Ten Books on Architecture/Book X

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192258Ten Books on ArchitectureBook XMorris Hicky MorganVitruvius

Book X

Introduction 281
Chapter I - Machines and Implements 283
Chapter II - Hoisting Machines 285
Chapter III - The Elements of Motion 290
Chapter IV - Engines for raising Water 293
Chapter V - Water Wheels and Water Mills 294
Chapter VI - The Water Screw 295
Chapter VII - The Pump of Ctesibius 297
Chapter VII - The Water Organ 299
Chapter IX - The Hodometer 301
Chapter X - Catapults or Scorpiones 303
Chapter XI - Ballistae 305
Chapter XII - The Stringing and Tuning of Catapults 308
Chapter XIII - Siege Machines 309
Chapter XIV - The Tortoise 311
Chapter XV - Hegetor's Tortoise 312
Chapter XVI - Measures of Defence 315
Chapter XVII - Note on Scamilli Impares 320
Index 321



1. I shall next 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 in the middle. The breadth of the post in the middle is equal to one hole and one eighth, the thickness, to one hole.

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 (Greek characters) 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...[12] holes, the thickness of the windlass to three quarters of a hole.

[Note 12: The dots here and in what follows, indicate lacunae in the manuscripts.]

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 (Greek characters), is eight holes long, three quarters of a hole broad, and two thirds thick. Its prop is twelve holes long, and has the same breadth and thickness as the smaller support just mentioned. Above the smaller support is its socket-piece, or what is called the cushion, two and a half holes long, one and a half high, and three quarters of a hole broad. The windlass cup is two and seven twelfths holes long, two thirds of a hole thick, and three quarters broad. The crosspieces with 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.



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 characters),... 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 characters), 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 characters), 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.



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 characters), 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.



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 tortoise. Inside of this was set the machinery of the ram, termed in Greek (Greek characters), in which was placed a roller, turned on a lathe, and the ram, being set on top of this, produced its great effects when swung to and fro by means of ropes. It was protected, like the tower, with rawhide.

7. He explained the principles of the borer as follows: that the machine itself resembled the tortoise, but that in the middle it had a pipe lying between upright walls, like the pipe usually found in catapults and ballistae, fifty cubits in length and one cubit in height, in which a windlass was set transversely. On the right and left, at the end of the pipe, were two blocks, by means of which the iron-pointed beam, which lay in the pipe, was moved. There were numerous rollers enclosed in the pipe itself under the beam, which made its movements quicker and stronger. Numerous arches were erected along the pipe above the beam which was in it, to hold up the rawhide in which this machine was enveloped.

8. He thought it needless to write about the raven, because he saw that the machine was of no value. With regard to the scaling machine, termed in Greek (Greek characters), and the naval contrivances which, as he wrote, could be used in boarding ships, I have observed that he merely promised with some earnestness to explain their principles, but that he has not done so.

I have set forth what was written by Diades on machines and their construction. I shall now set forth the methods which I have learned from my teachers, and which I myself believe to be useful.



1. A tortoise intended for the filling of ditches, and thereby to make it possible to reach the wall, is to be made as follows. Let a base, termed in Greek (Greek characters), be constructed, with each of its sides twenty-one feet long, and with four crosspieces. Let these be held together by two others, two thirds of a foot thick and half a foot broad; let the crosspieces be about three feet and a half apart, and beneath and in the spaces between them set the trees, termed in Greek (Greek characters), in which the axles of the wheels turn in iron hoops. Let the trees be provided with pivots, and also with holes through which levers are passed to make them turn, so that the tortoise can move forward or back or towards its right or left side, or if necessary obliquely, all by the turning of the trees.

2. Let two beams be laid on the base, projecting for six feet on each side, round the projections of which let two other beams be nailed, projecting seven feet beyond the former, and of the thickness and breadth prescribed in the case of the base. On this framework set up posts mortised into it, nine feet high exclusive of their tenons, one foot and a quarter square, and one foot and a half apart. Let the posts be tied together at the top by mortised beams. Over the beams let the rafters be set, tied one into another by means of tenons, and carried up twelve feet high. Over the rafters set the square beam by which the rafters are bound together.

3. Let the rafters themselves be held together by bridgings, and covered with boards, preferably of holm oak, or, this failing, of any other material which has the greatest strength, except pine or alder. For these woods are weak and easily catch fire. Over the boardings let there be placed wattles very closely woven of thin twigs as fresh as possible. Let the entire machine be covered with rawhide sewed together double and stuffed with seaweed or straw soaked in vinegar. In this way the blows of ballistae and the force of fires will be repelled by them.




1. From a MS. of the sixteenth century (Wescher's Poliorcétique des Grecs).

2. From a model made by A. A. Howard.]

1. There is also another kind of tortoise, which has all the other details as described above except the rafters, but it has round it a parapet and battlements of boards, and eaves sloping downwards, and is covered with boards and hides firmly fastened in place. Above this let clay kneaded with hair be spread to such a thickness that fire cannot injure the machine. These machines can, if need be, have eight wheels, should it be necessary to modify them with reference to the nature of the ground. Tortoises, however, which are intended for excavating, termed in Greek (Greek characters), have all the other details as described above, but their fronts are constructed like the angles of triangles, in order that when missiles are shot against them from a wall, they may receive the blows not squarely in front, but glancing from the sides, and those excavating within may be protected without danger.

2. It does not seem to me out of place to set forth the principles on which Hegetor of Byzantium constructed a tortoise. The length of its base was sixty-three feet, the breadth forty-two. The corner posts, four in number, which were set upon this framework, were made of two timbers each, and were thirty-six feet high, a foot and a quarter thick, and a foot and a half broad. The base had eight wheels by means of which it was moved about. The height of these wheels was six and three quarters feet, their thickness three feet. Thus constructed of three pieces of wood, united by alternate opposite dovetails and bound together by cold-drawn iron plates, they revolved in the trees or amaxopodes.

3. Likewise, on the plane of the crossbeams above the base, were erected posts eighteen feet high, three quarters of a foot broad, two thirds of a foot thick, and a foot and three quarters apart; above these, framed beams, a foot broad and three quarters of a foot thick, held the whole structure together; above this the rafters were raised, with an elevation of twelve feet; a beam set above the rafters united their joinings. They also had bridgings fastened transversely, and a flooring laid on them protected the parts beneath.

4. It had, moreover, a middle flooring on girts, where scorpiones and catapults were placed. There were set up, also, two framed uprights forty-five feet long, a foot and a half in thickness, and three quarters of a foot in breadth, joined at the tops by a mortised crossbeam and by another, halfway up, mortised into the two shafts and tied in place by iron plates. Above this was set, between the shafts and the crossbeams, a block pierced on either side by sockets, and firmly fastened in place with clamps. In this block were two axles, turned on a lathe, and ropes fastened from them held the ram.

5. Over the head of these (ropes) which held the ram, was placed a parapet fitted out like a small tower, so that, without danger, two soldiers, standing in safety, could look out and report what the enemy were attempting. The entire ram had a length of one hundred and eighty feet, a breadth at the base of a foot and a quarter, and a thickness of a foot, tapering at the head to a breadth of a foot and a thickness of three quarters of a foot.

6. This ram, moreover, had a beak of hard iron such as ships of war usually have, and from the beak iron plates, four in number, about fifteen feet long, were fastened to the wood. From the head to the very heel of the beam were stretched cables, three in number and eight digits thick, fastened just as in a ship from stem to stern continuously, and these cables were bound with cross girdles a foot and a quarter apart. Over these the whole ram was wrapped with rawhide. The ends of the ropes from which the ram hung were made of fourfold chains of iron, and these chains were themselves wrapped in rawhide.

7. Likewise, the projecting end of the ram had a box framed and constructed of boards, in which was stretched a net made of rather large ropes, over the rough surfaces of which one easily reached the wall without the feet slipping. And this machine moved in six directions, forward (and backward), also to the right or left, and likewise it was elevated by extending it upwards and depressed by inclining it downwards. The machine could be elevated to a height sufficient to throw down a wall of about one hundred feet, and likewise in its thrust it covered a space from right to left of not less than one hundred feet. One hundred men controlled it, though it had a weight of four thousand talents, which is four hundred and eighty thousand pounds.



1. With regard to scorpiones, catapults, and ballistae, likewise with regard to tortoises and towers, I have set forth, as seemed to me especially appropriate, both by whom they were invented and in what manner they should be constructed. But I have not considered it as necessary to describe ladders, cranes, and other things, the principles of which are simpler, for the soldiers usually construct these by themselves, nor can these very machines be useful in all places nor in the same way, since fortifications differ from each other, and so also the bravery of nations. For siege works against bold and venturesome men should be constructed on one plan, on another against cautious men, and on still another against the cowardly.

2. And so, if any one pays attention to these directions, and by selection adapts their various principles to a single structure, he will not be in need of further aids, but will be able, without hesitation, to design such machines as the circumstances or the situations demand. With regard to works of defence, it is not necessary to write, since the enemy do not construct their defences in conformity with our books, but their contrivances are frequently foiled, on the spur of the moment, by some shrewd, hastily conceived plan, without the aid of machines, as is said to have been the experience of the Rhodians.

3. For Diognetus was a Rhodian architect, to whom, as an honour, was granted out of the public treasury a fixed annual payment commensurate with the dignity of his art. At this time an architect from Aradus, Callias by name, coming to Rhodes, gave a public lecture, and showed a model of a wall, over which he set a machine on a revolving crane with which he seized an helepolis as it approached the fortifications, and brought it inside the wall. The Rhodians, when they had seen this model, filled with admiration, took from Diognetus the yearly grant and transferred this honour to Callias.

4. Meanwhile, king Demetrius, who because of his stubborn courage was called Poliorcetes, making war on Rhodes, brought with him a famous Athenian architect named Epimachus. He constructed at enormous expense, with the utmost care and exertion, an helepolis one hundred and thirty-five feet high and sixty feet broad. He strengthened it with hair and rawhide so that it could withstand the blow of a stone weighing three hundred and sixty pounds shot from a ballista; the machine itself weighed three hundred and sixty thousand pounds. When Callias was asked by the Rhodians to construct a machine to resist this helepolis, and to bring it within the wall as he had promised, he said that it was impossible.

5. For not all things are practicable on identical principles, but there are some things which, when enlarged in imitation of small models, are effective, others cannot have models, but are constructed independently of them, while there are some which appear feasible in models, but when they have begun to increase in size are impracticable, as we can observe in the following instance. A half inch, inch, or inch and a half hole is bored with an auger, but if we should wish, in the same manner, to bore a hole a quarter of a foot in breadth, it is impracticable, while one of half a foot or more seems not even conceivable.

6. So too, in some models it is seen how they appear practicable on the smallest scale and likewise on a larger. And so the Rhodians, in the same manner, deceived by the same reasoning, inflicted injury and insult on Diognetus. Therefore, when they saw the enemy stubbornly hostile, slavery threatening them because of the machine which had been built to take the city, and that they must look forward to the destruction of their state, they fell at the feet of Diognetus, begging him to come to the aid of the fatherland. He at first refused.

7. But after free-born maidens and young men came with the priests to implore him, he promised to do it on condition that if he took the machine it should be his property. When these terms had been agreed upon, he pierced the wall in the place where the machine was going to approach it, and ordered all to bring forth from both public and private sources all the water, excrement, and filth, and to pour it in front of the wall through pipes projecting through this opening. After a great amount of water, filth, and excrement had been poured out during the night, on the next day the helepolis moving up, before it could reach the wall, came to a stop in the swamp made by the moisture, and could not be moved forwards, nor later even backwards. And so Demetrius, when he saw that he had been baffled by the wisdom of Diognetus, withdrew with his fleet.

8. Then the Rhodians, freed from the war by the cunning of Diognetus, thanked him publicly, and decorated him with all honours and distinctions. Diognetus brought that helepolis into the city, set it up in a public place, and put on it an inscription: "Diognetus out of the spoils of the enemy dedicated this gift to the people." Therefore, in works of defence, not merely machines, but, most of all, wise plans must be prepared.

9. Likewise at Chios, when the enemy had prepared storming bridges on their ships, the Chians, by night, carried out earth, sand, and stones into the sea before their walls. So, when the enemy, on the next day, tried to approach the walls, their ships grounded on the mound beneath the water, and could not approach the wall nor withdraw, but pierced with fire-darts were burned there. Again, when Apollonia was being besieged, and the enemy were thinking, by digging mines, to make their way within the walls without exciting suspicion, and this was reported by scouts to the people of Apollonia, they were much disturbed and alarmed by the news, and having no plans for defence, they lost courage, because they could not learn either the time or the definite place where the enemy would come out.

10. But at this time Trypho, the Alexandrine architect, was there. He planned a number of countermines inside the wall, and extending them outside the wall beyond the range of arrows, hung up in all of them brazen vessels. The brazen vessels hanging in one of these mines, which was in front of a mine of the enemy, began to ring from the strokes of their iron tools. So from this it was ascertained where the enemy, pushing their mines, thought to enter. The line being thus found out, he prepared kettles of hot water, pitch, human excrement, and sand heated to a glow. Then, at night, he pierced a number of holes, and pouring the mixture suddenly through them, killed all the enemy who were engaged in this work.

11. In the same manner, when Marseilles was being besieged, and they were pushing forward more than thirty mines, the people of Marseilles, distrusting the entire moat in front of their wall, lowered it by digging it deeper. Thus all the mines found their outlet in the moat. In places where the moat could not be dug they constructed, within the walls, a basin of enormous length and breadth, like a fish pond, in front of the place where the mines were being pushed, and filled it from wells and from the port. And so, when the passages of the mine were suddenly opened, the immense mass of water let in undermined the supports, and all who were within were overpowered by the mass of water and the caving in of the mine.

12. Again, when a rampart was being prepared against the wall in front of them, and the place was heaped up with felled trees and works placed there, by shooting at it with the ballistae red-hot iron bolts they set the whole work on fire. And when a ram-tortoise had approached to batter down the wall, they let down a noose, and when they had caught the ram with it, winding it over a drum by turning a capstan, having raised the head of the ram, they did not allow the wall to be touched, and finally they destroyed the entire machine by glowing fire-darts and the blows of ballistae. Thus by such victory, not by machines but in opposition to the principle of machines, has the freedom of states been preserved by the cunning of architects.

Such principles of machines as I could make clear, and as I thought most serviceable for times of peace and of war, I have explained in this book. In the nine earlier books I have dealt with single topics and details, so that the entire work contains all the branches of architecture, set forth in ten books.