11I have explained the structure of catapultæ, their parts and proportions. The constructions of balistæ are various and different, though contrived to produce similar effects. Some of these are worked by windlasses, others by systems of pulleys, others by capstans, and others by wheels: no balista, however, is made without regard to the weight of the stones it is intended to throw. Hence the rules will only be understood by those who are acquainted with arithmetical numbers and their powers.
2For instance, holes are made in the capitals, and through them are brought the cords, made either of woman’s hair, or of gut, which are proportioned to the weight of the stone that the balista is to throw, as in the catapultæ the proportions are derived from the length of the arrow. But that those who are not masters of geometry and arithmetic, may be prepared against delay on the occasions of war, I shall here state the results of my own experience as well as what I have learnt from masters, and shall explain them, by reducing the Greek measures to their correspondent terms in our own.
3A balista capable of throwing a stone of two pounds should have the hole (foramen) in the capital five digits wide; for a stone of four pounds, six digits; for a stone of six pounds, seven digits; for a stone of ten pounds, eight digits; for a stone of twenty pounds, ten digits; for a stone of forty pounds, twelve digits and nine sixteenths; for a stone of sixty pounds, thirteen digits and one eighth; for one of eighty pounds, fifteen digits; for one of one hundred and twenty pounds, one foot and a half and a digit and a half; for one of a hundred and sixty pounds, two feet; for one of a hundred and eighty pounds, two feet and five digits; for one of two hundred pounds, two feet and six digits; for one of two hundred and ten pounds, two feet and seven digits: and lastly, for one of two hundred and fifty pounds, eleven feet and a half.
4Having thus determined the size of the hole, which in Greek is called περίτρητος, a sight hole (scutula) is described two holes and a quarter in length, and two holes and one sixth wide. Let the line described be bisected, and when so bisected, let the figure be obliquely turned till its length be equal to one sixth part, and its width on which it turns that of the fourth part of a hole. In the part where the curvature is, at which the points of the angles project, and the holes are turned, the contractions of the breadth return inwardly, a sixth part. The hole must be as much longer as the epizygis is thick. When it has been described, the extremity is to be so divided that it may have a gentle curvature.
5Its thickness must be nine sixteenths of a hole. The stocks are made equal to two holes and a quarter, the width to one hole and three quarters, the thickness, exclusive of that part which is inserted into the hole, one hole and a half; the width at the extremity, one hole and a sixteenth; the length of the side posts, five holes and nine sixteenths; the curvature one half of a hole, the thickness four ninths; in the middle the breadth is increased as it was near the hole above described; its breadth and thickness are each five holes; its height one quarter of a hole.
6The length of the slip on the table is eight holes, and it is to be half a hole wide and thick. The length of the tenon two holes and a sixth, and its thickness one hole: the curvature of the slip is to be one sixteenth and five quarters of a sixteenth; the breadth and thickness of the exterior slip the same; its length will be found by the turning, and the width of the side post and its curvature one sixteenth: the upper are equal to the lower slips, that is one sixteenth: the transverse pieces of the table two thirds and one sixteenth of a hole:
7the length of shaft of the small ladder (climacis) thirteen holes, its thickness three sixteenths: the breadth of the middle interval is a quarter of a hole, its thickness five thirty-seconds of a hole: the length of the upper part of the climacis near the arms, where it is joined to the table, is to be divided into five parts; of these, two are given to that part which the Greeks call χηλὸς (the chest), the width one sixteenth, the thickness one quarter, the length three holes and an eighth, the projecting part of the chest half a hole. The pteregoma (or wing), one twelfth of a hole and one sicilicus. The large axis, which is called the cross front, is three holes;
8the width of the interior slips, one sixteenth of a hole; its thickness five forty-eighths of a hole: the cheek of the chest serves to cover the dove-tail, and is a quarter of a hole: the shaft of the climacis five sixths of a hole and twelve holes and a quarter thick: the thickness of the square piece which reaches to the climacis is five twelfths, at its ends one sixteenth: the diameter of the round axis must be equal to the chêlos, but near its turning points three sixteenths less.
9The length of the spur is one twelfth and three quarters; its width at bottom one sixteenth, and its width at top a quarter and one sixteenth. The base, which is called εσχάρα, is a ninth of a hole long; the piece in front of the base (antibasis) four holes and one ninth; the width and thickness of each are to be the ninth of a hole. The half column is a quarter of a hole high, and its width and thickness half a hole; as to its height, that need not be proportioned to the hole, but made, however, of such size as may be fit for the purpose. Of the arm the length will be six holes, its thickness at bottom half a hole; at the bottom one twelfth of a hole. I have now given those proportions of the catapultæ and balistæ, which I consider most useful; I shall not, however, omit to describe, as well as I can by writing, the manner of preparing them with cords twisted of guts and hair.