CAPITVLO TERCIODEZIMO

De los movimientos de la Espada, y del brazo en el Ayre

CHAPTER THIRTEEN

On the movements of the sword, and the arm in the Air

Del miſmo que hemos conſiderado en el cuerpo tres diferencias de movimientos, que ſe hazen, ò por planos, ò por circulos, ò por lineas, ò ſuperficies mixtas; aſsi en la Eſpada conſideramos otras treas diferencias de movimientos, los vnos por los planos, y los otros por circulos, los otros por lineas, ò ſuperficies mixtas: y en la miſma forma que de los movimientos circulares que haze el cuerpo, los vnos ſon ſobre ſu centro proprio, y los otros ſobre otros circulos diferẽtes; tambien en la Eſpada conſideramos movimiento ſobre ſu centro proprio, para regular el lugar, y poſicion de los gavilanes en la formacion de las tretas, y la conſideramos mover por otras circunſerencias, y las vnas mayores, y las otras menores: y como de los mixtos no hazemos mucho caſo para con el cuerpo, tampoco en la Eſpada nos canſarèmos en la eſpeculacion de infinitos movimientos curvos que ella puede hazer, procurando en todo ſeguir à los varones doctos, que han eſcrito de los movimientos de los Cielos, que ſiendo aſsi que la mayor parte de los movimientos de los Planetas ſon mixtos, no obſtante nos los repreſentan todos por medio de circulos, para que por medio de ellos ſe pueda alcanzar facilmente lo que por otra via parecia muy intrincado, y dificultoſo.

Just as we have considered in the body three types of movements, which are made either on planes, or circles, or lines, or mixed surfaces; similarly, in the Sword, we consider three other types of movements: some on planes, some on circles, and others on lines or mixed surfaces. And just as the body makes some circular movements on its own center and others on different circles; likewise, in the Sword, we consider movement on its own center to regulate the position of the guard in the formation of techniques, and we consider it moving on other circumferences, some larger and others smaller. Just as we don’t emphasize mixed movements for the body, we also won’t dwell on the infinite curved movements the Sword can make, always following learned scholars who wrote about celestial movements. Although most planetary movements are mixed, they represent all of them through circles to make the complex and challenging easily understandable.

Mas para explica los movimientos de la Eſpada, neceſsitamos de valernos de laugnos terminos recibidos entre los Mathematicos, por no inventar otros nuevos, imitando en eſto los Autores que han eſcrito de las Armas, que han comenzado en muchos de ellos, como quando llaman à los tajos verticales, orizontales, diagonales, &c. ſiendio aſsi, que ſiempre que la punta de la Eſpada ſe huviere de mover, ſerà por plano, ò por circulo, ò por linea mixta: para poder explicarlas con mas facilidad, declararèmos quantas diferencias de planos puede aver, y los que han obſervado los Opticos para repreſentar todas las diferencias de planos, y lineas, que no ſolo ſe deſcubren en todo el Univerſo, mas tambien los que han imaginado en los Cielos, repreſentandonos por medio de vnas lineas, que pintan ò en los Planipherios, ò Aſtrolabios, ò en las peredes, los movimientos del Sol, de la Luna, y del Firmamento: y ſu pueſto que en la tierra no ay planos, ni lineas, que no ſean paralelas à algunos de los que ſe conſideran en el Cielo, declararèmos todas las diferencias de planos, ò circulos, definiciones que han conſiderado en la Eſphera celeſte, que con eſto podrèmos ſaber la eſpecie de plano que hizieremos à qual de ellos ſerà paralelo, y por conſiguiente conocerèmos ſu eſpecie.

To explain the movements of the Sword, we need to use some terms accepted by mathematicians, rather than inventing new ones. We mimic authors who have written about weapons, who have introduced many such terms, like calling cuts vertical, horizontal, diagonal, etc. Every time the tip of the Sword moves, it will do so on a plane, or a circle, or a mixed line. To explain this more easily, we’ll discuss the different possible planes. Opticians have noted these to represent all the differences in planes and lines found in the universe, and even those imagined in the heavens. They depict the movements of the Sun, the Moon, and the Firmament through lines painted on planispheres, astrolabes, or walls. And since there are no planes or lines on earth that aren’t parallel to those considered in the sky, we will explain all the differences in planes or circles they’ve considered in the celestial sphere. This way, we can know what type of plane we’re making and which it’s parallel to, consequently understanding its type.

Ademàs de los diez circulos principales, que ſe conſideran en la Eſphera, los ſeis mayores: es à ſaber, Orizonte, Meridiano, Equinocial, Zodiaco, y los dos Coluros, Artico, y Antartico, y fuera de otros circulos que llaman Horarios, y de poſicion, &c. ay vnos circulos à que llaman Verticales, ò Acimuthes, y otros de Altura, &c. Y para que el entendimiento quede ſatisfecho, pondrè las demonſtraciones ſiguientes, cuya delineacion hallarà el Dieſtro en la ſeptima Lamina.

Besides the ten main circles considered in the sphere, the six major ones are: Horizon, Meridian, Equatorial, Zodiac, and the two Colures, Arctic and Antarctic. Beyond other circles called Hourly and Position, etc., there are circles called Verticals or Azimuths, and others of Altitude, etc. To satisfy understanding, I will present the following demonstrations, the layout of which the Swordsman will find in the seventh plate.

FIGURA PRIMERA

FIGURE ONE

Todos los circulos de la Eſphera ò ſon paralelos al Orizonte, ò ſon perpendiculares al Orizonte, ò ſon obliquos al Orizonte. Los circulo paralelos al Orizonte ſe llaman circulos del Altura, ò almitæ cantarath. como ſon los que ſe repreſentan por eſtas lineas rectas paralelas al Orizonte A.E.B.

All the circles of the sphere are either parallel to the Horizon, or perpendicular to the Horizon, or oblique to the Horizon. The circles parallel to the Horizon are called circles of Altitude, or almucantars, as are those represented by these straight lines parallel to the Horizon A.E.B.

No ignorarà el Lector que los circulos, aſsi maximos, como menores, ſegun las diverſas proiecciones que ay, vnas vezes ſe repreſenta como circulo, otras como lineas rectas, y otras como elipſis, ù ovalo.

The Reader should be aware that circles, both large and small, depending on the various projections, are sometimes represented as a circle, sometimes as straight lines, and other times as ellipses or ovals.

Eſtos circulos en la Eſphera ſirven para ſaber la altura que tiene el Sol, ò las Eſtrellas ſobre el Orizonte; es aſaber, quanto ſe aparta vn Aſtro del Orizonte, ò del Zenith, que es el punto C. Los miſmos circulos ſe pudieran conſiderar en el emisferio interior A.D.B.

In the Sphere, these circles are used to determine the altitude of the Sun or the Stars above the Horizon; that is, how much a celestial body is distant from the Horizon or from the Zenith, which is point C. The same circles could be considered in the inner hemisphere A.D.B.

En la Deſtreza de las Armas, como ya eſtà dicho, ſe conſidera vn plano orizontal, ò paralelo al Orizonte, que es el ſuelo; y para regular el lugar de la punta de la Eſpada, ò de la guarnicion, ò por mejor dezir quanto ſe aparta del plano inferior, ò del ſuperior, que es vn plano que paſſa por los centros de los brazos de los dos combatientes, ſe conſideran algunos planos paralelos al Orizonte, como ſe dirà en ſu lugar.

In the Art of Fencing, as already mentioned, a horizontal plane or one parallel to the Horizon is considered, which is the ground. To determine the position of the sword’s tip or its guard, or more specifically, how far it is from the lower plane or the upper plane (a plane that passes through the centers of the arms of both combatants), some planes parallel to the Horizon are taken into account, as will be explained in due course.

FIGURA SEGUNA

FIGURE TWO

Los circulos perpendiculares al Orizonte ſe llaman verticales, porque paſſan por el Zenith, y todos ſon maximos; y aunque pueden ſer infinitos los dividen los Aſtronomos en tres diferencias, en eſta forma.

The circles perpendicular to the Horizon are called verticals because they pass through the Zenith, and all are maximal. Although there can be infinitely many, astronomers divide them into three types, as follows:

El ciruclo vertical que mira derechamente à Mediodia, y al Septentrion, ſe llama Vertical primero.

The vertical circle that directly faces Noon and the North is called the First Vertical.

El circulo vertical que paſſa por el punto de mediodia, ſe llama Meridiano, y corta al vertical primario en Angulos rectos, mirando derechamente al Orizonte, y Occidente.

The vertical circle that passes through the noon point is called the Meridian, and it intersects the first vertical at right angles, directly facing the Horizon and the West.

Qualquier otro circulo vertical intermedio à eſtos dos, ſe llama Delinante, y eſta declinacion ſe entiende del vertical primero: deſuerte, que ſi eſte circulo ſe aparta por 30. grados del vertical primero, dirèmos que declina 30. grados, ò que tiene 30. grados de declinacion del Mediodia, ò del Septentrion, al Oriente, ò al Poniente: como por exemplo, en la ſegunda figura ſe A.B.C.D. el Orizonte, en que A. ſea el punto del Mediodia, B. Occidente, C. Septentrion, y D. el Orizonte.

Any other vertical circle between these two is called the Declining circle, and this declination is understood from the first vertical: thus, if this circle deviates by 30 degrees from the first vertical, we will say it declines by 30 degrees, or it has 30 degrees of declination from Noon, or from the North, to the East, or to the West. For example, in the second figure, A.B.C.D. is the Horizon, where A. is the noon point, B. is the West, C. is the North, and D. is the Horizon.

El circulo repreſentado por la linea D.B. que mira al punto A. por vna parte, y por la otra al Septentrion en C. ſe llama Vertical primero, y paſſa por el punto E. que repreſenta el vertice.

The circle represented by the line D.B. that faces point A. on one side and the North on C. on the other is called the First Vertical and passes through point E. which represents the vertex.

El circulo, ò plano repreſentado por la linea A.C. que paſſa por el Mediodia, y Septentrion, ſe llama Meridiano, y eſtà en Angulos rectos ſobre el vertical primero, porque diſta de toda la quarta de circulo D.A. mira derechamente al Orizonte en D. y al Occidente en B.

The circle or plane represented by the line A.C., which passes through Noon and the North, is called the Meridian. It is at right angles to the first vertical because it spans the entire quarter-circle D.A., directly facing the Horizon at D. and the West at B.

El circulo repreſentado por la linea recta F.G. que tambien paſſa por el vertice E. por quanto ſe aparta por el arco D.F. de 30. grados, ſe llamarà Declinante de 30. grados; lo miſmo ſerà de qualquier otro circulo, como el de H.I. que declina de 60. grados la vna parte que mira al Oriente, porque ſe deſcubre deſde el punto del Septentrion, ſe dirà declinar deſde el Septentrional Oriente: y la otra parte, que mira al Poniente, porque mira tambien al punto de Mediodia, ſe dize declinar deſde Mediodia al Occidente, ſegun fuere el arco que ſe conſidera entre èl , y el vertical primero.

The circle represented by the straight line F.G., which also passes through the vertex E., and deviates by the arc D.F. of 30 degrees, will be called Declining by 30 degrees. The same will be true for any other circle, like the one of H.I. that declines by 60 degrees. The part facing the East, because it is seen from the North point, will be said to decline from the North-East. The other part facing the West, because it also looks at the noon point, is said to decline from Noon to the West, depending on the arc considered between it and the first vertical.

FIGURA TERCERA

FIGURE THREE

Esta miſma demonſtracion và pueſta en la tercera Figura, imaginando el circulo Meridiano como circulo, y el Orizonte como linea, y el Vertical primero como linea tambien; mas el Declinante ſe repreſenta como Elipſis: y para que ſe vea mas claro, he procurado valerme de la miſmas letras en la vna que en la otra, ſalvo, que para explicar el Nadir he añadido en la tercera la letra K.

The same demonstration is presented in the third Figure, imagining the Meridian circle as a circle, the Horizon as a line, and the First Vertical as a line as well; however, the Declining circle is represented as an Ellipse. For clearer visualization, I’ve used the same letters in both figures. However, to explain the Nadir, I’ve added the letter K in the third figure.

Mas para poder explicar otras tres diferencias de circulos, ò planos, que nos faltan, es neceſſario ſaber primero, que qualquier circulo, aſsi mayor, como menor, tiene ſus Polos, y la linea que los junta ſe llama Axis ò Exe, ſobre que ſe mueve, ò ſe imagina moverſe.

But to explain the other three types of circles, or planes, that we have yet to discuss, it’s essential to know that every circle, both major and minor, has its Poles, and the line joining them is called the Axis or Axle, upon which it moves or is imagined to move.

El Polo en la ſuperficie de la Eſphera es vn punta que diſta igualmente por todas partes de ſu circunferencia, como el centro en la ſuperficie plana diſta igualmente de la circunferencia.

The Pole on the surface of the Sphere is a point that is equidistant from all parts of its circumference, much like the center on a flat surface is equidistant from its circumference.

En la ſegunda figura el Polo del Orizonte A.B.C.D es el punto E. que repreſenta el Zenith, ò Vertice; y por repreſentarſe en vn plano, y no en la ſuperficie de la Eſphera, no ay otro punto que pueda ſer Polo en eſte genero de proieccion ino el centro.

In the second figure, the Pole of the Horizon A.B.C.D is point E, representing the Zenith, or Vertex; and because it’s represented on a plane, not on the surface of the Sphere, there’s no other point that can be the Pole in this type of projection but the center.

El Vertical primero, repreſentado por la linea D.B. tiene ſus Polos en A. y C. que ſon el punto de Mediodia, y el Septentrion, y diſtan igualmente de la circunferencia repreſentada por D.B. por aver por qualquier parte vna quarta parte de circulo, como A.B.A.D.C.B.C.D. ſu Axis ſerà la linea A.C.

The First Vertical, represented by line D.B., has its Poles at A. and C., which are the Noon point and the North, and they are equidistant from the circumference represented by D.B. because anywhere there’s a quarter-circle, like A.B., A.D., C.B., C.D. Its Axis will be the line A.C.

Los Polos del Meridiano repreſentado por A.C. por la miſma razon, ſeràn los dos puntos D.B. el verdadero Oriente, y el verdadero Occidente, y ſu Axis D.B.

The Poles of the Meridian, represented by A.C. for the same reason, will be the two points D.B., the true East, and the true West, and its Axis D.B.

Lo miſmo ſe repreſenta en la tercera figura, en que ſiendo A.C. el Orizonte, ſu Polo ſerà el punto E. Vertice, y el Nadir en K. Los Polos del Meridiano ſon D.B. que correſponden à ſu centro, los Polos del vertical primero los miſmos A.C. los Polos de los declinantes eſtaràn en el Orizonte, y ſe apartaràn del Meridiano la miſma cantidad que tuiveren de declinacion.

The same is represented in the third figure, where A.C. is the Horizon, its Pole will be point E., Vertex, and the Nadir at K. The Poles of the Meridian are D.B. corresponding to its center; the Poles of the first vertical are the same A.C. The Poles of the declining circles will be on the Horizon and will deviate from the Meridian by the same amount of their declination.

Todo eſto ſe comprehendiera mejor por medio de vn Eſphera material, mas no obſtante con eſta inteligencia procurarè explicar las otras tres diferencia de Planos, que ſon inclinantes al Orizonte, declinantes de el Orizonte, y inclinantes, y declinantes juntamente.

All of this will be better understood through a tangible Sphere, but nonetheless, with this understanding, I’ll attempt to explain the other three types of Planes: those that lean towards the Horizon, those that decline from the Horizon, and those that both lean and decline simultaneously.

FIGURA QVARTA

FIGURE FOUR

En eſta figura ſupongamos que el circulo A.C.B.D es el Meridiano, A.B. el Orizonte, C.D. el Vertical primero; ſi el Vertical primero, moviendoſe ſobre los Polos del Meridiano, que correſponden al punto G. y ſe ſueſſe inclinando la linea C.D. el punto C. moviendoſe deſde C. por C.B. haſta F. y el punto D. por la circunferencia D.A. haſta E. llamariamos eſte circulo Inclinante al Orizonte, de tantos grados, quantos fueſſe el arco. B.F.

In this figure, let’s assume that the circle A.C.B.D is the Meridian, A.B. the Horizon, and C.D. the First Vertical. If the First Vertical, moving over the Poles of the Meridian that corresponds to point G, and if the line C.D. were to incline with point C. moving from C. through C.B. to F. and point D. moving along the circumference D.A. to E., this circle would be called Inclining to the Horizon, by as many degrees as the arc B.F. represents.

FIGURA QVINTA

FIGURE FIVE

Si el Meridiano ſe movieſſe ſobre los Polos A.C. del vertical primero, y ſe fueſſe inclinando al Orizonte, ò el Orizonte ſe fueſſe moviendo ſobre los miſmos puntos A. y C. vendria à repreſentar algun circulo, como A.F.C.G. que aunque eſtà inclinado al Orizonte, para hazer diftincion dèl con el paſſado ſe llama Declinante al Orizonte.

If the Meridian were to move over the Poles A.C. of the First Vertical and were to incline towards the Horizon, or if the Horizon were to move over the same points A. and C., it would come to represent some circle, such as A.F.C.G. Even though it is inclined towards the Horizon, to differentiate it from the previous one, it is called Declining to the Horizon.

FIGVRA SEXTA

FIGURE SIX

Mas ſi circulo declinante ſe fueſſe inclinando al Orizonte, acercandoſe à èl eſte circulo, ſe llamaria inclinante, y Declinante, como el circulo C.G.F.I que ademàs de la declinacion que ſe cuente con el arco G.H.G.I tambien tiene la inclinacion, que ſe cuneta por el arco C.D.

However, if the Declining circle were to incline towards the Horizon, approaching it, this circle would be called both Inclining and Declining, like the circle C.G.F.I. In addition to the decline measured by the arc G.H.G.I, it also has an inclination, which is measured by the arc C.D.

FIGVRA SEPTIMA

FIGURE SEVEN

De todo lo referido ſe ſigue, que todas las diferencias de planos ſe reducen à 7. que ſon Orizontales, Vertical primero, Vertical ſegundo, ò Meridiano, Declinantes, Inclinantes al Orozionte, Declinantes del Orizonte, y Inclinante, y Decliante juntamente.

From all that has been mentioned, it follows that all the distinctions of planes can be reduced to seven, which are Horizontal, First Vertical, Second Vertical or Meridian, Declining, Inclining to the Horizon, Declining from the Horizon, and both Inclining and Declining together.

Veamos aora como aplicarèmos eſto à la Eſpada, y ſi de eſtas imaginaciones ſe podrà ſacar alguna vltilidad.

Let’s now see how we can apply this to the Sword, and if any utility can be derived from these concepts.

Ya hemos dicho que el movimiento de la punta de la Eſpada ſe puede conſiderar moverſe por la ſuperficie de vna Eſphera, por cuya cauſa ſe puede llamar Eſpherico, ſi el circulo A.B.C.D. &c. formado con la Eſpada, quando el Dieſtro afirmado en I. en Angulos rectos, ſobre Angulos Rectos diere vna revolucion ſobre ſu centro, ò ſe conmſideraſſe moverſe ſobre ſu Diametro A.D. ò C.G cauſaria con ſu revolucion vn globo, como ya eſtà declarado en la Definicion del globo; y eſte globo propriamente ſe llamaria el globo de la Eſpada, y ſu juriſdiccion, porque ſe formaria del circulo particular de la Eſpada: en eſte globo podemos conſiderar las miſmas 7. diferencias de planos, por los quales ſe podrà mover la Eſpada, para la formacion del qualquier treta.

We have already stated that the movement of the tip of the Sword can be considered as moving across the surface of a Sphere. For this reason, it can be called Spherical. If the circle A.B.C.D. &c., formed with the Sword, when the Fencer stands firmly in position I at right angles, were to revolve around its center, or were considered to move around its Diameter A.D. or C.G, it would create a globe, as already defined in the Definition of the globe. This globe would precisely be called the globe of the Sword, and its jurisdiction because it is formed from the particular circle of the Sword. In this globe, we can consider the same seven distinctions of planes, through which the Sword can move for the formation of any technique.

El primero ſerà el orizontal, que ſe forma en el plano ſuperior A.B.C.D. &c.

The first will be the horizontal, formed on the upper plane A.B.C.D. &c.

El ſegunodo ſerà el circulo que ſe repreſenta por la linea recta C.G. que por paſſar por el vertice I. Polo del Orizonte, y Zenith, y por conſiderarſe paſſar por el centro del brazo derecho del adverſario, ſe llamarà Vertical primero; y ſe cauſaria eſte plano con la Eſpada àzia arriba, ò abaxo, cauſando en aquel plano los tres Angulos, que llaman Angulo Recto, Obtuſo, y Agudo, ò las tres poſturas, ò rectitudines, que llaman Recta ò Adelante, Alta y Baxa.

The second will be the circle represented by the straight line C.G. Since it passes through the vertex I, the Pole of the Horizon and Zenith, and is considered to pass through the center of the opponent’s right arm, it will be called the First Vertical. This plane with the Sword will be caused upwards or downwards, creating in that plane the three Angles, called Right Angle, Obtuse, and Acute, or the three postures or alignments, named Forward or Front, High, and Low.

El circulo que ſe repreſenta por la linea A.E. que en el globo Celeſte ſerìa Meridiano, aqui le llamarèmos Vertical ſegundo: eſte plano ſe podrà cauſar ſiempre que el Dieſtro levantare el brazo perpendicular, y moviere ſu Eſpada à vno lado, y à otro; eſte movimiento pocas vezes acontecerà, mas podrà formar otro movimiento con la Eſpada ſola, poniendola perpendicular, y el brazo recto: y aunque eſte circulo, que paſſa por el centro del brazo, tenga poco vſo, otro circulo, que paſſa por la muñeca, paralelo à èl, ſe puede entender por Vertical ſegundo; y ſi no fuere eſte, otro circulo, que paſſe por medio de la Eſpada, y dividia por medio el circulo comun tendrà las vezes de eſte, y ſerà de mucho vſo para regular los movimientos, ò poſicion de la Eſpada en qualquier de ſus rectitudines, ò poſturas, como por exemplo.

The circle represented by the line A.E., which in the celestial globe would be the Meridian, here we will call it the Second Vertical. This plane can always be caused when the Fencer raises his arm perpendicular and moves his Sword to one side and then the other. This movement will rarely happen, but another movement with the Sword alone, placing it perpendicular and the arm straight can be formed. Although this circle, passing through the center of the arm, is seldom used, another circle, passing through the wrist and parallel to it, can be understood as the Second Vertical. If not this, another circle, passing through the middle of the Sword and dividing the common circle in half, will serve as this and will be very useful to regulate the movements or position of the Sword in any of its alignments or postures, as an example.

DASE POR EXEMPLO LA FIGURA OCTAVA

FIGURE EIGHT IS GIVEN AS AN EXAMPLE

Si el circulo A.B.C.D. fueſſe circulo comun, que ſe conſidera entre los dos combatientes, el Dieſtro en D. y ſu adverſario en A. el circulo, ò plano que paſſa por A.D. ſerìa el plano Vertical primero; y el que paſſa por B.C. ſerìa el que llamamos Vertical ſegundo, que ſervirà infinito para la formacion de las Pyramides, y para conſiderar la poſicion de la Eſpada, aſsi del Dieſtro, como de ſu adverſario.

If the circle A.B.C.D. were the common circle, considered between the two combatants, with the Fencer at D. and his opponent at A., the circle or plane that passes through A.D. would be the First Vertical plane; and the one passing through B.C. would be what we call the Second Vertical, which will be infinitely useful for the formation of Pyramids and to consider the position of the sword, both of the Diestro and his opponent.

Los circulos, ò planos, que paſſando por el Vertice I. ſe apartan del Vertical primero, como ſon en la figura antecedente D.H. y B.F. ſe llamaràn Declinantes derechos, ò ſinieſtros, ſegun la parte adonde fuere la declinacion, y ſe formaràn ſiempre que el Dieſtro aviendo apartado ſu Eſpada del plano Vertical primero, como deſde I.C. à I.D. la levantare arriba, ò la baxare abaxo, cauſando en eſte plano los tres Angulos, Recto, Obtuſo, u Agudo, ò las tres rectitudines que llaman alta, y à vn lado, baxa, y à vn lado: y los movimientos que ſe hazen por eſtos planos ſe llaman violentos para ſubir, y naturales para baxar: lo miſmo ſe entenderà de los planos que ſe pudieren formar à la mano izquierda.

The circles or planes that, passing through the Vertex I., deviate from the First Vertical, such as D.H. and B.F. in the previous figure, will be called Right Declining or Left Declining, depending on the direction of the decline. They will form every time the Diestro, having moved his sword away from the First Vertical plane, such as from I.C. to I.D., raises it upwards or lowers it downwards, creating in this plane the three angles: Right, Obtuse, or Acute, or the three positions they call high and to one side, low and to one side. The movements made by these planes are called violent to go up and natural to go down. The same understanding applies to the planes that can be formed on the left hand.

El plano que ſe llama Inclinante al Orizonte, ſe formarà todas las vezes que el Dieſtro eſtuivere afirmado en Angulo recto en ſu plano Vertical primero, y moviere ſu Eſpada al Angulo Agudo, ò Obtuſo de alguno de los planos declinantes: como por exemplo, eſtando ſobre I.C. en Angulo recto, ſi ſe paſſare al plano I.D. no con movimiento orizontal, ſino obliquo à la poſtura alta de la linea, ò Plano I.D. el plano que hizere ſerà inclinante al Orizonte: y ſi deſde alli ſe volviere à reducir, y paſſare à la poſtura baxa del plano I.B. tambien ſerà por el miſmo plano inclinante al Orizonte: mas eſte movimiento ſe haze para formar los tajos que llaman Diagonales, y aſsi no pretendo innovar los terminos recibidos, ſino ſolo dar à entender, que no ay movimiento que no pueda ſer regulado, y ajuſtado con la Eſpada, ſi querèmos atender à ello, porque qualquier movimiento que ſe hiziere con la Eſpada, es preciſo que ſea por alguno de eſtos ſiete planos, los quales bien entendidos, podremos en la formacion de qualquier treta conocer la naturaleza de qualquier movimiento que la compuſiere.

The plane called Inclining to the Horizon will form every time the Diestro is positioned at a right angle in his First Vertical plane and moves his sword to the Acute or Obtuse angle of one of the declining planes. For example, being on I.C. at a right angle, if one moves to the plane I.D., not with a horizontal movement but oblique to the high posture of the line or Plane I.D., the created plane will be inclined to the Horizon. If from there one returns and moves to the low posture of the plane I.B., it will also be through the same plane inclining to the Horizon. However, this movement is made to form the cuts called Diagonals. So, I do not intend to change the accepted terms, but only to make clear that there isn’t a movement that cannot be regulated and adjusted with the sword if we pay attention to it. Because any movement made with the sword must necessarily be through one of these seven planes. If we understand them well, we will be able to recognize the nature of any movement that composes any tactical move.

Los planos declinantes de Orizonte ſe formaràn todas las vezes que eſtando el Dieſtro afirmado en Angulos agudo en ſu plano vertical primero, paſſare ſu Eſpada al Angulo agudo, ò poſtura baxa de algun plano declinante, à la otra parte; y de eſte movimiento ſe valen para tirar canillazos algunas vezes, ò para formar otras diferencias de tretas, como verèmos en ſu lugar.

The Declining Planes from the Horizon will be formed every time that, with the Diestro positioned at an acute angle in his First Vertical plane, he moves his sword to the acute angle or low posture of some declining plane, to the other side. This movement is sometimes used to strike at the shins or to form other variations of tactics, as we will see in due course.

Eſto es lo que he juzgado por aora dezir de los diferentes planos, que ſe pueden cauſar con la Eſpada, y aunque al preſente parezca eſto algo confuſo, y obſcuro, deſpues verà el Dieſtro la claridad, y diſtincion, que le cauſarà el vſo de eſtas imaginaciones en lo eſpeculativo, y practico de la Deſtreza.

This is what I have deemed appropriate to say for now about the different planes that can be created with the sword. Although at present this may seem somewhat confusing and unclear, the Diestro will later see the clarity and distinction that the use of these concepts will provide in both the theoretical and practical aspects of the art of fencing.

FIGURA NONA

FIGURE NINE

Tambien los Opticos han conſiderado ſiete diferencias de planos, y de lineas, para reprefentar en vn lienço de pintura, por medio de la perſpectiva, todas las coſas viſibles, eſpecialmente las coſas que tocan à los Edificios; ſi bien con alguna diferencia de los que ſe conſideran en la Eſphera Celeſte, comparando eſtas lineas, y planos con el lienço en que ſe han de repreſentar, como por exemplo.

The optical artists have also identified seven different planes and lines to represent on a canvas, through perspective, all visible things, especially architectural structures. Even though there’s some variation compared to those considered in the Celestial Sphere, these lines and planes can be compared with the canvas they are to be represented on. Let’s explain with an example:

Supongamos que el lienço en que ſe huviere de pintar fueſſe el quadrado A.B.C.D. que ſe conſidera perpendicular al Orizonte, y que la linea que llaman del plano, adonde ſe imagina tocar el ſuelo, fueſſe la linea A.B.

Imagine the canvas upon which a painting is to be made is the square A.B.C.D., considered perpendicular to the horizon, and the line that they refer to as the plane, where the ground is imagined to meet, is the line A.B.

Todas las linea que caen perpendicularmente ſobre A.B. ſe llaman lineas Directas, como la linea E.F.

All lines falling perpendicular onto A.B. are called Direct lines, like the line E.F.

Las lineas que ſon paralelas à A.B. ſe llaman Adverſas, como la I.G.

Lines parallel to A.B. are called Adverse, like I.G.

Las lineas que por la vna, ò otra parte ſe apartan de la E.F. ſe llaman Declinantes, como la E.H. Todas eſtas lineas ſe conſideran en el Plano orizontal, ò paralelo à èl.

Lines that deviate to one side or the other from E.F. are called Declining, like E.H. All these lines are considered in the horizontal plane or parallel to it.

Si la linea directa E.F. ſe fueſſe levantando por alguna de ſus extremidades en F. ò en E. quedando la otra extremidad en el ſuelo, ſe llamaria Inclinante al Orizonte.

If the direct line E.F. were to rise from one of its endpoints, either F. or E., leaving the other endpoint on the ground, it would be called Inclining to the Horizon.

Si la linea adverſa ſe fueſſe levantando en la miſma forma, ſe llamaria Declinante del Orizonte.

If the adverse line were to rise in the same manner, it would be called Declining from the Horizon.

Si la linea declinante E.H. ſe fueſſe levantando en la forma referida, ſe llamaria Declinante y Inclinante juntamente: todas eſtas teres diferencias de lineas eſtaràn obliquas al Orizonte. Y la linea perpendicular al Orizonte ſe llama Erecta: con que tenemos eſtas ſiete diferencias de lineas, que aplicadas à la Eſpada, ſe conſideran en eſta forma.

If the declining line E.H. were to rise as mentioned, it would be called both Declining and Inclining simultaneously. All these three different lines are oblique to the horizon. And the line perpendicular to the horizon is called Erect. Thus, we have these seven different lines. When applied to the sword, they are considered in the following manner:

Todas las vezes que el Dieſtro eſtuviere afirmado con ſu contrario deſuerte, que ſu Eſpada eſtè paralela al Orizonte, y que la punta mire rectamente derecha à ſu contrario, deſuerte que eſtè perpendicularmente ſobre ſu cuerpo, diremos que la linea de la Eſpada ſerà directa.

Every time the Diestro stands opposite his adversary such that his sword is parallel to the horizon, and its tip points directly at his adversary, so that it’s perpendicular to his body, we’ll say the sword’s line is direct.

Todas las vezes que la fuere apartando de eſta rectitud paralela al Orizonte, y llegare à alguno de los planos declinantes, à vno, ò à otro lado, ſe dirà declinante.

Every time he deviates from this parallel alignment with the horizon, and it reaches one of the declining planes, either to one side or the other, it’s said to be declining.

Todas las vezes que conſervando la paralela al Orizonte, la cruzare delante del cuerpo deſuerte, que haga Angulo recto ſobre la del contrario, que eſtè en el Diametro comun, ſe llamarà Adverſa.

Every time, while maintaining its parallel alignment with the horizon, he crosses it in front of his body in such a way that it forms a right angle with his adversary’s sword, which is on the common diameter, it’s called Adverse.

Si eſtando afirmado en Angulo recto en ſu plano ſertical primero levantare, ò baxare la punta, ſin apartarle à vno, ni à otro lado, eſta linea ſe llamarà Inclinante al Orizonte, que ſerà eſtando en Angulo obtuſo, ò agudo.

If, while standing at a right angle on his initial vertical plane, he raises or lowers the tip without moving it to one side or the other, this line will be called “Inclined to the Horizon”, which will be when it’s at an obtuse or acute angle.

Siempre que teniendo la Eſpada en Angulo agudo, ò obtuſo, la apartare del plano vertical primero, y la llevare à vno, ò à otro plano declinante, ſe llamarà Declinante, y Inclinante juntamente. Y ſiempre que eſtando adverſa la inclinare, ſe llamarà Declinante del Orizonte. Y ſi la levantare el alto deſuerte que eſtè perpendicular al Orizonte, ſe llamarà Erecta.

Whenever holding the sword at an acute or obtuse angle, if he moves it away from the initial vertical plane and takes it to one or another declining plane, it will be called “Declining and Inclining simultaneously”. And every time, if he inclines it while it’s adverse, it will be called “Declining from the Horizon.” And if he raises it so high that it’s perpendicular to the horizon, it will be called “Upright”.

Todo eſto que ſe ha dicho de las lineas, ſe entenderà de los planos, porque como los planos ſe conſideran contenidos de lineas, ſegun la naturaleza de las lineas de que fueren comprehendidos tomaràn ellos el nombre: deſuerte, que ſi vn plano fuere contenido de lineas directa, ſe llamarà Directo; ſi de lineas declinantes, ſe llamarà Declinante; ſi de inclinantes, ſerà Inclinante; y lo miſmo de las demàs.

Everything that has been said about the lines will be understood about the planes because as the planes are considered contained by lines, according to the nature of the lines by which they are understood, they will take their name: so, if a plane is contained by direct lines, it will be called “Direct”; if by declining lines, it will be called “Declining”; if by inclining ones, it will be “Inclining”; and the same for the others.

Lo que haſta aora ſe ha dicho de las lineas, que ſe pueden conſiderar en la Eſpada, ſe ha de atender en las lineas, que ſe conſideran en la linea del braço, y de cada vna de ſues partes, porque para poder eſpecificar la poſicion, aſsi del todo el brazo, com de la parte que eſtà entre ſu centro, ſangria, como de la reſtante, que eſtà la ſangria, y la muñeca, hemos de conſiderar las miſmas diferencias de lineas.

What has been said so far about the lines that can be considered in the sword must be attended to in the lines that are considered in the arm’s line, and each of its parts, because to specify the position, both of the entire arm and of the part that is between its center and the blood groove, as well as the remaining part between the blood groove and the wrist, we must consider the same differences in lines.

Mas como es dificultoſo regular la declinacion, y la inclinacion tan diferente, que pueden tener eſtas partes, he juzgado mas à propoſito valerme del miſmo medio de que ſe valen los Aſtronomos para ſenalar el lugar de alguna Eſtrella, ò Cometa en el Cielo; es à ſabre, por medio de vnos circulos verticales, y otros orizontales, porque ſi vna vez determinamos el lugar de la punta de la Eſpada, es à ſaber, en què plano declinante, ò vertical eſtuviere, y luego ay forma para determinar ſu altuira en aquel plano, y lo miſmo hizieremos del pomo, no podrà faltar el conocimiento de la verdadera poſicion de todas la Eſpada.

But as it is difficult to regulate the declination and the very different inclination that these parts can have, I have found it more appropriate to use the same method that astronomers use to mark the place of some star or comet in the sky; that is, by means of some vertical circles and others horizontal, because if once we determine the position of the sword tip, that is, in which declining or vertical plane it is, and then there’s a way to determine its height in that plane, and we would do the same for the pommel, we won’t lack the knowledge of the true position of the entire sword.

Los planos verticales que he conſiderado, para ſaber la declinacion que la Eſpada tuviere del plano vertical primero, ſon nueve, y ſe comiençan v contar en la forma figuiente.

The vertical planes that I have considered, to know the declination that the sword has from the first vertical plane, are nine, and they begin to be counted in the following manner.

FIGURA DEZIMA

TENTH FIGURE

Sea el Orbe particular del Dieſtro A.B.C.D. ò el mayor, y ſea A.C. el que repreſenta el plano vertical derecho, y izquierdo, ò el plano que paſſa por ambas verticales derecha, y ſinieſtra, y B.D. las que repreſenta el plano que paſſa por la vertical del pecho, y de las eſpaldas, dividaſe la quarta C.B. y B.A. en partes iguales con las lineas E.F.G.H. y ſeràn los planos que correſponden à las colaterales, como ya eſtà dicho; dividaſe cada arco en dos partes iguales en K.L.M.N. y ſaquenſe lineas del centro: eſtas lineas repreſentaràn los planos verticales, de que neceſsitamos para regular el movimiento de la Eſpada, en quanto lo que ſe apartare del plano vertical primero; y para que ſu conocimiento ſea mas facil, y mas inteligible al plano que correſponde al vertical derecho repreſentado por la linea I.C. le llamarèmos Primero al que le ſigue inmediatamente repreſentado por I.K. ſegundo. Al plano I.E. entre el colateral dercho, y vertical del pecho, le llamarèmos quarto. Al vertical del pecho, le llamarèmos quinto: y aſsi conſecutivamente de los demàs haſta el plano vertical izquierdo I.A. que es el 9.

Let the individual sphere of the fencer be A.B.C.D., or the larger one, and let A.C. represent the right and left vertical plane, or the plane that passes through both the right and left verticals, and B.D. the one that represents the plane that passes through the vertical of the chest and back. Divide the fourth C.B. and B.A. into equal parts with the lines E.F.G.H. and these will be the planes corresponding to the collaterals, as already mentioned. Divide each arc into two equal parts at K.L.M.N. and draw lines from the center: these lines will represent the vertical planes that we need to regulate the movement of the sword, in relation to how much it deviates from the first vertical plane; and for easier understanding, we will call the plane corresponding to the right vertical represented by the line I.C. as “First” and the one immediately following it, represented by I.K., as “Second”. The plane I.E. between the right collateral and the chest vertical will be called “Fourth”. The vertical of the chest will be called “Fifth”: and so on for the rest up to the left vertical plane I.A., which is the 9th.

Si eſtas lineas ſe vàn ſubiendo con todo el circulo arriba haſta el nivel de la cabeza, no ſolo iràn ſeñalando los planos verticales, que hemos de conſiderar, mas tambien moſtraràn, y ſeñalaràn las lineas verticales principales, y ſus intermedias en la ſuperficie del cuerpo del Dieſtro, como ſe vè en la figura, en que la linea C.A. que repreſenta el plano vertical derecho, y izquierdo, forma con ſu movimiento en la ſuperficie del cinlindro, en que ſe conſidera el Dieſtro, las lineas O.T. vertical derecha, y S.V. vertical izquierda.

If these lines rise with the entire circle upwards to the level of the head, they will not only mark the vertical planes that we need to consider, but will also display and mark the main vertical lines and their intermediates on the surface of the fencer’s body, as seen in the figure, where the line C.A. representing the right and left vertical plane, forms with its movement on the surface of the cylinder, which represents the fencer, the lines O.T. for the right vertical and S.V. for the left vertical.

Los planos colaterales E.F.G.H. cauſan las dos lineas P.X. colateral derecha, y R.S. colateral izquierda. Y el diametral del pecho B.D. cauſan en la ſuperficie del cuerpo la vertical del pecho, ò Diametral Q.Y. como ſe vè en la miſma figura; y las lineas de puntos intermedias cauſan ſus lineas intermedias à las verticales, y colaterales.

The collateral planes E.F.G.H. create the two lines P.X. for the right collateral and R.S. for the left collateral. And the chest’s diametrical B.D. causes the chest’s vertical, or Diametrical Q.Y., as seen in the same figure; and the intermediate dotted lines cause their intermediate lines to the verticals and collaterals.

Para la conſideracion de los planos paralelos al Orizonte hemos imaginado que al tiempo que el circulo del plano inferior A.B.C.D. ſe và levantando paralelo al Orizonte, và dexando ſus verſtigios en ciertos lugares, como ſe repreſenta por las lineas que eſtan tiradas paralelas à la linea 1.9. del plano inferior; y eſto ſe ha pueſto aſsi para mayor claridad, y he imaginado otros nueve planos, contando el plano inferior: y eſto es para conſiderar la altura, que la punta de la Eſpada eſtarà del plano inferior, y lo vamos graduando en eſta forma.

For the consideration of the planes parallel to the horizon, we’ve imagined that as the circle of the lower plane A.B.C.D. rises parallel to the horizon, it leaves its traces in certain places, as represented by the lines that are drawn parallel to the line 1.9. of the lower plane; and this is done for clarity, and I’ve imagined another nine planes, including the lower plane: and this is to consider the height at which the sword’s tip will be from the lower plane, and we are grading it in this manner.

El primero ſerà el plano inferior, ò el ſuelo en que ſe halare el Dieſtro. El ſegundo paſſarà por el intermedio del plano inferior, y de las rodillas. El tercero por las rodillas. El quarto por entre las rodillas, y la cintura. El quinto por la cintura. El ſexto por entre la cintura, y los centros de los brazos. El ſeptimo por los centros de los brazos. El octavo pora la boca, ò por las narices. El nono por la extremidad de la cabeza.

The first will be the lower plane, or the ground on which the fencer stands. The second will pass through the midpoint between the lower plane and the knees. The third through the knees. The fourth between the knees and the waist. The fifth at the waist. The sixth between the waist and the centers of the arms. The seventh through the centers of the arms. The eighth through the mouth or nose. The ninth at the top of the head.

Aqui repararàn los curioſos en que para determinar el lugar fixo de la punta de la Eſpada, no baſta ſeñalar el plano vertical, y orizontal en que eſtuviere, que eſto ſe entiende lo hazen los Aſtronomos, para determinar el lugar de las Eſtrellas fixas, que todas ſe conſideran en el Firmamento; mas no vaſtan eſtos dos circulos, para determinar el lugar verdadero de los Planetas, que eſtàn en otros Cielos inferiores, y que para hazerlo neceſsitan de ſaber la diſtancia fixamente el lugar del Planeta, lo qual ſe halla por medido de la Paralaxis, ò diverſidad de aſpecto; y que para poder determinar fixamente el lugar de la punta, ò pomo de la Eſpada, ò del codo, era neceſſario determinar la diſtancia de cada vno de eſtos puntos à la linea de direccion, que ſe conſidera paſſar por medio del cilindro en que ſe conſidera el Dieſtro; y eſto tambien ſerà facil, mas no ſerà neceſſario, porque como el codo tiene ya ſu longitud determinada deſde ſu centro, ſi vna vez ſe determina el plano orizontal en que eſtuviere aquel plano, no puede ſer mas de vno, y aſsi ſervirà como de lugar comun para aquel punto: y ſi ademàs de eſto le determinamos ſu plano vertical, tambien ſerà lugar comun, y no podrà eſtar en vn tiempo en diferentes verticales; luego en la interſeccion de eſtos dos planos, que ſerà vna linea recta, avrà de eſtar el centro del codo, y en eſta linea determinarà el lugar la longitud del brazo deſde el centro haſta el codo, ò ſangria.

Curious readers will note that to determine the fixed position of the sword’s tip, it is not enough to just mark the vertical and horizontal plane where it is located. Astronomers do this to determine the position of the fixed stars, all of which are considered in the Firmament. However, these two circles are insufficient to determine the true position of the planets, which are in other lower heavens. To do so, it’s necessary to know the distance, which is found by measuring Parallax, or the difference in appearance. To precisely determine the position of the sword’s tip, hilt, or elbow, it is necessary to determine the distance of each of these points to the direction line, considered to pass through the middle of the cylinder in which the fencer is considered. This is easy but not necessary because the elbow already has its determined length from its center. If we determine its horizontal plane, it can only be one, and thus it will serve as a common place for that point. If, in addition to this, we determine its vertical plane, it will also be common, and it cannot be in different verticals at the same time. Therefore, at the intersection of these two planes, which will be a straight line, the center of the elbow must be located. The location along this line will be determined by the arm’s length from the center to the elbow or the “sangria”.

Determinado el punto del codo ſe podrà hazer lo miſmo del centro de la guarnicion, con que ſe ſabrà preciſamente ſu lugar, y poſicion por la miſma razon, porque ſon dadas las tres coſas que ſe piden, que es la interſeccion de los dos planos orizontales, y vertical, y el lugar determinado en aquella linea, por ſaber la diſtancia que au deſde el codo à la muñeca; y pueſto eſta determinado, y ſabido el lugar del codo, ſe ſabrà el de la muñeca por medio de vn circulo, que ſe forma con la longitud que ſe halla deſde el codo à la muñeca.

Having determined the elbow’s point, the same can be done for the center of the guard, thus precisely knowing its place and position for the same reason. These are the three things required: the intersection of the two horizontal and vertical planes, and the determined place on that line, knowing the distance from the elbow to the wrist. Once this is determined and the elbow’s location is known, the wrist’s location will be known through a circle formed by the length from the elbow to the wrist.

La miſma razon ſe ſigue para ſaber determinar el lugar de la punta de la Eſpada, ſi bien, que como la Eſpada puede ſubir mucho mas alto que la cabeza, podemos imaginar otros quatro planos ſobre los referidos, diſtantes cada vno de ſu inferior vn pies, que ſeràn quatro pies en todo, que ſerà todo lo que la punta de la Eſpada podrà ſubir en la formacion de las tretas: con que por medio de eſtos planos no avrà poſicion, ni rectitud, aſsi del brazo, como de la Eſpada, que no ſe pueda explicar, para poder declarar con individualidad la perfecta formacion de las tretas, aſsi en ſu principio, y medio, como en ſu fin.

The same logic follows to determine the position of the sword’s tip. However, since the sword can rise much higher than the head, we can imagine another four planes above the mentioned ones, each one foot apart from its lower counterpart, totaling four feet, which is the maximum height the sword’s tip can reach in the formation of tactics. Thus, with these planes, there will be no position or straightness, both of the arm and of the sword, that cannot be explained to be able to declare with specificity the perfect formation of tactics, both in their beginning, middle, and end.

Lamina ſeptima del Libro ſegundo.

Plate seven of the second book.