1. I SHALL explain the symmetrical principles on which scorpiones and ballistae may be constructed, inventions devised for defence against danger, and in the interest of self-preservation.
The proportions of these engines are all computed from the given length of the arrow which the engine is intended to throw, and the size of the holes in the capitals, through which the twisted sinews that hold the arms are stretched, is one ninth of that length.
2. The height and breadth of the capital itself must then conform to the size of the holes. The boards at the top and bottom of the capital, which are called “peritreti,” should be in thickness equal to one hole, and in breadth to one and three quarters, except at their extremities, where they equal one hole and a half. The sideposts on the right and left should be four holes high, excluding the tenons, and five twelfths of a hole thick; the tenons, half a hole. The distance from a sidepost to the hole is one quarter of a hole, and it is also one quarter of a hole from the hole to the post
3. The opening in the middle post, where the arrow is laid, is equal to one fourth of the hole. The four surrounding corners should have iron plates nailed to their sides and faces, or should be studded with bronze pins and nails. The pipe, called su=pic in Greek, has a length of nineteen holes. The strips, which some term cheeks, nailed at the right and left of the pipe, have a length of nineteen holes and a height and thickness of one hole. Two other strips, enclosing the windlass, are nailed on to these, three holes long and half a hole in breadth. The cheek nailed on to them, named the “bench,” or by some the “box,” and made fast by means of dove-tailed tenons, is one hole thick and seven twelfths of a hole in height. The length of the windlass is equal to . . . [*](The dots here and in what follows, indicate lacunae in the manuscripts) holes, the thickness of the windlass to three quarters of a hole.
4. The latch is seven twelfths of a hole in length and one quarter in thickness. So also its socket-piece. The trigger or handle is three holes in length and three quarters of a hole in breadth and thickness. The trough in the pipe is sixteen holes in length, one quarter of a hole in thickness, and three quarters in height. The base of the standard on the ground is equal to eight holes; the breadth of the standard where it is fastened into the plinth is three quarters of a hole, its thickness two thirds of a hole; the height of the standard up to the tenon is twelve holes, its breadth three quarters of a hole, and its thickness two thirds. It has three struts, each nine holes in length, half a hole in breadth, and five twelfths in thickness. The tenon is one hole in length, and the head of the standard one hole and a half in length.
5. The antefix has the breadth of a hole and one eighth, and the thickness of one hole. The smaller support, which is behind, termed in Greek a)nti/basis, is eight holes long, three quarters of a hole broad, and two thirds thick. Its prop is twelve holes long,
6. These engines are constructed according to these proportions or with additions or diminutions. For, if the height of the capitals is greater than their width—when they are called “high-tensioned,”—something should be taken from the arms, so that the more the tension is weakened by height of the capitals, the more the strength of the blow is increased by shortness of the arms. But if the capital is less high,—when the term “low-tensioned ” is used,—the arms, on account of their strength, should be made a little longer, so that they may be drawn easily. Just as it takes four men to raise a load with a lever five feet long, and only two men to lift the same load with a ten-foot lever, so the longer the arms, the easier they are to draw, and the shorter, the harder.
I have now spoken of the principles applicable to the parts and proportions of catapults.