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