BALLISTAE
1. Ballistae are constructed on varying principles to produce an
identical result. Some are worked by handspikes and windlasses, some by
blocks and pulleys, others by capstans, others again by means of drums.
No ballista, however, is made without regard to the given amount of
weight of the stone which the engine is intended to throw. Hence their
principle is not easy for everybody, but only for those who have
knowledge of the geometrical principles employed in calculation and in
multiplication.
2. For the holes made in the capitals through the openings of which are
stretched the strings made of twisted hair, generally women's, or of
sinew, are proportionate to the amount of weight in the stone which the
ballista is intended to throw, and to the principle of mass, as in
catapults the principle is that of the length of the arrow. Therefore,
in order that those who do not understand geometry may be prepared
beforehand, so as not to be delayed by having to think the matter out at
a moment of peril in war, I will set forth what I myself know by
experience can be depended upon, and what I have in part gathered from
the rules of my teachers, and wherever Greek weights bear a relation to
the measures, I shall reduce and explain them so that they will express
the same corresponding relation in our weights.
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 [Greek: peritrêtos],... 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 fourth of its breadth at the (obtuse) angles. In the
part composed by the curvatures into which the points of the angles run
out, let the holes be situated, and let the breadth be reduced by one
sixth; moreover, let the hole be longer than it is broad by the
thickness of the bolt. After designing the scutula, let its outline be
worked down to give it a gentle curvature.
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
crosspieces of the "table," one half of a hole.
7. The shafts of the "ladder" are thirteen holes in length, one hole in
thickness; the space between them is one hole and a quarter in breadth,
and one and one eighth in depth. Let the entire length of the ladder on
its upper surface--which is the one adjoining the arms and fastened to
the table--be divided into five parts. Of these let two parts be given
to the member which the Greeks call the [Greek: chelônion], its breadth
being one and one sixth, its thickness one quarter, and its length
eleven holes and one half; the claw projects half a hole and the
"winging" three sixteenths of a hole. What is at the axis which is
termed the... face... the crosspieces of three holes?
8. The breadth of the inner slips is one quarter of a hole; their
thickness one sixth. The cover-joint or lid of the chelonium is
dove-tailed into the shafts of the ladder, and is three sixteenths of a
hole in breadth and one twelfth in thickness. The thickness of the
square piece on the ladder is three sixteenths of a hole,... the
diameter of the round axle will be equal to that of the claw, but at the
pivots seven sixteenths of a hole.
9. The stays are... holes in length, one quarter of a hole in breadth at
the bottom, and one sixth in thickness at the top. The base, termed
[Greek: eschara], has the length of... holes, and the anti-base of four
holes; each is one hole in thickness and breadth. A supporter is jointed
on, halfway up, one and one half holes in breadth and thickness. Its
height bears no relation to the hole, but will be such as to be
serviceable. The length of an arm is six holes, its thickness at the
base two thirds of a hole, and at the end one half a hole.
I have now given those symmetrical proportions of ballistae and
catapults which I thought most useful. But I shall not omit, so far as I
can express it in writing, the method of stretching and tuning their
strings of twisted sinew or hair.