CAPITVLO TREINTA Y DOS

Para mas verificacion de los alcances del Angulo recto, y de ſu juriſdiccion, en comprobacion de lo demonſtrado, buelvo à facilitarlo en tres figura de cuerpo.

CHAPTER THIRTY-TWO

For further verification of the reach of the right angle, and of its jurisdiction, in confirmation of what has been demonstrated, I return to facilitate it in three figures of the body.

Aunque las demonſtraciones que hemos hecho el mayor, y menor alcance de los Angulos rectos, que ſe pueden cauſar en ſu juriſdiccion, ſon evidentes, y claras; todavia, para que lo vno, y otro ſe pueda vèr con mas diſtincion, y ſea mas perceptible al ſentido de la viſta, nos ha parecido poner aqui las tres figuras principales en que ſe fundan las dichas demonſtraciones; en la afirmado el Dieſtro de perfil en ſu plano vertical derecho, en la ſegunda afirmado en ſu plano colateral del miſmo lado, y la terecera afirmado en ſu plano vertical del pecho, para que en la diferencia de eſtas poſiciones ſe pueda hazer juicio del mayor, y menor alcance en cada vna de ellas, cuyo conocimiento podrà ſervir para los que no ſe quieren canſar en las demonſtraciones Mathematicas. Y ſe advierte, que en la demonſtracion Mathematica, que ſe ha hecho, por donde ſe podràn regular todas las demàs de los Angulos rectos en ſu juriſdiccion, ſuponemos que el cilindro en que imaginamos al Dieſtro ſe eſtà quedo, y que ſolo el brazo ſe mueve deſde el plano vertical derecho, haſta el plano vertical del pecho, y que deſde eſte plano ſe vuelve el brazo al plano vertical derecho,porque aſsi convino à lo que ſe demonſtrò; pero en eſtas tres figuras, que hemos pueſto an alzado, con las conſideraciones, que ſe han de tener en el plano inferior para el conocimiento de ellas, es preciſo ſuponer, para mas claridad, que el brazo, y Eſpada no ſe mueven, y que el cilindro, ò cuerpo es el que ſe mueve, mediante el pie izquierdo, al rededor de la linea que paſſa por el centro del brazo derecho, y ſe termina en el centro tambien del pie derecho, como ſe vè en la ſegunda, y tercera figura, y la cantidad que en cada vna acerca el Dieſtro el cuerpo à ſu contrario, que es lo que pierde de alcance para con èl; y primero ponemos la primera figura, en que eſtè el Dieſtro afirmado de perfil en Angulo recto, y ſobre Angulo recto, como fundamento por donde ſe ha de regular el conocimiento de las otras dos.

Although the demonstrations we have made of the greater and lesser reach of the right angles that can be caused in their jurisdiction are evident and clear; still, for one and the other to be seen with more distinction and to be more perceptible to the sense of sight, we have thought it appropriate to include here the three principal figures on which said demonstrations are based; in the first, the Fencer is affirmed in profile in his right vertical plane, in the second affirmed in his same side collateral plane, and the third affirmed in his chest vertical plane, so that in the difference of these positions one can judge the greater and lesser reach in each of them, whose knowledge can serve those who do not want to tire in the Mathematical demonstrations. And it is noted, that in the Mathematical demonstration, which has been made, where it is supposed that the cylinder in which we imagine the Fencer stays still, and only the arm moves from the right vertical plane to the chest vertical plane, and from this plane the arm returns to the right vertical plane, because so it was convenient to what was demonstrated; but in these three figures, which we have placed in elevation, with the considerations that must be had in the lower plane for the knowledge of them, it is necessary to suppose, for more clarity, that the arm and Sword do not move, and that the cylinder, or body is the one that moves, by means of the left foot, around the line that passes through the center of the right arm and ends also in the center of the right foot, as seen in the second and third figure, and the amount that in each one the Fencer brings the body closer to his opponent, which is what he loses in reach with him; and first we place the first figure, in which the Fencer is affirmed in profile in right angle, and on right angle, as the foundation by which the knowledge of the other two is to be regulated.

Explicacion de la primera figura, para el plano vertical derecho

Explanation of the first figure, for the right vertical plane

Dado que el Dieſtro eſtè afirmado en ſu plano vertical derecho en Angulo recto I.C.E. que correſponda al plano vertical primario, y en la baſa de ſu cilindro E.G.F.H. en el plano inferior, en que E.F. repreſente el miſmo plano vertical derecho, y la linea K.B. repreſente ſu plano colateral derecho, y la G.H. ſu plano vertical, que paſſa por la diametral del pecho, y que tenga opoſicion à ſu contrario, en cuerpo, y Armas iguales, afirmado en la miſma opoſicion ſin diferencia. En eſte caſo, acercandoſe el vno al otro, ſe podràn alcançar en ſus lineas verticales C.E. que paſſan por los centros de los brazos, y de ſus pies derechos en los puntso de tocamento que les correſpondieren.

Given that the Fencer is affirmed in his right vertical plane in right angle I.C.E. corresponding to the primary vertical plane, and on the base of his cylinder E.G.F.H. in the lower plane, where E.F. represents the same right vertical plane, and the line K.B. represents his right collateral plane, and G.H. his chest vertical plane, and that he has opposition to his opponent, in equal body and arms, affirmed in the same opposition without difference. In this case, approaching one another, they will be able to reach each other in their vertical lines C.E. passing through the centers of their arms, and their right feet at the points of contact corresponding to them.

Demueſtraſe la ſegunda figura para el plano colateral derecho.

The second figure is demonstrated for the right collateral plane.

En eſta ſegunda figura para ſu inteligencia, dezimos, que como en la antecedente eſtaba afirmado con el brazo, y Eſpada en el pano vertical derecho, y en el miſmo plano ſobre angulo recto con los pies en el plano inferior; en eſta ſegunda, mediante aver paſſado el pie izquierdo en punto F. y hecho la mocion neceſſaria ſobre el centro E. del pie derecho, queda afirmado en al plano vertical derecho F.E. con los pies en la parte, como ſe ſè en la figura, con que opone à ſu contrario ſu plano colateral derecho B.K. cauſado en el primario, en cuyo plano tambien eſtarà ſu Eſpada por el movimiento del pie izquierdo en F. y acerca el cuerpo à ſu contrario poco mas de tres dedos, que es la cantidad del cuerpo que ſale de la linea C.E. termino de ſu cilindro; y tambien ſe reconoce lo miſmo en que el roſtro ſe acerca la miſma cantidad à la miſma linea C.E. reſpecto de la poſicion que tiene en la primera figura, y es la miſma cantidad que hallamos en la dicha demonſtracion Mathematica.

In this second figure for its understanding, we say, that as in the previous one he was affirmed with the arm and Sword in the right vertical plane, and in the same plane on right angle with the feet in the lower plane; in this second, by having moved the left foot to point F. and having made the necessary motion over the center E. of the right foot, he remains affirmed in the right vertical plane F.E. with the feet on the side, as seen in the figure, with which he opposes his opponent his right collateral plane B.K. caused in the primary plane, in which plane his Sword will also be due to the movement of the left foot to F. and he brings the body closer to his opponent a little more than three fingers, which is the amount of body that comes out of the line C.E. end of his cylinder; and the same is recognized in that the face comes closer the same amount to the same line C.E. regarding the position it has in the first figure, and it is the same amount we found in the said Mathematical demonstration.

Explicaſe la tercera figura de cuerpo, repreſentando el plano vertical del pecho afirmado de quadrado.

The third figure of the body is explained, representing the chest vertical plane affirmed in square.

En eſta tercera figura, como ſe è en ella, para ponerſe el Dieſtro de quadrado, paffa ſu pie izquierdo en punto F. acabando la quarta parte del circulo P.F. que ſe requeria para ello, y ſu plano vertical F.E. en la parte que ſe vè en la figura, con que opone à ſu contrario ſu plano vertical del pecho B.G. cauſando en èl el plano primario; y en eſta poſicion acerca el cuerpo à ſu contrario medio pie, poco mas, ò menos, por la parte que de èl eſtà fuera del cilindro, donde le imaginamos en la primera figura, y à la linea C.E. que paffa por los centros del brazo, y de ſu pie derecho, y es la miſma cantidad que hallamos perdia de alcance en dicha demonſtracion Mathematica, y la miſma que en eſta figura ſe halla acercarſe el roſtro; y ambas hemos ajuſtado por ſus plantas con todo en rigor poſsible.

In this third figure, as seen in it, to place the Fencer in square, he passes his left foot to point F. completing the fourth part of the circle P.F. required for it, and his vertical plane F.E. on the part that is seen in the figure, with which he opposes his opponent his chest vertical plane B.G. causing in it the primary plane; and in this position, he brings the body closer to his opponent by half a foot, more or less, by the part of him that is outside the cylinder, where we imagine him in the first figure, and to the line C.E. that passes through the centers of the arm, and of his right foot, and it is the same amount we found he lost in reach in the said Mathematical demonstration, and the same that in this figure is found to bring the face closer; and both we have adjusted by their footprints with all possible rigor.

Lamina treinta y vna del Libro ſegundo.

Plate thirty-one of the second book.