On Architecture

3. A ballista intended to throw a two-pound stone will have a hole of five digits in its capital; four pounds, six digits, and six pounds, seven digits; ten pounds, eight digits; twenty pounds, ten digits; forty pounds, twelve and a half digits; sixty pounds, thirteen and a half digits; eighty pounds, fifteen and three quarters digits; one hundred pounds, one foot and one and a half digits; one hundred and twenty pounds, one foot and two digits; one hundred and forty pounds, one foot and three digits; one hundred and sixty pounds, one foot and a quarter; one hundred and eighty pounds, one foot and five digits; two hundred pounds, one foot and six digits; two hundred and forty pounds, one foot and seven digits; two hundred and eighty pounds, one foot and a half; three hundred and twenty pounds, one foot and nine digits; three hundred and sixty pounds, one foot and ten digits.

4. Having determined the size of the hole, design the “scutula,” termed in Greek peri/trhtos, . . . holes in length and two and one sixth in breadth. Bisect it by a line drawn diagonally from the angles, and after this bisecting bring together the outlines of the figure so that it may present a rhomboidal design, reducing it by one sixth of its length and one

5. It should be given the thickness of seven twelfths of a hole. The boxes are two holes (in height), one and three quarters in breadth, two thirds of a hole in thickness except the part that is inserted in the hole, and at the top one third of a hole in breadth. The sideposts are five holes and two thirds in length, their curvature half a hole, and their thickness thirty-seven forty-eighths of a hole. In the middle their breadth is increased as much as it was near the hole in the design, by the breadth and thickness of . . . hole; the height by one fourth of a hole.

6. The (inner) strip on the “table” has a length of eight holes, a breadth and thickness of half a hole. Its tenons are one hole and one sixth long, and one quarter of a hole in thickness. The curvature of this strip is three quarters of a hole. The outer strip has the same breadth and thickness (as the inner), but the length is given by the obtuse angle of the design and the breadth of the sidepost at its curvature. The upper strips are to be equal to the lower; the cross-pieces of the “table,” one half of a hole.