entity is achieved, either by Problem, or in Theorem, which precisely makes infallible the external knowledge of the Mathematical entity.

Through both means, argumentation and proof are applied in this Science, as will be seen in the second Book, where the theoretical is reduced to practical, distinguishing the propositions of Tactics, and wounds, some of which can be theorems (demonstrating themselves as infallible) and others problematic (which are understood as possible) and in these contingency takes place, not on the part of the proposition, but of the operation: noting that in one way or another, a demonstration is not perfect that does not have evident certainty in its genus and species, because only demonstration is given of what is necessary, or evident.

Given the above, it is a common question in Schools whether First principles are science, and if they are, on what are they based? The Philosopher’s sentence resolves this, The first principles are known first, and more than the conclusion. From the reason the consequence is deduced, because the Conclusion in the Demonstration must be known, and evident, and produced from antecedent principles: therefore, the First principles are known more, and before the conclusion.

For further clarity, it is assumed that the term Science, is admitted variously by the Philosophers, saying Being that certain knowledge, which the understanding acquires by necessary means. In this way, knowledge through first principles can be called Science: in another it will be when the certain knowledge of the conclusion is acquired by Demonstration, although in this strictly it is not acquired by science in the Schools, but by intelligence, as the Conimbricenses, and Louvanists argue.

From such opinions arises the inquiry, in what way is the knowledge of the First principles generated in the understanding? To this difficulty, the Platonists respond, that such knowledge is in man, as inherent by nature, because (as Plato himself suggests) the rational soul was created with the knowledge of the essential first principles. Aristotle, and with him all the Peripatetics, oppose the Platonists, affirming, that the rational soul at the beginning of its creation, is like a blank slate, on which nothing is painted, from where they induce, that the knowledge of the First principles is acquired by man by induction from the sense, passing to memory, and from repeated memory to experience, and from experience to indubitable knowledge, originating from all that is named First principles: e.g. reasoning will be said: The whole is greater than the part.

This common notion is recognized, that it is by induction of the sense, which passed to the memory, and from memory to experience, and from experience to indubitable knowledge, which acquires by such means what is a First principle, defined as: Being a collection of singulars contained under a common demonstration or reason, with which a universal principle was generated in the understanding, that the whole is greater than the part. The same is found in the other First principles, from whose certainty the species of science is achieved, which, although it is not by causes, comes to be so by infallible Demonstration, acquired in the understanding before the conclusion by principles, which are in such a way that they not only signify infallible concept, but numerically they are what is known with certainty.

As a complement to the above, the difference between Opinion and Science must be considered, and how they are distinguished: because (according to the most common) Science properly is the knowledge of effects by causes, from where the Poet said:

Happy is the one who is able to understand the causes of things.

Opinion is understood as that knowledge, acquired by objective concepts; or at most, by reason entity, with which probability and fallacy fit, and is distinguished in true and fallacious: True is that where the essence of the believed is, as it is believed. The Uncertain, or false opinion is defined by this, that it is the one that is produced from a mediated, fallacious, or contingent proposition. The reason is, because that from which opinion is formed (although to make it, it is estimated to be the same as the true essence) in so far as it is not demonstrable, it cannot be estimated as a certain and necessary thing, and so it arises from a mediated or contingent proposition, which does not admit infallible demonstration: if it admitted it, it would cease to be opinion, and it would be science; but it is not science, because it is only based on a mediated or contingent proposition. Mediated proposition in the Schools is understood as the one that admits other intermediates, and these do not make a demonstration as long as they are not reduced to immediate ones in the infallible conclusion, for whose cause, by the immediate ones, science is achieved.

From all this, three differences can be gleaned between Science and Opinion: the first, that Science is certain and necessary knowledge, and Opinion is uncertain, deceptive, or not necessary; the second, that Science is about necessary and permanent things, and Opinion about contingent or variable things; the third, that Science works by demonstration, and Opinion (at most) by probable reasoning, even though in appearance it induces demonstration. Concluding in good philosophy, that true science works by demonstration, without admitting pure opinion, because of one same thing in one same subject, and time, man cannot have opinion and science, because they cannot be given, because certain and uncertain knowledge do not coincide in one understanding, since they necessarily exclude one another; and thus, two diametrically repugnant contradictories do not exist in the same one, such as white not white, right not right, etc.

For all this, in the Science of the Sword, Science and Opinion are diverse, because the actions of man, and his way of understanding, and acting is diverse, and those that are done with science admit infallible demonstration, and are done with perfect knowledge; and those that are only of opinion, are subject to the contingency of being certain or uncertain; for example, any Treta (trick or ruse) that is done and formed with science, admits a demonstration that completely satisfies reason and understanding; and the one that is only by opinion, is subject to uncertainty, and deception.

Having taught the Philosopher in the posterior Analytics the essence of Demonstration, and Science, he formed the eight books, which he titled Topics, which is the same as places, which make the basis in the thesis, or hypothesis of the argument, from where the true syllogism arises, which receives the name of Topic, which means the Potissimo probable, just as the Elencho, or defective, we reduce the Topics places to the ten most received in the Schools, excluding those who put more number, to which various questions are introduced, which are omitted, for not being proper to our subject.

If we look at the Etymology of the term Topic, it is a Greek word, whose meaning is thing of place, from where the term to find places for arguments was chosen, as Cicero widely showed, and Aristotle taught, qualifying the second species of probable syllogisms, to whose sin are investigated those who are named common places: of the arguments, in which for any question the probability is found: and for this reason also to these places Topics are given the same name, and that of invention: because with such a medium, common places are recognized, which make a foundation to the arguable, which in its whole such art is titled Dialectic.

The utilities that result from topical places are many: among others, the Philosopher notes four: the first, that they are beneficial in the conflict of disputes in any science; the second, for the understanding they lend in the dialogues and writings of the Philosophers, to refute some sentences, and accept others; the third, because they produce the most probable consequences in difficulties; the fourth, because they demonstrate the first principles, because the topics themselves are first principles.

The first contains those propositions that are accepted by everyone, like axioms, or like notions, that they call pronouncements, which are especially used by mathematicians; the second, those that, if not by everyone, are received by many; the third, those that are confirmed by classic authors; the fourth, those that result from what is the common consensus of the wise, both in sciences and in arts; the fifth, what the experience and demonstration produce; the sixth, those that are composed of authority, and reason, with which the understanding agrees. From everything it results the difference, that exists between probable and necessary, because from the probable one does not achieve more than opinion; and from the necessary, science: and this is permanent, and the probable is not, because it depends on what is opinable.

An argument is reason, that makes faith in the doubtful thing. It says Reason, because not everything that makes faith, is an argument. It is proven by example: sight makes faith, as far as what is seen. And yet, it is not an argument, because it is not discourse. Discourse, then, is reasoning, and not physical sight, and the argument is discourse, and reasoning: then sight, although it makes faith, is not an argument: then not everything that makes faith, is an argument but probably by reasoning.

It manifests mathematically in the difference that there is from speculative geometry to the practical one, and from working with ruler and compass, or by speculation: because the speculative is by mathematical entity, acquired by reasoning, that makes faith in things, as probable: not like sight, that makes it without giving reasoned faith, but by visible evidence, in which there is no argument.

In the Science of the Sword, these two differences are found in Tricks and Wounds: some are achieved and proven by argument, in which there is a probability that makes reasoned faith, and others by visible experimental operation, in which no reasoned argument precedes. These are the ones that are performed without Science, by observations of those who only have empirical exercise, unlike those that are done with perfection, in which science concurs. For these, the places called Topics are sought, and also to make evident the imperfection of the others. And the Topics are defined, according to the understanding and explanation of various Authors, in this form.

Cicero called them Place, or seat, receptacle, or treasure of the argument, in which indication of what is sought is found on one side or the other, facilitating the demonstration in the disputable, by means of the explanation of places. And the same Cicero distinguishes that this receptacle, or treasure, should be considered, like gold in the mine.

Aristotle, more Philosopher than Rhetorician, defined: Place, or Topic is the element of the enthymeme; that is, place, or principle, from where the enthymematic arguments are taken. Rodolphus Agricola compared the Topic places to the receptacles, or boxes of the Boticas, where the simples from which the antidote is composed are found by the labels.

As for how many these places are, due to the variety of opinions, it admits a large dispute (alien to our intention), so we refer the curious to Aristotle, who put many in eight books: and in the Rhetorics reduced them to 28. other Ancients, and Moderns to 23. and to 24. and to more, and to fewer numbers, as seen in Santo Thomás, Alexandro Aphrodisiense, Theophrastus, Rodolphus Agricola, etc.

In line with our objective, following the Moderns to Dr. Pedro Juan Nuñez and others, who have sought to reduce these topical places to a few, we choose ten, the most accepted in the Schools, which are: 1. Causes, 2. Effects, 3. Subjects, 4. Adjuncts, 5. Comparison, 6. Differentials, or opposites, 7. Definition, 8. Division, 9. Etymology, 10. Authority.

1 Cause is where the effect depends: so the cause is first, then the effect, and always distinct and essential as far as itself is concerned, because there is nothing created without cause, although cases of causes occur, as Aristotle exclaimed: natural causes in Philosophy are four: 1. Material, 2. Formal, 3. Efficient, 4. Final. Place them in Philosopher, as they have been put, and the Schools concur in the same order, for the reason that Pedro Gregorio gave, conceding that matter and form are causes, and are principles, with the distinction that form comprehends the subject matter; the efficient, which comprehends matter and form; and the final, which comprehends the efficient: and to this method of linking causes the Greeks signified with the word Symerasmatha, which means as much as Linkages among themselves, from where with the current of Philosophers the same Pedro Gregorio noticed, that some causes can be causes of others, although in their placement they are respected for comprehension and dignity, more than for another reason, the Schools agreeing that the first is the Material cause, second the Form, third, the Efficient, and fourth the Final.

Causes are distinguished into universal and particular: universal are God, Nature, the Sun, etc. in the particular are Father, Mother, Craftsman, Fighter, Expert, non-Expert, etc. Causes are given by accident, such as Occasion, Chance, etc. that do not produce universal causes. Of this kind are the Tactics of the opposing fighter, who as a free agent forms them; and being of this quality, the Expert with his universal knowledge acts against them with science and art, and such Tactics are called accidental, because the Expert, although à priori he has knowledge of all the possibility of his opponent, the individualizations that precede from it, are accidental acts.

Causes are also distinguished as intelligible and operative: intelligible ones are those that the understanding perceives without reaching the executed operation. Such are the Tactics, which in terms of premeditation are metaphysically perceived in the intelligence, by the discourse, and the reason of the Master, in such a way that it is not purely by being of reason, which is subject to being a chimera, but by real being, that can pass to mathematical being, although it achieves no more than aptitude for execution. Physical ones are those that are physically and naturally considered and executed; and in both, this Science consists of intelligence and exercise.

Material is that which has the aptitude to receive form. Matter is divided into sensible and insensible: sensible is that which the sense perceives, such as metal, accepting various forms, and like movement, which admits various Tactics, etc. Insensible is called that matter, which is only perceived by the understanding; and from such cause it is named intelligible: and in both ways in this Science, Matter is considered in its causal principle, compared to the prime Matter, which philosophers call.

Properly in this Science, movement is given as material cause, because it has aptitude to receive various forms in genus, and species, as is demonstrated in the second Book, and remains touched in its place, where Movement, and stillness were treated.

Form is that which comprehends the matter, and constitutes in it a formed thing, distinct from another. It is divided into essential and accidental: essential is that which constitutes perfect, natural, and physical formality, like the rational soul, which is the essential form of man, in whom, as a physical and organic instrument, the soul vivifies, and provides the essential formality, constituting a living animal, participant of reason, distinct from the brute: accidental form is understood as that, which is considered by some accident, in respect to the subject, as taught by the Philosopher, although in the common sense of the Schools it is applied to the Predicament of Quality, and the Expositors move the questions in the explanation of the fourth species, and touch the terms conform and deform, beauty and ugliness.

From this place arguments are produced by formal cause, both affirmative and negative: for example, in affirmative, does it have a soul participating in reason? Then it is capable of science and discipline, etc. Is it constituted by coupled terms? Then it is a figure in terminated quantity, etc. in the negative, is it an animal participating in reason? Then it is not a brute: is it not constituted by coupled terms? Then it is not a figure, etc. and note that if the form were accidental, it would not produce a firm argument, but at most, probable.

Concluding for this Science, that in natural forms, which are considered by intelligence and exercise, the form is conjoined with the matter; and in the formal it comprehends it, because the material power passes to actual, which is form introduced by efficient cause, just as the metal passes to statue by the Craftsman, who reduces to formal act the potential, with which the matter comprehended by formal cause, is reduced to formality of statue, or other figure, by the Craftsman. The Expert also forms the Tactics, and wounds, in which the matter, which is the movement, or movements, are comprehended by the form, or forms, that by the efficient cause (just like the Craftsman in the metal) the material passes from potential of material cause to act of formal cause, constituting Tactics, and wounds, formed with distinction from one form to others, as experienced by the Expert, that being the material cause the movement in genre, he comprehends it, and reduces it to forms of Tactics, and distinct wounds, which by the form are different from each other, with distinction from one to another. In them is also found the division of essential and accidental formal cause, in which the referred doctrines are applied, by the common consideration of causes, from which places are taken for the arguments topically; for example, by affirmation is it a cutting wound? Then Slash, Chop, Reverse, etc. is it a puncture wound? then Thrust in its genre and species, etc. and by the negative is it such a Trick, or wound? Then it is not its contrary. Is it a wound of first intention? Then not of second.

From what has been discussed in the Material and Formal causes, we come to the knowledge of the Efficient cause, which is defined: Efficient cause is that which produces effect in something, comprehending matter and form.

This definition permits numerous divisions, as the Efficient Cause is considered in various ways. Initially, it is distinguished in two manners of operation: one, that follows the necessity in the operation, restraining the will to the potency, as in the unskilled person, who is compelled by the skilled person to act necessarily against his own will or power; or because the same nature necessitates the operation, as in the fire, which heats; and in the snow, which cools, etc.

In another way, the Efficient Cause operates, either freely, or as obstructed: freely, in the wounds, and Tactics of First-intention; obstructed, in the wounds, and Tactics of Second-intention, with respect to the skilled and unskilled person, because the skilled person acts without impediment, as an efficient cause, free in power, in will, and in scientific knowledge, with regard to the same skilled person.

Philosophers consider another division in the Efficient Cause, which is in two ways: one, when the cause produces an effect by itself alone, like the Sun, which produces the artificial day, the skilled person the Tactic, and the wound, etc. Another, when the effect is produced, not solely from the pure and unadulterated efficient cause, but also another coincides, like the natural day, which is caused by two movements, the rotation, and the Sun: or as in this Science, when from the movement, or Tactic, that a combatant formed, a disposition is given for another movement, or Tactic to the contrary.

Another division is recognized in the efficient cause, for at times it acts subjugating, and at other times it acts as subjected to another cause, with such a distinction that when it acts subjugating, its effects are independent of another efficient cause, and when it acts subjected, it is in regard to another cause.

Another way to consider efficient causes, as philosophers call them, are Instrumental causes. These also allow for divisions, in terms of the instrument. For example, in this science, if the instrument - the sword - were absent in the efficient cause, which is the combination of a man with a sword, the actions of both the man and the sword would cease. Just as a man with sight, if he were missing his eyes (the instruments of seeing), his ability to see would end due to the lack of the visual instrument. In another way, there are instrumental causes that would not completely end all of the efficient cause, as they don’t provide the absolute action, but rather more aptitude, or comfort in the act, like a horse in cavalry actions, on the journey, or in combat. Even if it were missing, it would not completely remove the ability for the agent to fight or make the journey. The same can be said about the Skilled person. Even though a regular and perfectly proportioned sword gives him the aptitude to execute a perfect Tactic, if he were missing it, he could use a shorter or more defective sword to defend himself and attack his opponent, not with as much aptitude, but at least with the courage and skill that such an instrument could provide.

The efficient cause allows for divisions in other ways. One is when it produces the effect and preserves the power within itself to produce other similar ones. Like the sun, which with its presence and movements produces greater and lesser days, referred to as artificial, and conserves the power within itself to produce others. Similarly, the Skilled one, who produces Tactics and wounds, preserves the power within himself to reproduce and repeat many other Tactics and wounds.

These efficient causes are called preservative, in contrast to those that are efficient; sufficient, and not preservative, which are those that do not conserve power for new acts. For example, in the case of the unskilled one, who forms some Tactic and wound, but does not conserve power to immediately produce with knowledge and skill other similar or dissimilar Tactics and wounds.

From all this, it is concluded for this science that in it the efficient cause is the combination of a man with a sword in his hand. Including matter and form of movement, Tactic, and wound, it produces the effect of Skill through intellectual knowledge and exercise. This includes the five aforementioned divisions and others that can be found by ingenuity. From this, they establish areas for the efficient cause to form the basis of their Topical arguments, as is recognized and demonstrated in the second book in their appropriate places.

The fourth and final cause is for the sake of, and is defined as: The final cause is the ultimate end of the material, formal, and efficient causes; it comprehends them by terminating them. The end is divided into apparent and true: the apparent end is one that rests on opinion; the true one, on demonstrable evidence. The ends, generically, are either useful, pleasurable, or honest; these touch more on moral and natural philosophy than on this Science, which admits the consideration and argument, due to causes in the proper terms of understanding and practice of this Science. The final cause is defense and offense, which includes the preceding causes, as it is their ultimate end; and as far as the essential goes, we refer to the Discourse on Offense and Defense, where the most important aspects were attempted to be inferred; and here we conclude, that in Skill there are both apparent and true ends. The apparent end is one that operates by opinion, which at most seems probable: the true end is one that operates by knowledge, demonstrating topical places, because defense and offense are due to the final cause in the understanding and practice of the Sword.

2 The effect is what proceeds from cause to causes: like the day, which is the effect of the Sun, and of the swift and natural movement; the construction of the Architect, the defense and offense with a sword by the Skilled one. The effects are distinguished and receive names (as Rodolphus Agricola said) by the work, and the work by the cause; if by the material, they are material; if by the formal, formal, if by the efficient, ordered; if by the final, dedicated, or in other terms, that suggest the effects by the causes; and of one kind and another, for the arguments, they choose places, which they call Topical by effects, and in this Science the same considerations are held, looking at the causes, and the effects that proceed from them.

3 The subject is defined as: It is the receptacle of the adjuncts, such as the soul, which is the subject of the powers, memory, understanding, and will, and of science; and the living body, subject to health and sickness; and the whole man with a sword in hand, subject to Skill, etc.

This subject, Man armed with a Sword (as described in the first and last Predicament), is considered with different qualities, with respect to the individuals, with which they admit distinction, some with respect to others; and although the generic definition is one comprehensive in the lowest species, there are distinct definitions, according to the concurrence of the adjuncts, of which each subject is a receptacle, considered in its lowest species.

The subject admits another distinction, which is in three ways: the first is called of Inhesion, the second of Action, the third of Circumstance. Subject of Inhesion is that in which the adjuncts persist, such as color in the animal, in the plant, in the flower, in the armed man, in the unarmed man, etc., such qualities are specific inhesion in the adjuncts that persist in the subject. Subject of Action is that in which the essential subject acts with the adjuncts, and the adjuncts with it, as the fire in the wood, or another combustible matter: the man with a Sword, and other weapons: the Trick, and wound, with respect to the Skilled one; the statue with respect to the Sculptor, etc. Thus in this way all the objects of the senses, which concur in the work, are said to be subjects of action with respect to the sense, which deals with the object, and concurs in the operation, like the painting, the surface, the body, and every visible object, with respect to sight; the combatant, with respect to another combatant; the Sword, with respect to another Sword; the rational subjects, with respect to the Sciences, and moral and physical acts; the human body, with respect to Medicine; the numbers, with respect to Arithmetic; the Straight and Curved lines, the figures, the bodies, etc. with respect to Geometry; the Stars, and their movements, aspects, and positions, with respect to Astronomy; their influences, with respect to Astrology; the harmonic proportions, with respect to Music, etc. and in conclusion, these, and the other objects, which act as adjuncts with the essential subject, are called subject of Action in this second way.

Subject of Circumstance is that which is surrounded by adjuncts, like the Captain, who is a subject of circumstance, with respect to the Soldiers, who he commands in company; the Field Master with respect to the Military Third; the General, with respect to the entire Army; the City, with respect to its Citizens; the man, with respect to the habit and weapons, that surround him, etc. From this place to Subjects, theses, and hypotheses are taken for arguments by Inhesion, by Action, and by Circumstance, all considered in the subject, as a receptacle of adjuncts.

4 Adjuncts are directly associated with subjects because they are the accidents that persist in the subject. Therefore, topical places can be taken for arguments from any kind of accidents, because subjects and adjuncts are related, where any entity that admits adjuncts is named a subject, and adjuncts are those that are inherent, with respect to the subject in the three pointed out modes, of Inhesion, Action, and Circumstance.

5 This place is defined by saying: Repugnant, or Dissentaneous are those that oppose each other, such as disease and health; the combatant and the combatant, etc. These, and their likes, in which there is opposition of contrariness, are considered Dissentaneous, or Repugnant in two ways, because they are either discrepant or contrary.

Discrepant are those, not absolutely contrary ex diametro (like white to black, day to night, clear light to dark darkness), but that partly disagree among themselves, without becoming evident contraries in the whole.

Contrary in the whole are those, which oppose each other ex diametro, according to their greater opposition, as touched on in the title of Opposites, and Contraries, after the Predicaments, see the logicians in the true and simulated contradictories, dissenting, and repugnant, where the curious will find a wide field for this Topical place, drawing out very useful arguments for this Science; where there are Tactics, and wounds, that are only discrepant in the manner of their formation; and others, which oppose each other ex diametro by absolute contradictories, as demonstrated in the second Book.

6 Compared are those that have similarity among themselves, or can be Parallel, or consist of some analogy. This place includes the third Predicament of His, quæ ad aliquid, and after the Predicaments, what Logicians, and Philosophers discuss in the Similes, and Dissimiles, because all relatives and similar ones admit comparison, like in this Science all the point wounds (which they call Thrusts) and all the cutting wounds (which they call Slashes) and their species, like the Cut to the Cut, the Backhand to the Backhand, etc. The same in the Tactics, which admit relation, or analogy, from which you can draw out places of comparison, to form fundamental probable arguments in this Science.

7 That which is Definition, is extensively explained where its proper place was, and here it is only considered as a Topic for arguments, in which one must enter by the definition, which is rigorously antecedent to the question, because it is either the thesis, or hypothesis of the argument, and all of this Science, (just like in the others) have the Definition as their basis.

8 In Division we also refer where it was properly discussed; and here it is considered as a Topical place for the probable arguments, by the term that Logicians, and Dialecticians call Distinction; for example, Slash? I distinguish. Either it is a Cut, or Backhand, Half Cut, or Half Backhand. Tactic, and wound? I distinguish. Either it is of first intention, or it is of second intention, etc.

9 Etymology is a Greek term (as according to Cicero) it signifies Veriloquium: Correct way of speaking: this, as the same Orator explains, is properly a note of the thing that is preached. The word Etymology is composed of two Greeks, Etymos, which is the same as true; and Logos, which is locution.

The Philosopher named it Symbol, which means Origination. Favio, for more common phrase says, that the Scholastics call it interpretation, by the composition of words, from where the property of the term is interpreted. Topical places are extracted to argue by Etymology, inquiring the origin of the name. Such is seen in the common of this Science in the Thrust, whose etymology comes from Estoc, a weapon, that can only wound with its point, because in the rest of its form, strictly speaking it does not have cutting edges; and Slash by an armed instrument, which has cutting edges like a knife, from where the Greek calls the Sword Xiphius, and the Latin Gladius, both terms are generic for a cutting Sword is named Blade, from where Slash, and thus in this Science, other Etymologies are investigated, to form arguments.

10 Testimonies are worth as much in this Science, and others, as maxims, or sentences, or resolutions commonly accepted as true, or in such an authorized way, that they attest in the arguments, and one stands by them. Cicero divides this genre into divine, and human resolutions, or sentences, or maxims, drawing from all different species, which he subdivides into mediate, and immediate.

Those that touch this Science, are the ones that the same Orator divides into three generic Species: one, that touches on the authority, another on the will, another on discourse. Those of authority are those, which are admitted, as known principles, or by the common feeling of scientists, and wise men; in such a way, that authorized, they have acquired credibility, and as irrefutable they are used as true, and authorized testimonies. Those that touch on the will, are the opinions, that although probable, are not for that reason evident by demonstration, as was touched on, dealing with the difference between Science, and Opinion. Those that touch on the discourse, or reasoning, are those, to which reason assents, and are proven, like a Topical place; in such a way, that they can be placed as the major premises in the Topical syllogism, and also in its minor ones, with such certainty, that they produce true consequences, etc.

I have been unavoidably forced to shape this book (which includes the philosophical aspects of this Science) because it has been given, and is still referred to, as the Philosophy of the Sword; however, I acknowledge that in all those who have written, although they have qualified it as such, none have taught, demonstrated, or treated it as a science; they have instead overlooked its principles and foundations, which lead to the problems that any moderately ingenious person can notice. Many add to this the common question about the term Weapons, which is considered in schools as one of the seven servile Arts (as touched upon), and until now among ancient and modern Masters, none is found to have acknowledged the sword, the weapon-bearing instrument that common people call Dexterity, as a Science or Philosophy. This lies mainly in the responsibility of the wise (especially Spanish) who rightly affirm that it is a science, as it truly is one of understanding and practice, distinguishing itself like Logic and Dialectic. In strict scholastic terms, Logic is a science because it involves reasoning; and Dialectic is an Art because it consists of collected rules and precepts that compose the Art of dispute; and in the same way, the understanding of the sword, which involves reasoning, is a proper science, from which the exercise is produced, consisting of rules and precepts collected, in which it is the art of disputing the truth of this science with a sword in hand, and all together is the Philosophy of Arms, which in common terms is named Skill, and to the scientific Skilled: and this doctrine would be badly followed if, like its predecessors, it fled the difficulty, dealing only with what is Art, omitting what is Science, without demonstrating it, seeming blind, falling into the error that is criticized in the first; an inexcusable cause, that has obliged me with special studies and sleepless nights to demonstrate scientifically and philosophically the responsibility of such an issue, treating this science with method, order, and the formality of a science, following the Philosopher and his Expositors, entering through the most important foundation of Defense and Offense, which is made with the instrument Sword, from whose dignity and principle light is given, moving on to investigate its science, proving that it is of understanding and exercise, declaring of what species and in what speculative or practical way, and how from it Art is produced, which is perfected with experience, putting in order of Schools, what is Definition, what Division, what Universal voices, or Predicables of Porphyry? What, and how many are the Predicaments of the Philosopher? What is Substance? And what are Accidents in this science? What is the main subject of it? What is Essence, and Existence in man? And if they admit distinction? What is Potential, and Act? How is it considered? The man is defined and described in his whole, and in his parts. What does the Predicament Substance include? The partition of the real being in this science? What is continuous and Discrete Quantity in it, and in what do they differ? What is Relation and Analogy? What is Quality with its species and demonstrations? What is Predicamental Action? What is Passion, and Passive? What are the other Predicaments Where, When, Situation, and Habit? What is meant by Opposites, and Contraries, Similars, and Dissimilars? What is Priority? What is Demonstration? What are Science and Opinion? What are Topical Places? What are Dialectic Syllogisms? What is Argument and Topical Place? Reducing it to the ten most essential and proper to this Science, which are, to Causes, to Effects, to Subjects, to Adjuncts, to Dissimilar, to Comparison, to Definition, to Division, to Etymology, and Authority: all explained and understood in the priority and rigor of this Science of the Sword, gathering its Philosophy, so that from here onwards it can be recognized, treated, and disputed, understood, made to understand, and demonstrated as the Science of the usual and noble Arms, which are the Sword and its adjuncts, Dagger, etc., overcoming, as first, the difficulties that are manifested, and can be considered, having thus fulfilled such an issue, pledging, and opening the main door so that through it may enter those fans of the Skill of Arms, who profess, studying, and acquiring its Science for its true causes, in which wise and common people (I judge) will recognize my zeal, making an appreciation of this new essential, and forceful work (which until now no one has done) being as inexcusable as seen by examples; since neither the art is perfected without the science on which it depends; nor is the science useful in exercise if it does not produce art; this is seen in navigation, where the management of the Vessel, by route, and height, has its fundamental principles in Cosmography, which embraces as science the great construction, since it needs the Theoretical of the First Mobile, the Firmament, the Luminaries, Sun, and Moon, to recognize the elevations of Pole, the declinations of the Sun, the position, and movement of the fixed and wandering Stars, the Horizons, the Meridians, Zodiac, Equinoctial, Colures, Tropics, and other circles that are considered in the Sphere, including Astronomical Science, observing in the inferior Globe what is proper in Geography, to recognize the Coasts, Ports, Islands, etc. in their true latitudes, and longitudes, being all in the navigator, as principles for the Hydrography, recognizing the Seas, how the winds, bearings, and parallels are constituted, how they are considered, what they consist of, and vary by different places, the tides, and the currents, making use, as of subalterns, of Geometry, and Arithmetic, taking from all the scientific the right exercise of certain and safe navigation.

In the same way, the Philosophy of Arms can be considered, which is a Science of understanding and exercise, like navigation, in which that one understands and acts more perfectly, who knows more fundamentally the scientific, from which precepts and rules are drawn, that form art, corroborated with experience, which are the three cognitive powers admitted by philosophers, and have been touched upon for this Science, whose foundations have been outlined in this First Book, because without them, one would blindly enter into the Second. Just as the Architect would destroy the mountains, if he built them without their due foundations, because the consistency is not only in what appears to the sight, but in what is premeditated in understanding; so too the true Skill has its fundamental scientific principles, which are the bases of what appears visual, with which the necessary, not excusable, that this First Book contains, becomes evident, with which one will securely enter into what is demonstrable, which is given in the Second.

End of the First Book