The Ten Books on Architecture
their tenons have the length of... holes, the breadth of three quarters,
and the thickness of two thirds of a hole. The length of an arm is seven
holes, its thickness at its base two thirds of a hole, and at its end
one half a hole; its curvature is equal to two thirds of a hole.
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.
CHAPTER XI
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.
CHAPTER XII
THE STRINGING AND TUNING OF CATAPULTS
1. Beams of very generous length are selected, and upon them are nailed
socket-pieces in which windlasses are inserted. Midway along their
length the beams are incised and cut away to form framings, and in these
cuttings the capitals of the catapults are inserted, and prevented by
wedges from moving when the stretching is going on. Then the bronze
boxes are inserted into the capitals, and the little iron bolts, which
the Greeks call [Greek: epizygides], are put in their places in the
boxes.
2. Next, the loops of the strings are put through the holes in the
capitals, and passed through to the other side; next, they are put upon
the windlasses, and wound round them in order that the strings,
stretched out taut on them by means of the handspikes, on being struck
by the hand, may respond with the same sound on both sides. Then they
are wedged tightly into the holes so that they cannot slacken. So, in
the same manner, they are passed through to the other side, and
stretched taut on the windlasses by means of the handspikes until they
give the same sound. Thus with tight wedging, catapults are tuned to the
proper pitch by musical sense of hearing.
On these things I have said what I could. There is left for me, in the
matter of sieges, to explain how generals can win victories and cities
be defended, by means of machinery.
CHAPTER XIII
SIEGE MACHINES
1. It is related that the battering ram for sieges was originally
invented as follows. The Carthaginians pitched their camp for the siege
of Cadiz. They captured an outwork and attempted to destroy it. But
having no iron implements for its destruction, they took a beam, and,
raising it with their hands, and driving the end of it repeatedly
against the top of the wall, they threw down the top courses of stones,
and thus, step by step in regular order, they demolished the entire
redoubt.
2. Afterwards a carpenter from Tyre, Bright by name and by nature, was
led by this invention into setting up a mast from which he hung another
crosswise like a steelyard, and so, by swinging it vigorously to and
fro, he threw down the wall of Cadiz. Geras of Chalcedon was the first
to make a wooden platform with wheels under it, upon which he
constructed a framework of uprights and crosspieces, and within it he
hung the ram, and covered it with oxhide for the better protection of
the men who were stationed in the machine to batter the wall. As the
machine made but slow progress, he first gave it the name of the
tortoise of the ram.
3. These were the first steps then taken towards that kind of machinery,
but afterwards, when Philip, the son of Amyntas, was besieging
Byzantium, it was developed in many varieties and made handier by
Polyidus the Thessalian. His pupils were Diades and Charias, who served
with Alexander. Diades shows in his writings that he invented moveable
towers, which he used also to take apart and carry round with the army,
and likewise the borer, and the scaling machine, by means of which one
can cross over to the wall on a level with the top of it, as well as the
destroyer called the raven, or by others the crane.
4. He also employed the ram mounted on wheels, an account of which he
left in his writings. As for the tower, he says that the smallest should
be not less than sixty cubits in height and seventeen in breadth, but
diminishing to one fifth less at the top; the uprights for the tower
being nine inches at the bottom and half a foot at the top. Such a
tower, he says, ought to be ten stories high, with windows in it on all
sides.
5. His larger tower, he adds, was one hundred and twenty cubits high and
twenty-three and one half cubits broad, diminishing like the other to
one fifth less; the uprights, one foot at the bottom and six digits at
the top. He made this large tower twenty stories high, each story having
a gallery round it, three cubits wide. He covered the towers with
rawhide to protect them from any kind of missile.
6. The tortoise of the battering ram was constructed in the same way. It
had, however, a base of thirty cubits square, and a height, excluding
the pediment, of thirteen cubits; the height of the pediment from its
bed to its top was seven cubits. Issuing up and above the middle of the
roof for not less than two cubits was a gable, and on this was reared a
small tower four stories high, in which, on the top floor, scorpiones
and catapults were set up, and on the lower floors a great quantity of
water was stored, to put out any fire that might be thrown on the