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.
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.
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.
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.
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.
- Either it is considered by defined extremes, which the Vulgar call Equivalences, or Differential proportions, such as
