CAPITVLO TREINTA Y TRES

Buelvo tercera vez a hazer demonſtracion en orden à los alcances de la Eſpada en cada vno de los tres planos, y juriſdiccion del Angulo recto, en comprobacion de las demonſtraciones antecedentes

CHAPTER THIRTY-THREE

I return for the third time to demonstrate in order the reaches of the Sword in each of the three planes, and jurisdiction of the right angle, in confirmation of the previous demonstrations

Aunque en las demonſtraciones antes de eſta ſe ha probado vaſtantemente los alcances del Angulo recto en los tres planos, vertical derecho, colateral del miſmo lado, y vertical, que paſſa por la diametral del pecho, que ſe reducen à las tres poſturas de perfil, de medio perfil, y de quadrado, y dado noticia ſuficiente para que ſe puedaN regular los alcances de los planos intermedios de eſtos tres; todavia, deſeando dar todas la claridad poſsible à los que no ſe quiſieren canſar en examinar eſtas demonſtraciones, nos ha parecido, para mas inteligencia, poner en figuras planos los cilindros en que imaginamos los dos contrarios, y el brazo, y Eſpada del Dieſtro, para que luego inmediatamente ſe pueda hazer juicio de las cantidades que ſe pierden de alcance, reſpecto del Angulo recto, que ſe cauſa en el plano vertical derecho en los otros dos planos colateral del miſmo lado, y vertical del pecho; y que con eſtas demonſtraciones tan viſibles, no ſolo ſe perciban ſin trabajo, pero que ſe conozca conforman en todo con las otras dos antecedentes, para que no quede duda en ſu realidad, y evidencia el Dieſtro eſtà afirmado con ſu brazo, y Eſpada en ſu plano vertical derecho.

Although in the demonstrations before this one, the reaches of the right angle in the three planes, right vertical, same side collateral, and chest vertical, which are reduced to the three postures of profile, half-profile, and square, have been sufficiently proven, and sufficient notice given to be able to regulate the reaches of the intermediate planes of these three; yet, desiring to provide all possible clarity to those who would not wish to tire themselves in examining these demonstrations, it seemed appropriate to us, for greater understanding, to put in figures the cylinders in which we imagine the two opponents, and the arm and Sword of the Fencer, so that immediately one can judge the amounts of reach lost, regarding the right angle, which is caused in the right vertical plane in the other two planes, collateral of the same side, and chest vertical; and with these so visible demonstrations, not only can they be perceived without effort, but it can be recognized that they conform in everything to the other two previous demonstrations, so that there can be no doubt in their reality and evidence the Fencer is affirmed with his arm and Sword in his right vertical plane.

Explicacion de la primera figura, para el plano vertical derecho

Explanation of the first figure, for the right vertical plane

Dado, pues, que el Dieſtro afirmado en la primera figura en ſu cilindro Q.O.M.K. dividio en ſus ocho planos principales deſuerte, que A.K. ſea ſu plano vertical derecho, en que lo imaginamos afirmado con ſu brazo, y Eſpada A.O. ſu plano vertical del pecho A.Q. ſu plano vertical, que le correſponde à las eſpaldas A.L. ſu plano colateral derecho A.P. ſu plano colateral, que le correſponde à ſu lado izquierdo de las eſpaldas A.N. ſu plano colateral izquierdo, y A.R. ſu plano colateral derecho, que le correſponde à las eſpaldas.

Given, then, that the Fencer affirmed in the first figure in his cylinder Q.O.M.K. divided into its eight principal planes so that A.K. is his right vertical plane, in which we imagine him affirmed with his arm and Sword A.O. his chest vertical plane A.Q. his vertical plane corresponding to the back A.L. his right collateral plane A.P. his collateral plane corresponding to his left side of the back A.N. his left collateral plane, and A.R. his right collateral plane corresponding to the back.

K.H. es la cantidad del brazo deſde ſu centro K. haſta H. pomo de la Eſpada, y linea racepta del miſmo brazo, de cantidad de dos pies geometricos. H.B. es la longitud de la Eſpada deſde el pomo, ò linea recepta, haſta la punta, de cantidad de quatro pies geometricos. Y punto M. es el que tiene la punta de la Eſpada de tocamento en el cilindro del contrario en el plano vertical del pecho, cuyo cilindro eſtà dividido con los miſmos ocho planos, como los del Dieſtro, con que avrà cauſado en ſu plano vertical derecho del plano vertical primario, y lo avrà aplicado en el plano vertical del pecho de ſu contrario.

K.H. is the length of the arm from its center K. to H. hilt of the Sword, and the straight line of the same arm, of a length of two geometric feet. H.B. is the length of the Sword from the hilt, or straight line, to the tip, of a length of four geometric feet. And point M. is the one where the tip of the Sword has the point of contact in the opponent’s cylinder in the chest vertical plane, whose cylinder is divided with the same eight planes, as those of the Fencer, with which it will have caused in its right vertical plane of the primary vertical plane, and applied it in the chest vertical plane of his opponent.

Explicacion de la ſegunda figura, para el plano colateral derecho.

Explanation of the second figure, for the right collateral plane.

En la demonſtracion precedente ſe vè claro, que con la longitud del brazo, y Eſpada, afirmado el Dieſtro en ſu plano vertical derecho en la comun ſeccion del plano vertical primario, y el plano ſuperior, alcançarà à ſu contrario en el cilindro en que le imaginamos afirmado en ſu plano vertical del pecho en punto M.

In the previous demonstration, it is clear that with the length of the arm and Sword, the Fencer affirmed in the right vertical plane in the common section of the primary vertical plane and the upper plane, will reach his opponent in the cylinder in which we imagine him affirmed in his chest vertical plane at point M.

Aora conſideramos al Dieſtro afirmado en eſta ſegunda figura en ſu cilindro (dividido en los miſmos planos que el primero) en ſu plano colateral derecho A.L. aviendo precedido la mocion al rededor de la linea de direccion, que repreſenta en el cilindro el punto A. deſuerte, que el punto K. ſea el centro de ſu brazo, y que la K.H. ſea la longitud de èl, y la H.B. la longitud de la Eſpada, que ocupa la comun ſeccion del plano vertical primario con el plano ſuperior, correſpondiente à ſu plano colateral derecho A.L. en que ſe reconoce, que la mocion que hizo el Dieſtro en apartar ſu vertical derecho K.O. del plano del vertical primario A.H. perdiò de alcance, reſpecto de ſu contrario, la cantidad de B.M. que es poco mas de tres dedos, y es la miſma que tenemos demonſtrada en las otras dos demonſtraciones; y en eſta figura el Dieſtro ha cauſado ſu plano primario en ſu plano colateral derecho A.L. y la punta de la Eſpada correſponde al plano vertical de el pecho del contrario; aunque no es circunſtancia, porque qualquier otro punto que correſpondiere à la punta de la Eſpada, vertificarà lo miſmo que pierde de alcance.

Now, we consider the Fencer affirmed in this second figure in his cylinder (divided into the same planes as the first) in his right collateral plane A.L. having preceded the motion around the direction line, which represents in the cylinder the point A. so that the point K. is the center of his arm, and K.H. is the length of it, and H.B. the length of the Sword, which occupies the common section of the primary vertical plane with the upper plane, corresponding to his right collateral plane A.L. It is recognized that the motion the Fencer made in moving his right vertical K.O. away from the primary vertical plane A.H. lost reach, regarding his opponent, by the amount of B.M. which is just over three fingers, and it is the same that we have demonstrated in the other two demonstrations; and in this figure, the Fencer has caused his primary plane in his right collateral plane A.L. and the tip of the Sword corresponds to the chest vertical plane of his opponent; although it is not circumstantial because any other point corresponding to the tip of the Sword will verify the same loss of reach.

Explicacion de la tercera figura, para el plano diametral del pecho.

Explanation of the third figure, for the chest diametral plane.

Suponiendo en eſta figura tercera al Dieſtro en ſu cilindro, dividido en los miſmos planos que los dos precedentes, afirmado de quadrado, que es quando el plano vertical derecho A.K. cauſa Angulo recto con el plano vertical primario A.H. deſuerte, que el centro de ſu brazo correſponde al punto K. y la longitud de ſu brazo K.H. y H.B. longitud de la Eſpada, que eſtà en Angulo recto, ocupando la comun ſeccion del plano vertical primario con el plano ſuperior; y en eſta poſtura, como ſe vè en ella, pierde medio pie de alcance, poco mas, que es la cantidad de B.M. que es el punto adonde avia de llegar la punta de la Eſpada, para tener tocamento en el cilindro del contrario, y eſta miſma cantidad es la que queda demonſtrada en las dos demonſtraciones antecendentes perdia de alcance en eſta poſtura, y en ella cauſa el Dieſtro al plano primario en ſu plano vertical del pecho, y la Eſpada la aplica en el miſmo plano de ſu contrario, aunque por no alcançar à ſu cilindro, no tiene punto de tocamento en èl.

Assuming in this third figure the Fencer in his cylinder, divided into the same planes as the two preceding ones, affirmed in square, which is when the right vertical plane A.K. causes a right angle with the primary vertical plane A.H. in such a way that the center of his arm corresponds to point K. and the length of his arm K.H. and H.B. the length of the Sword, which is at a right angle, occupying the common section of the primary vertical plane with the upper plane; and in this posture, as seen in it, loses a half foot of reach, a little more, which is the amount of B.M. that is the point where the tip of the Sword would have reached to make contact in the cylinder of the opponent, and this same amount is what was demonstrated in the two previous demonstrations as lost in reach in this posture, and in it, the Fencer causes the primary plane in his chest vertical plane, and the Sword applies it in the same plane of his opponent, although it does not reach his cylinder, it does not have a point of contact on it.

Corolario

Corollary

De eſtas tres demonſtraciones ſe ſigue, que para examinar los alcances en cada vno de los tres planos principales, y ſus intermedios, es lo miſmo mover la Eſpada, y brazo, y aplicandola en los planos quedando el cuerpo fixo, como en la primera demonſtracion, que eſtar fixo el brazo, y Eſpada, y aplicar à ella los planos, por medio de la mocion del cuerpo, ſobre el centro de ſu pie derecho, como en la ſegunda demonſtracion, ò al rededor de la linea de direccion, como en la eſta tercera.

From these three demonstrations, it follows that to examine the reaches in each of the three principal planes and their intermediates, it is the same to move the Sword and arm, applying it to the planes while the body remains fixed, as in the first demonstration, as it is to keep the arm and Sword fixed and apply the planes to them through the motion of the body, over the center of the right foot, as in the second demonstration, or around the line of direction, as in this third one.

Lamina treinta y dos del Libro ſegundo.

Sheet thirty-two of the second book.