CAPITVLO NONO

BREVE EPILOGO, O RECOPILACION DE LOS puntos mas eſſenciales de la Deſtreza de las Armas, y del modo del diſcurrir en ella; cuyo fundamento ſerà moſtrar ſer ſciencia ſubalternada à las Mathematicas, argumentando en eſta forma.

CHAPTER NINE

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

La Reyna de las Mathematicas, que es la Geometira, tiene por objeto de ſus demonſtraciones, y evidencias quatro generos de cantidad continua, que ſon la Linea, el Angulo, la Superficie, y el Cuerpo, como conſta de los Elementos de Euclides, de Apoolonio, en los Libros de Archimedes, Pappo Alexandrino, y otros infinitos, &c. La Deſtreza de las Armas eſtà fundada en la conſideracion de los miſmos quatro generos de cantidad continua de Lineas, Angulos, Superficies ò Planos, y Cuerpos cauſados de los movimientos de la Eſpada, como conſta de todos los que han eſcrito en eſta materia, y quedò eſpecificado en el Prologomenon que hize en el Libro de la Sciencia, cuya repeticion no le canſe al Lector, porque tambien conviene en eſte lugar: de que ſe ſigue, que la Deſtreza de las Armas es vna de las Sciencias Mathematicas, ſubalternada à la Geometira. Pruebaſe al menor, moſtrando que la Deſtreza de las Armas tiene por objeto defenderſe, ò herir à ſu contrario, ſi ocnviene en orden à ſu defenſa; y eſto es preciſo que ſea por medio de movimientos del Cuerpo, y de la Eſpada, y brazo; no ſe pueden hazer eſtos movimientos ſin la formacion de eſtos quatro generos de cantidad; luego la Deſtreza de las Armas ſe funda en los generos de cantidad.

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

Puebaſe la menor con la demonſtracion evidente de que toda cantidad continua con ſu movimiento cauſa candidata algunas vezes del miſmo genero que ella es, y otras de diferente; como por exemplo, la linea que moviendoſe lateralmente cauſa Superficie, que es de diferente genero que la linea; pero ſi ſe mueve derechamente cauſa linea recta: la Superficie, quando ſe mueve ſegun ſu longitud, ò latitud, cauſa Superficie; pero moviendoſe ſegun la variedad de ſu movimiento, y de ſus terminos, que ſon las lineas: los cuerpos tambien cauſan el miſmo efecto; como por exemplo, la Eſphera, que movida ſobre ſu Exe conſerva ſu miſma forma; pero de qualquiera otra forma que ſe mueve rectamente cauſa vn Cilindro; y el Punto que no es cantidad, moviendoſe de qualquiera manera cauſa linea recta, circular, ò mixta.

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

En la Deſtreza de las Armas la punta de la Eſpada repreſenta vn punto, la qual moviendoſe es preciſo que cauſa alguna linea recta, circular, ò mixta, ſegun la eſpecie de ſu movimiento cauſarà linea, ò ſuperficie plana, ò curva; y eſta ſuperficie con ſu movimiento tambien cauſarà cupero; y el Angulo fe forma de la interſeccion de las lineas que ſe conſideran en eſtos tres generos de cantidad: con que ſe prueba evidentemente, que no ſe pueden regular los movimientos ſin tener primero atencion à la cantidad que ſe forma de ellos, porque para tratar las Sciencias con methodo, lo que es primero en la reſolucion, es lo poſtrero en la compoſicion: todo lo qual ſupueſto, para que podamos hablar en eſta materia con orden, y claridad, ſerà neceſſario, ſegun la doctrina de Ariſtoteles en ſu Analytica, comenzando à conſiderar la Deſtreza por ſu objeto principal, que es herir, ò defenderſe, hallaremos, que preciſamente ha de ſer por medio de los movimientos del cuerpo, y de la Eſpada, que es lo mas vniverſal que ſe halla en eſta materia; deſpues baxar à los particulares, que es conſiderar de quantas maneras pueden ſer eſtos movimientos, para que tomemos noticia individual de cada vno: y conſiderando bien la potencia del cuerpo, y del brazo, que es quien ha de mover la Eſpada hallarèmos que cada vno ſe pude mover de dos maneras diferentes, es aſaber recta, ò circularmente; quando el cuerpo ſe mueve rectamente puede ſer adelante, atràs, à vn lado, y à otro, y por las medias diviſiones, que vienen à ſer ocho caminos, ò rumbos, que ſe conſideran para los compaſes; y quando ſe mueve circularmente puede ſer por la circunferencia de tres circulos diferentes; es aſaber, el proprio, el del medio de proporcion, cuyo centro ocupar el adverſario, y el comun.

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

La Eſpada ſe puede mover rectamente, ò circularmente: rectamente ſerà, quando fuere por linea recta: circularmente, quando con el centro del brazo, del codo, ò de la muñeca, deſcribiere algunos circulos con la punta de la Eſpada: eſte movimiento circular ſe conſidera de dos maneras, el vno quando la Eſpada ,formando circulo con la punta, ſe mueve por plano: y el otro es quando ſe mueve por ſuperficie curva, formando Pyramides: los Planos pueden ſer verticales, orizontales, y obliquos, como de todo irèmos noticiando al Dieſtro.

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

Adviertaſe, que del perfecto conocimiento de eſtos Planos, y Pyramides, ſe llega à la total perfeccion de eſta ſciencia, porque no ſolamente por ellos ſe regular el movimiento de la Eſpada en el ayre; pero tambien el del cuerpo en el Plano inferior, aviendoſe de hallar ſiempre tal correſpondencia entre el todo, y ſus partes, que es neceſſario que tengan olo vn norte por guia, y eſte ſe halla en la eſpeculacion de los Planos, y Pyramides.

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