CAPITVLO VEINTE Y CINCO

En que se trata del conocimiento de las Pyramides de defenſa, que el Dieſtro puede, y ha de hazer con la Eſpada, y ſu brazo, y guarnicion, aſsi en el medio de proporcion, como en los proporcionados, para poner, ò contener la Eſpada de ſu contrario fuera de los dos planos imaginarios de ſu defenſa.

CHAPTER TWENTY-FIVE

On the knowledge of defense Pyramids that the Diestro can and must create with their Sword, arm, and guard, both in the middle of proportion and in proportioned positions, to place or contain their opponent’s Sword outside the two imaginary planes of their defense.

Esta propoſicion tiene diferentes caſos, y los mas eſſenciales ſe iràn explicando por ſu orden, y empezando por los tres que pertenecen à la poſtura de perfil, ò plano vertical primario, los pongo en vna Lamina, para poner conſecutivo à eſtos, los caſos que pertenecen à las otras dos poſturas, ò planos.

This proposition has various cases, and the most essential ones will be explained in order, starting with the three that belong to the profile posture or primary vertical plane. They are presented in one Plate, followed by the cases that pertain to the other two postures or planes.

Caso Primero

First Case

Dado que eſtèn afirmados los dos combatientes en A.B. ſobre Angulo recto D.C. y F.E. en el medio de proporcion, con ſus Eſpadas en el plano vertical primario, que paſſe por ſus planos verticales derechos, ſe quiere examinar, què cantidad de movimiento, ò porcion de Pyramide ha de hazer el Dieſtro à ſu lado derecho, y ſinieſtro, para poner ò contener la Eſpada de ſu contrario fuera de los dos planos imaginarios de ſu defenſa: deſuerte, que la punta no tenga direccion à ſu cuerpo, y cilindro en que le conſideramos.

Given that both combatants are affirmed in A.B. on the right angle D.C. and F.E. in the middle of proportion, with their Swords in the primary vertical plane passing through their right vertical planes, we want to examine the amount of movement or portion of the Pyramid the Diestro must make to the right and left to place or contain the opponent’s Sword outside the two imaginary defense planes, ensuring that the tip doesn’t have a direction toward their body and the cylinder in which we consider them.

Saqueſe la linea A.B. de nueve pies, en la qual imaginamos el plano vertical primario, tomeſe la linea A.C. y B.E. cada vna de medio pie, y quedarà la C.E. de ocho pies, que es la diſtancia que hemos demonſtrado ha de tener el medio de proporcion, y centro A. y B. intervalo A.C. y B.E. deſcribaſe los circulos C.D. y E.F. que ſeràn las baſas de los cilindros, en que conſideramos los dos contrarios, tomeſe la C.G. deſde el centro C. del brazo del contrario haſta G. centro de los gavilanes de ſu Eſpada, de cantidad de dos pies, y quarto, y otra tanta cantidad deſde el centro del brazo E. del Dieſtro, haſta H. centro de los gavilanes de ſu Eſpada; ſaqueſe deſde el centro G. de los gavilanes de la de el contrario las dos tangentes G.K.G.L. por las quales imaginamos paſſan los dos planos verticales de defenſa, que tocan al cilindro, que comprehenden al Dieſtro en la poſtura en que eſtà afirmado.

Draw the line A.B. of nine feet, in which we imagine the primary vertical plane. Take the lines A.C. and B.E., each one of half a foot, and the remaining C.E. will be eight feet, the distance we have demonstrated must be the middle of proportion, and centers A. and B. The interval A.C. and B.E. describe the circles C.D. and E.F., which will be the bases of the cylinders in which we consider the two opponents. Take the C.G. from the center C. of the opponent’s arm to G. the center of the guard of their Sword, measuring two feet and a quarter, and the same measurement from the center of the Diestro’s arm E. to H. the center of the guard of their Sword. Draw from the center G. of the opponent’s guard the two tangents G.K.G.L., through which we imagine pass the two vertical defense planes that touch the cylinder containing the Diestro in the posture they are affirmed in.

Dividaſe la H.G. por medio, en punto T. tomeſe la T.O. de quatro dedos, y ſaqueſe la O.P. perpendicular à G.K. ſerà O.P. la menor cantidad que avrà de hazer de movimiento el Dieſtro, para poner la Eſpada del contrario à ſu lado izquierdo en el plano de defenſa G.K. y à ſu lado derecho en G.L. deſde eſta interſecacion O. de las Eſpadas en el plano vertical primario A.B. y ſe examina de eſta fuerte.

Divide H.G. in the middle at point T. Take T.O. of four fingers and draw O.P. perpendicular to G.K. O.P. will be the smallest movement the Diestro must make to place the opponent’s Sword on their left side in the defense plane G.K. and on their right side in G.L. from this intersection O. of the Swords in the primary vertical plane A.B., and it’s examined in this manner.

Saqueſe la linea B.K. la qual, por la propoſicion 18. del tercero de los Elementos de Euclides, ſerà perpendicular à la G.K. y por ſer tambien la O.P. perpendicular à la miſma por la conſtruccion, ſeràn paralelas entre sì;y por conſiguiente, por la propoſicion ſegunda del ſexto de los Elementos de Euclides, quedaràn divididos los lados del triangulo G.B.K. en la miſma proporcion, y ſeràn ſemejantes los triangulos G.B.K. y G.O.P. y ſerà como G.B. de ſeis pies, y quarto, que ſon 100. dedos à B.K. de medio pie, que ſon ocho dedos, aſsi G.O. de dos pies que ſon 32. dedos à otra quarta proporcional, y vendrà por cociente 256/100, que ſon dos dedos, y poco mas de medio; y eſta es la cantidad de la O.P. y la que avrà de hazer el Dieſtro de movimiento, para poner con ſu que avrà de hazer el Dieſtro de movimiento, para poner con ſu Eſpada la del contrario, por vna y otra parte, deſde el plano vertical primario A.B. en los dos planos de deſenſa G.K. y G.L. como lo manifieſta la figura primera.

Draw the line B.K., which, by proposition 18 of the third book of Euclid’s Elements, will be perpendicular to G.K. And as O.P. is also perpendicular to the same by construction, they will be parallel to each other. Consequently, by proposition two of the sixth book of Euclid’s Elements, the sides of the triangle G.B.K. will be divided in the same proportion, and the triangles G.B.K. and G.O.P. will be similar. So, as G.B. is six feet and a quarter, or 100 fingers, to B.K. of half a foot, or eight fingers, so will G.O. of two feet, or 32 fingers, to another fourth proportional, which comes out as 256/100, which is two fingers and a little more than half. This is the amount of O.P. and the movement the Diestro must make to place their Sword, from the primary vertical plane A.B., into the two defense planes G.K. and G.L., on either side, as demonstrated in the first figure.

Caso Segundo

Case Two

Dado lo miſmo que en el caſo atecedente, excepto que en eſte ſuponemos que los dos contrarios eſtèn en diſtancia del medio proporcionado de las eſtocadas que eſtan en la circunferencia del ſexto orbe del Dieſtro, por aver dado el contrario compàs de dos pies deſde el de proporcion, deſde punto C. à punto M. con que el centro de la guarnicion de ſu Eſpada ſe paſsò punto I. para herir de eſtocada.

Given the same conditions as in the previous case, except that in this one, we assume that both opponents are at the distance of the proportionate medium for thrusts that are on the circumference of the sixth orb of the Diestro, having moved two feet from the proportionate medium, from point C to point M. Consequently, the center of his sword guard has moved to point I to strike with a thrust.

Saquenſe las dos tangetes I.K.I.L. al cilindro, ſaqueſe la B.L. al punto del contacto, y ſerà perpendicular à la I.L. ſaqueſe la H.N. perpendicular à la I.B. y quedaràn formados dos triangulos ſemejantes, pueſtos ſubcontrariamente, proque ambox ſon rectangulos, y tienen el Angulo en I. comun, con que tendràn los lados homologos proporcionales, y ſeràn como I.L. à L.B. aſsi I.H. à H.N. pero como ay tan poca diferencia de la I.L. à I.B. en lugar de la I.L. tomamos la I.B. diziendo como la I.B. à B.I. aſsi al I.H. à H.N. pero de eſtas quatro proporcionales las tres ſon conocidas, la I.B. de quatro pies y quarto, que ſon 68. dedos, la B.L. de medio pie, que ſon ocho, y la I.H. de pie y medio, que ſon 24. dedos; y haziendo la regla de tres, vendrà por cociente la H.N. poco menos de tres dedos: con que ſe haze evidencia, que como el Semidiametro de la guarnicion del Dieſtro es de quatro dedos pro vna y otra parte, con los tres dedos referidos, ſin hazer movimiento el Dieſtro, conſigue la defenſa con ſu guarnicion, como lo verifica la ſigura ſegunda.

Draw the two tangents I.K.I.L. to the cylinder, draw B.L. to the point of contact, and it will be perpendicular to I.L. Draw H.N. perpendicular to I.B., and two similar triangles will be formed, placed subcontrarily, because both are right-angled and have the common angle at I. Thus, the corresponding sides will be proportional, and it will be as I.L. to L.B. is to I.H. to H.N. But since there is so little difference between I.L. and I.B., instead of I.L., we take I.B., saying as I.B. to B.L. is to I.H. to H.N. But of these four proportionals, three are known: I.B. is four feet and a quarter, which is 68 fingers, B.L. is half a foot, which is eight fingers, and I.H. is one and a half feet, which is 24 fingers; and performing the rule of three, the result for H.N. is slightly less than three fingers. Thus, it becomes evident that with the semi-diameter of the Diestro’s guard being four fingers on each side, with the aforementioned three fingers, without the Diestro making a move, he achieves defense with his guard, as verified by the second figure.

Caso Tercero

Case Three

Dado lo miſmo que en los dos caſos antecendentes, excepto que en eſte el contrario diò vn compàs de tres pies, deſde el medio de proporcion, para piſar el Orbe quito, que es el medio de los tajos para executarle: deſuerte, que el centro de la guarnicion de ſu Eſpada viene à eſtar diſtante del Dieſtro tres pies menos quarto.

Given the same conditions as in the previous two cases, except that in this one the opponent took a three-foot step from the medium of proportion to step on the fifth orb, which is the medium for cuts, intending to execute them. Consequently, the center of his sword guard comes to be three feet less a quarter away from the Diestro.

Saquenſe las dos tangentes I.K.I.L al cilindro del Dieſtro, y la B.L. al punto del contacto, y en los gavilanes de la Eſpada del Dieſtro la N.H. perpendicular à I.B. quedaràn formados los triangulos ſemejantes, que ſon I.L.B. y I.N.H. y por la miſma racon que ſe dà en el caſo antecedente, ſeràn como I.B. à B.L. aſsi I.H. à H.N. pero la I.B es de tres pies y quarto, que ſon cinquenta y dos dedos, y la B.L. de medio pie, que ſon ocho, y la I.H. de medio pie, que ſon otros ocho, y la H.N. la quarta; y formando la regla de tres, viene por cociente vn dedo, y tres quartos de otro: y ſiendo el Semidiametro de la guarnicion del Dieſtro de quatro dedos, ſobre abunda para ſu defenſa en la guarnicion por vnoa y otra parte, dos dedos y vn quarto, como lo demueſtra la figura terecera.

Draw the two tangents I.K.I.L. to the Diestro’s cylinder, and B.L. to the point of contact, and at the Diestro’s sword guard, draw N.H. perpendicular to I.B. This will form the similar triangles I.L.B. and I.N.H. By the same reasoning given in the previous case, it will be as I.B. is to B.L. is to I.H. to H.N. However, I.B. is three feet and a quarter, which is fifty-two fingers, B.L. is half a foot, which is eight fingers, I.H. is another eight fingers, and H.N. will be a quarter; and forming the rule of three, the result is one finger and three quarters of another finger. Since the semi-diameter of the Diestro’s guard is four fingers, this exceeds the necessary amount for his defense in the guard on both sides by two fingers and a quarter, as demonstrated in the third figure.

Para el Plano Vertical derecho

For the Right Vertical Plane

En la Lamina atecedente que dan declarados los tres caſos que pertenecen al plano vertical derecho, y en eſta que ſe ſigue manifeſtarèmos otros tres caſos pertenecientes al plano colateral derecho.

In the previous diagram, the three cases pertaining to the right vertical plane were explained. In this following diagram, we will demonstrate another three cases pertaining to the right collateral plane.

Caso Quarto

Case Four

Dado que los dos contrarios eſtèn afirmados en el medio de proporcion C.E. como en los caſos atecedentes, el contrario en ſu plano vertical derecho en Angulo recto, y ſobre Angulo recto en la planta de ſu cilindro de vn pie de Diametro en D.C. y el Dieſtro en ſu plano colateral derecho, tambien en Angulo recto ſobre Angulo recto en F.E. y porque deſcubre en eſte plano mas latidud, ſe ha dado de baſa à ſu cilindro K.L. vn pie y quarto de Diametro, ſe quiere examinar, què cantidad de movimiento, ò porcion de Pyramide ha de hazer el Dieſtro con ſu Eſpada ſinieſtro, ò al derecho, para ponerla, ò contenerla fuera de los dos planos verticales de ſu defenſa.

Given that both opponents are affirmed in the medium of proportion C.E. as in the previous cases, the opponent is in his right vertical plane at a right angle and above the right angle on the base of his cylinder, which has a diameter of one foot at D.C., and the Diestro in his right collateral plane, also at a right angle and above the right angle at F.E. Since more width is exposed in this plane, the base of his cylinder K.L. is given a diameter of one and a quarter feet. We want to examine how much movement or portion of a pyramid the Diestro must make with his sword to the left or right to place it or contain it outside the two vertical planes of his defense.

Saquenſe las tangentes G.K. y G.L. ſaqueſe la B.K. al punto del contacto, dividaſe la G.H. que eſtà entre los dos centros de los gavilanes, por medio en T. tomeſe vn quarto de pie de T. à O. ſaqueſe la O.P. paralela à B.K. y ſerà perpendicular à la G.K. y quedaràn formados dos triangulos ſemejantes G.B.K. y G.O.P y ſus lados homologos ſeràn proporcionales, y ſeràn como G.B. à B.K. aſsi G.O. à O.P. pero de eſtas quatro proporcionales, las tres ſon conocidas: la G.B. de ſeis pies, que ſon treinta y dos dedos; formando por eſta orden la regla de tres, ſe halla que la O.P. es de tres dedos y vn noveno, que es la cantidad de movimiento que en eſta dos y vn noveno, que es la cantidad de movimiento que en eſta interſeccion de las Eſpadas ha de hazer el Dieſtro con ſu Pyramide de defenſa P.H.Q. para poner con la porcion della la Eſpada de ſu contrario, deſde el plano vertical primario, por vno y otro lado, fuera de los planos de ſu defenſa G.K. y G.L. como ſe vè en la figura.

Draw the tangents G.K. and G.L. Draw the B.K. to the point of contact. Divide the G.H. which is between the two centers of the quillons in half at T. Take a quarter of a foot from T. to O. Draw O.P. parallel to B.K., which will be perpendicular to G.K., forming two similar triangles G.B.K. and G.O.P, and their corresponding sides will be proportional. It will be as G.B. is to B.K. as G.O. is to O.P. However, of these four proportional values, three are known: G.B. is six feet, which is thirty-two fingers; forming the rule of three in this order, it is found that O.P. is three fingers and one ninth, which is the amount of movement that the Diestro must make at this intersection of the swords with his defensive Pyramid P.H.Q. to place with a portion of it the opponent’s sword, from the primary vertical plane, on both sides, outside the planes of his defense G.K. and G.L., as seen in the figure.

Caso Quinto

Case Five

Dado lo miſmo que en el caſo antecendente, excepto que el contrario dà compàs de C. à G. de dos pies para herir de eſtocada al Dieſtro, y llega con el centro de los gavilanes de ſu guarnicion deſde punto G. à punto I. como que queda eſte punto I. diſtante del cilindro del Dieſtro F.E. quatro pies menos quarto: quierſe examinar, què cantidad de movimiento, ò porcion de Pyramide ha de hazer el Dieſtro deſde el plano vertical primario A.B. à ſu lado izquierdo, para poner ò contener la Eſpada del contrario en la ſuperficie de ſu cilindro.

Given the same conditions as in the previous case, except that in this instance, the opponent steps forward two feet from point C to point G to strike a thrust at the Diestro, moving the center of his quillon guard from point G to point I. This results in point I being four feet less a quarter away from Diestro’s cylinder F.E. The query is to determine how much movement, or what portion of a pyramid, the Diestro must perform from the primary vertical plane A.B. to his left side to place or contain his opponent’s sword on the surface of his cylinder.

Saquenſe las dos tangentes I.K.I.L. y la B.K. al punto de contacto, y la H.N. perpendicular à la I.B. y quedaràn formados dos triangulos ſemejantes I.B.K. y I.H.N. pueſtos ſubcontrariamente, y ſeràn ſus lados homologos proporcionales; pero por la razon que ſe ha dado en el ſegundo caſo, de eſtas quatro proporcionales las tres ſon conocidas, porque I.B. es de quatro pies y vn quarto, que ſon 68 dedos, y B.K. de 10. y I.H. de vn pie y tres quartos, que ſon 28. dedos, luego la quarta H.N. formando la regla de tres, ſe hallarà ſer de quatro dedos; y aſsi el Dieſtro avrà de apartar el centro de le guarnicion, y ſus gavilanes, por vna y otra parte, quatro dedos, para poner la Eſpada del contrario fuera de los dos planos verticales de ſu defenſa I.K.I.L. para quedar defendido.

Draw the two tangents I.K.I.L. and B.K. to the point of contact, and H.N. perpendicular to I.B. This results in the formation of two similar triangles I.B.K. and I.H.N., placed subcontrarily, with their corresponding sides proportional; but for the reason given in the second case, of these four proportionals, three are known, as I.B. is four feet and a quarter, which is 68 fingers, B.K. is 10, and I.H. is one foot and three quarters, which is 28 fingers. Forming the rule of three, it is found that H.N. is four fingers; thus, the Diestro must move the center of his guard, and his quillons, four fingers to the left and right to place the opponent’s sword outside the two vertical planes of his defense I.K.I.L. to remain defended.

Caso Sexto

Case Six

Dado lo miſmo que en el caſo antecendente, excepto que en eſte ſe ſupone, que el contrario dà vn compàs de tres pies de punto C. à punto O. para que piſe el Orbe de los tajos, y reveſes verticales, y diagonales, y medios tajos, y medios reveſes de la miſmas eſpecies, y llega con eſte compàs el centro de ſu guarnicion à punto I. con que viene à quedar de ſu contrario tres pies menos quarto, y puede herir con vn pie de Eſpada; quiereſe examinar quanto avrà de apartar el Dieſtro el centro de la guarnicion de ſu Eſpada del plano vertical primario A.B. à vna y otra parte, para quedar defendido.

Given the same conditions as in the previous case, except that it is assumed the opponent steps forward three feet from point C to point O to step on the Orb of cuts, vertical and diagonal reverses, and half cuts, and half reverses of the same species, and reaches with this step the center of his guard to point I. This point is three feet less a quarter away from the Diestro and allows striking with one foot of the sword; the query is to examine how much the Diestro must move the center of his guard and quillons from the primary vertical plane A.B. to both sides to remain defended.

Saquenſe las tangentes I.K.I.L. y la B.K. al punto del contacto, y H.N. perpendicular à I.B. y quedaràn formados dos triangulos ſemejantes ſubcontrariamente pueſtos I.B.K. y I.H.N. y ſeràn ſus lados homologos proporcionales, por la razon que ſe ha dado en el ſegundo caſo; y eſtas quatro proporcionales ſon como la I.B. à B.K. aſsi I.H. à H.N. pero las tres ſon conocidas, porque la I.B. es de tres pies, y vn quarto, que ſon 52. dedos, y B.K. de 10. y la I.H. de doze dedos, y formando la regla de tres, ſe hallarà, que la quarta H.N. es de dos dedos y 1/3, poco menos; y aſsi el Dieſtro avrà de apartar el centro de ſu guarnicion, y de los gavilanes, deſde el lado vertical primario à ſu lado izquierdo, y derecho: eſte cantidad, para tener, ò contener la Eſpada del contrario fuera de los dos planos verticales de ſu defenſa I.K.I.L. para quedar defendido de las eſpecies de heridas referidas, como ſe vè por la figura 6.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. and B.K. to the point of contact, and H.N. parallel to it, or perpendicular to I.K. This forms two similar triangles I.B.K. and I.H.N., with their corresponding sides proportional, as I.B. is to B.K. so is I.H. to H.N. However, of these four proportionals, three are known, as I.B. is three feet and a quarter, which is 52 fingers, B.K. is 12, and I.H. is 20 fingers. Forming the rule of three, it is found that the fourth proportional H.N. is four fingers and three-fifths, which is the amount of movement the Diestro must make from the primary vertical plane A.B. to both sides, with the center of the guard and quillons of his sword, to place and contain his opponent’s sword outside the two vertical defense planes I.K. and I.L. to remain defended from any of the circular and semicircular tricks and species of them with which he may be attacked in the jurisdiction from the superior plane upwards, as verified by figure nine.

Para el plano colateral derecho

For the right colateral plane

En las dos Laminas antes de eſta que ſe ſigue, quedan declarados, aſsi lso tres caſos que pertenecen al plano vertical derecho, como los tres que tocan al plano colateral del miſmo lado, y en eſta ſe manifeſtaràn los tres que pertenecen al plano Diametral del pecho, ò poſtura de quadrado.

In the two plates preceding this one, the three cases pertaining to the right vertical plane, as well as the three cases related to the right collateral plane, are declared. In this current plate, the three cases belonging to the Diametral plane of the chest or square posture will be presented.

Caso Septimo

Case Seven

Dado lo miſmo que en los caſos primero, y quarto, excepto que en eſte el Dieſtro eſtà afirmado con ſu brazo, y Eſpada en ſu plano vertical del pecho, en cuya poſicion pierde alcance medio pie, y deſcubre toda ſu latidud, que es medio pie mas de lo que dimos al Diametro del cilindro del primer caſo, en el qual ſe ſupone eſtar afirmado en ſu plano vertical derecho; y para que en eſta poſtura de quadrado quede defendido, comprehendiendo los ombros, es la razon de que à ſu cilindro F.E. le damos de Diametro pie y medio; quierſe examinar, què cantidad de movimiento, ò porcion de Pyramide avrà de hazer el Dieſtro con el centro de ſu guarnicion, deſde el plano vertical primario à ſu lado izquierdo, y derecho, para poner, ò contener la Eſpada de ſu contrario en los dos planos verticales de ſu defenſa.

Given the same conditions as in the first and fourth cases, except that in this case, the Diestro stands with his arm and sword in his vertical plane of the chest. In this position, he loses half a foot of reach and exposes all his width, which is half a foot more than what was given to the diameter of the cylinder in the first case, where he is supposed to stand in his right vertical plane. To remain defended in this square posture, including the shoulders, the diameter of his cylinder F.E. is given as one and a half feet. The query is to determine how much movement or what portion of a pyramid the Diestro must perform with the center of his guard, from the primary vertical plane to his left and right, to place or contain his opponent’s sword in the two vertical defense planes.

Saquenſe las tangentes G.K. y G.L. al cilindro del Dieſtro F.E. ſaqueſe la B.K. al punto del contacto, dividaſe la G.K. por medio en T. tomeſe la T.O. de quatro dedos, ſaqueſe la O.P. paralela à B.K. ò perpendicular à G.K. y quedaràn formados dos triangulos ſemejantes G.B.K. y G.O.P. y ſeràn ſus lados homologos proporcionales, como G.B. y G.O.P. y ſeràn ſus lados homologos proporcionales, como G.B. à B.K. aſsi G.O. à O.P. pero de eſtas quatro proporcionales las tres ſon conocidas, porque la G.B. es de ſeis pies y quarto, que ſon 100. dedos, y la B.K. de 12. y la G.O. de dos pies, y quarto, que ſon 26. dedos; y formando la regla de tres, ſe hallarà que la quarta proporcional O.P. es de quatro dedos, y vn tercio, y eſta es la cantidad de movimiento que el Dieſtro avrà de hazer deſde el plano vertical primario A.B. en eſta interſeccion, à vna y otra parte, con la Pyramide de ſu defenſa H.P.Q. para poner, y contener la Eſpada de ſu contrario fuera de los dos planos verticales de defenſa G.K. y G.L. tangentes à ſu cilindro F.E. con el centro de ſu guarnicion, para quedar defendido.

Draw the tangents G.K. and G.L. to Diestro’s cylinder F.E. Draw B.K. to the point of contact, divide G.K. in the middle at T. Take T.O. as four fingers, draw O.P. parallel to B.K. or perpendicular to G.K. This results in the formation of two similar triangles G.B.K. and G.O.P., with their corresponding sides proportional, as G.B. to B.K. so is G.O. to O.P. However, of these four proportionals, three are known, as G.B. is six feet and a quarter, which is 100 fingers, B.K. is 12, and G.O. is two feet and a quarter, which is 36 fingers. Forming the rule of three, it is found that the fourth proportional O.P. is four fingers and a third. This is the amount of movement the Diestro must make from the primary vertical plane A.B. at this intersection, to both sides, with the defense pyramid H.P.Q. to place and contain his opponent’s sword outside the two vertical defense planes G.K. and G.L. tangent to his cylinder F.E. with the center of his guard, to remain defended.

Caso Octavo

Case Eight

Dado lo miſmo que en el caſo antecedente, excepto que en eſte ſe ſupone que el contrario dà vn compàs de dos pies de punto C. à punto G. haſta piſar el primer Orbe de los medios de las eſtocadas, y en eſta poſicion llega el centro de la guarnicion, y de los gavilanes de ſy Eſpada à punto I. para herir de eſtocada al Dieſtro, cuyo punto eſtà diſtante de èl quatro pies menos quarto; quiereſe examinar, què cantidad de movimiento avrà de hazer el Dieſtro con el centro de ſu guarnicion, y de ſus gavilanes, para poner, y contener la Eſpada de ſu contrario fuera de los dos planos verticales I.K.I.L. de defenſa, tangente à ſu cilindro F.E.

Given the same conditions as in the previous case, except that it is assumed the opponent takes a step of two feet from point C to point G to reach the first Orb of thrusts, and in this position, the center of the guard and quillons of his sword reach point I to strike a thrust at the Diestro, whose point is four feet less a quarter away. The query is to examine how much movement the Diestro must perform with the center of his guard and quillons to place and contain his opponent’s sword outside the two vertical defense planes I.K.I.L. tangent to his cylinder F.E.

Saquenſe las dos tangentes I.K.I.L. al cilindro del Dieſtro F.E. y B.K. al punto del contacto, y la H.N. paralela à B.K. ò perpendicular à la I.K. y quedaràn formados dos triangulos ſemejantes I.B.K. y L.H.N. y ſeràn ſus lados homologos proporcionales, como la I.B. à B.K. aſsi I.H. à H.N. pero de eſtas quatro proporcionales, las tres ſon conocidas, porque la I.B. es de quatro pies y quarto, que ſon 68. dedos, y la I.B. de 12 y la I.H. de dos pies, que ſon 32. dedos, y haziendo la regla de tres ſe hallarà, que la H.N. es de cino dedos, y dos tercios, que es la cantidad que avrà de hazer de movimiento el Dieſtro, deſde el plano vertical primario A.B. con el centro de ſu guarnicion, y de los gavilanes à vno y à otro lado para poner, ò contener la Eſpada de ſu contrario en los dos planos verticales de defenſa I.K. y I.L. tangentes à ſu cilindro F.E. para quedar defendido, como ſe vè en la figura.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. and B.K. to the point of contact, and H.N. parallel to B.K. or perpendicular to I.K. This results in the formation of two similar triangles I.B.K. and I.H.N., and their corresponding sides are proportional, as I.B. to B.K. so is I.H. to H.N. Of these four proportionals, three are known, as I.B. is four feet and a quarter, which is 68 fingers, B.K. is 12, and I.H. is two feet, which is 32 fingers. Forming the rule of three, it is found that H.N. is five fingers and two-thirds. This is the amount of movement the Diestro must make from the primary vertical plane A.B. with the center of his guard and quillons to both sides to place and contain his opponent’s sword in the two vertical defense planes I.K. and I.L. tangent to his cylinder F.E. to remain defended, as shown in the figure.

Caso Nono

Case Nine

Dado lo miſmo que en los dos caſos antecedentes, excepto que ſe ſupone que el contrario dà vn compàs de tres pies de punto C. à punto O. para piſar el Orbe ſegundo de los medios proporcionados para las heridas circulares, y ſemicirculares; y en eſta poſicion llega el centro de ſu guarnicion à punto I. que es diſtante del Dieſtro tres pies menos quarto, qpara executar con vn pie de Eſpada ſus tretas en el Dieſtro; quiereſe examinar, què cantidad de movimiento avrà de hazer el Dieſtro à ſu lado izquierdo, y derecho, deſde el plano vertical primario A.B. para poner, y contener la Eſpada de ſu contrario fuera de los dos planos verticales de ſu defenſa.

Given the same conditions as in the two previous cases, except that it is assumed the opponent takes a step of three feet from point C to point O to step on the second Orb of proportionate means for circular and semicircular wounds; and in this position, the center of his guard reaches point I, which is three feet less a quarter away from the Diestro, to execute with one foot of his sword his tricks on the Diestro. The query is to examine how much movement the Diestro must make to his left and right sides, from the primary vertical plane A.B. to place and contain his opponent’s sword outside the two vertical defense planes.

Saquenſe las dos tangentes I.K.I.L al cilindro del Dieſtro F.E. ſaqueſe la B.K. al punto del contacto, y ka H.N. paralela à ella, ò perpendicular à la I.K. y quedaràn formados dos triangulos ſemejantes I.B.K. y I.H.N. y ſeràn ſus lados homologos proporcionales, como I.B. à B.K. aſsi I.H. à H.N. pero de eſtas quatro proporcionales las tres ſon conocidas, porque las I.B. es de tres pies y quarto, que ſon 52. dedos, y la B.K. de 12. y la I.H. de 20 dedos; y haziendo la regla de tres, ſe hallarà que la quarta proporcional H.N. es de quatro dedos, y tres quintos, que es la cantidad de movimiento que el Dieſtro ha de hazer, deſde el plano vertical primario A.B. à vno y otro lado, con el centro de la guarnicion, y de los gavilanes de ſu Eſpada, para poner, y contener la de ſu contrario fuera de los dos planos verticales de defenſa I.K. y I.L. para quedar defendido de qualquiera de las tretas circulares, y ſemicirculares, y eſpecie de ellas con que le quiſiere ofender en la juriſdiccion, deſde el plano ſuperior arriba, como todo ve verifica por la figura nona.

Draw the two tangents I.K.I.L. to Diestro’s cylinder F.E. Draw B.K. to the point of contact, and H.N. parallel to it, or perpendicular to I.K. This results in the formation of two similar triangles I.B.K. and I.H.N., with their corresponding sides proportional, as I.B. to B.K. so is I.H. to H.N. However, of these four proportionals, three are known, as I.B. is three feet and a quarter, which is 52 fingers, B.K. is 12, and I.H. is 20 fingers. Forming the rule of three, it is found that the fourth proportional H.N. is four fingers and three-fifths. This is the amount of movement the Diestro must make from the primary vertical plane A.B. to both sides, with the center of the guard and quillons of his sword, to place and contain his opponent’s sword outside the two vertical defense planes I.K. and I.L. to remain defended from any circular and semicircular tricks and their species aimed at him in the jurisdiction, as verified by figure nine.

Para el plano diametral del pecho

For the diametral plane of the chest