CAPITVLO DECIMOOCATVO

Symmetria del brazo, y Espada, y de las diviſiones que ſe conſideran en ambas coſas, de cuya revolucion reſultand los ſeis Orbes neceſſarios para regular los movimientos del cuerpo en el plano inferior, para conocer y determinar la perfecta eleccion de los medios proporcionados.

CHAPTER EIGHTEEN

Symmetry of the Arm and Sword, and of the Divisions Considered in Both, from Whose Revolution Result the Six Necessary Orbs to Regulate the Movements of the Body on the Lower Plane, to Understand and Determine the Perfect Selection of Proportional Means.

Aſsi en el Libro de la Sciencia, como en eſte del Arte de regir, y governar el inſtrumento Armigero Eſpada, hemos moſtrado que la Deſtreza de las Armas es ſciencia ſubalternada à las Mathematicas, particularmente à la Geometria, por eſtar fundada en el conſideracion de todos los quatro generos de cantidad, &c. Y que à imitacion de los Philoſophos antiguos, y Coſmographos, que para hallar los movimientos de los Aſtros en el Cielo, y regular el de los Navios en el Agua, ſe han valido forzoſamente de ſciencias Mathematicas, no ſiendoles poſibles por otra via; y que à noſotros tambien nos ha ſido fuerça ampararnos de ellas, para regular el movimiento de la Eſpada en el Ayre, y del cuerpo en la Tierra: ademàs, que los que tratan del Arte Militar, para ſaber no ſolo el movimiento, ò el camino, que haze la bala por el Ayre, el que ha de hazer la Artilleria, y Eſquadrones por los Aproches, para acercarſe à la Plaza; pero tambien el que ſe ha de hazer para dirigir las minas por debaxo de la tierra à la parte conveniente al efecto que ſe pretende, las reglas que dan, eſtan fundadas en Mathematicas: todo lo qual ſienso aſsi, darèmos principio à la conſtruccion de vna figura, por medio de la qual ſe alcança, y aclara mas el fundamento de eſta ſciencia, ſuponiendo para ella lo que todos los que han tratado de Mathematicas: es à ſaber, que todo punto ſe mueve por linea recta, ò curva; toda linea ſe mueve por linea, ò forma ſuperficie; toda ſuperficie ſe mueve por ſuperficie, ò cauſa cuerpo, ſegun Euclides libro 11. Definicion 12. y 18. Todo cuerpo, quando ſe mueve, ſi es ſu movimeinto local, cauſa cuerpo de otra eſpecie; pero ſi ſobre ſu axis algunos deſcriben cuerpo diferentes, y otros no. Mediante lo qual, paſſo à la conſtruccion, ò explicacion de la figura.

Both in the Book of Science and in this one on the Art of Managing and Governing the Armed Instrument, the Sword, we have shown that the Skill of Arms is a science subordinated to Mathematics, particularly to Geometry, as it is founded on the consideration of all four types of quantity, etc. And that, following the example of ancient Philosophers and Cosmographers, who, in order to find the movements of the Stars in the Sky and to regulate the movement of Ships on Water, necessarily relied on Mathematical sciences, as it was impossible by other means; and that we too have been forced to rely on them to regulate the movement of the Sword in the Air, and of the body on the Earth. Moreover, those dealing with Military Art, to know not only the movement or path of the bullet through the Air, the movement to be made by the Artillery and Squadrons through the Approaches to get closer to the Fortress, but also the movement to be made to direct mines beneath the earth to the part convenient for the intended effect, give rules based on Mathematics: all of which I mention so that we can begin the construction of a figure, through which the foundation of this science becomes clearer and more understandable, assuming what all those who have dealt with Mathematics have assumed: namely, that every point moves in a straight or curved line; every line moves in a line or forms a surface; every surface moves in a surface or causes a body, according to Euclid Book 11, Definitions 12 and 18. Every body, when it moves, if its movement is local, causes a body of another kind; but if it moves about its axis, some describe different bodies, and others do not. With this in mind, I move on to the construction or explanation of the figure.

Explicacion de la Symmetria del brazo, y Eſpada.

Explaining the Symmetry of the Arm and Sword.

Eſta explicacion ſe puede hazer en dos maneras, la primera tomando en el plano inferior la cantidad A.B. de ſeis pies Geometricos, dividida en ſeis partes, como ſeñalan los numeros deſde B. haſta A.1.2.3.4.5.6. y centro A. con el punto de cada vna de eſtas diviſiones, ſi ſe diere vna revolucion, quedarà formado el circulo B.D.F.H. que repreſentarà el orbe de la Eſpada, y cada punto avrà deſcripto vno de los otros cinco orbes, como ſe vè en la figura.

This explanation can be made in two ways, the first taking on the lower plane the quantity A.B. of six Geometric feet, divided into six parts, as indicated by the numbers from B to A.1.2.3.4.5.6., and with the center A, if a revolution is given from each of these divisions, the circle B.D.F.H. will be formed, representing the orb of the Sword, and each point will have described one of the other five orbs, as seen in the figure.

El ſegundo modo es ſuponer al Dieſtro afirmado ſobre Angulo recto en A.N. y en Angulo recto con ſu brazo, y Eſpada M.L.A. con las miſmas diviſiones en el brazo, y Eſpada, en el plano ſuperior 1.2.3.4.5.6. y deſde la extremidad de la punta de la Eſpada, y de cada vna de las diviſiones, ſu perpendiculo el plano inferior B.D.F.H. que ſe termine en la linea B.A. en los miſmos numeros 1.2.3.4.5.6. correſponientes à los del plano inferior, como ſe vè en la figura que eſtà en alzado.

The second method is to suppose the Fencer affirmed on a right angle at A.N. and at a right angle with his arm and Sword M.L.A., with the same divisions in the arm and Sword, on the upper plane 1.2.3.4.5.6., and from the extremity of the tip of the Sword and from each one of the divisions, draw a perpendicular to the lower plane B.D.F.H. that ends on the line B.A. at the same numbers 1.2.3.4.5.6. corresponding to those of the lower plane, as seen in the figure that is in elevation.

Imagineſe que el Dieſtro dà vna revolucion ſobre el centro de ſu pie derecho, conſervandoſe en la miſma poſtura de cuerpo, brazo, y Eſpada, con que cada vna de las extremidades de los ſeis perpendiculos, cauſarà ſu circulo en el plano inferior, y quedaràn formados ſeis circulos concentricos, cuyos eſpacios intermedios llamamos Orbes de vn pie Geometrico, cada vno que ſeñalan los miſmos numeros 1.2.3.4.5.6 En eſtos Orbes hemos pueſto la proieccion de la Eſpada en las diviſiones de los ocho rumbos que imaginamos como veſtigos que dexa con la revolucion en el Ayre, quando paſſa por los ocho planos principales, que tambien imaginamos que por ſe de tanto vſo, y fundamento en la Deſtreza nos ha parecido ſeñalarlos con las Eſpadas, dexando ſu explicacion para adelante en ſu lugar; y eſtos ocho planos tienen ſu comun ſeccion en el centro A. de la figura, y ſon los caminos mas eſſenciales por dodnde el Dieſtro ha de regular ſus operaciones: y porque las ſiguras en alzado no ſon para todos inteligibles, hemos pueſto la que ſe figue à ella, con las miſmas proiecciones en plano, que es la primera que queda explicada, como mas facil de percibir. Y en ambas ſe ha eſcuſado multiplicar letras, porque para ſu inteligencia baſta las que ſe han pueſto, para no cauſa confuſion.

Imagine that the Fencer makes a revolution around the center of his right foot, maintaining the same posture of body, arm, and Sword, with each of the extremities of the six perpendiculars causing its circle on the lower plane, and six concentric circles will be formed, whose intermediate spaces we call Orbs of one Geometric foot each, indicated by the same numbers 1.2.3.4.5.6. In these Orbs, we have placed the projection of the Sword in the divisions of the eight directions that we imagine as traces left by the revolution in the Air when it passes through the eight main planes, which we also imagine to be of so much use and foundation in Skill that we have deemed it appropriate to mark them with the Swords, leaving their explanation for later in their place; and these eight planes have their common section in the center A. of the figure, and are the most essential paths through which the Fencer must regulate his operations: and because the figures in elevation are not intelligible to all, we have put the one that follows it, with the same projections in plan, which is the first one explained, as it is easier to perceive. And in both, we have avoided multiplying letters, because for their understanding it is enough with those that have been placed, to avoid confusion.

Explicada la idea de nueſtro Fuerte, y la cantidad, ò tamaño que ha de tener el eſcudo para ſu defenſa, lo mas inmediato es dar conocimiento, en virtud de que ſe avrà de obrar, por la orden que eſtà diſpueſto, para que pueda el Dieſtro conſeguir los dos fines, defenſa, y ofenſa ſi conviniere; y aſsi para hazer evidencia en què conſiſten, y como ſe podràn formar los valuartes interiores, y exteriores de nueſtro Fuerte, nos valdrèmos de la extatica, para por medio de ella demonſtrar quan facil es ſu poſsibilidad.

Having explained the idea of our Fortress and the size or dimensions that the shield must have for its defense, the most immediate thing is to provide knowledge, according to the order that has been established, so that the Fencer can achieve both ends, defense and offense if appropriate; and so to make evident what they consist of, and how the inner and outer bulwarks of our Fortress can be formed, we will use statics, to demonstrate through it how easy its possibility is.

Lamina doze del Libro ſegundo

Plate twelve of Book Two.