In the noble and ample city of the Greeks, Ephesus, an ancient law is said to have been established by the ancestors with a hard condition, but in justice not inequitable. For when an architect undertakes the charge of a public work, he promises at what expense it will be. The estimate being delivered to the magistrate, his goods are pledged until the work be completed. When it is finished, if the cost answers to what was said, he is adorned with decrees and honors. Likewise if no more than a fourth is to be added to the estimate, it is paid from the public, and he is held to no penalty. But when more than a fourth is consumed on the work, money is exacted from his goods to bring it to completion. §1
Would that the immortal gods had granted that this law had been established also for the Roman People, not only for public but also for private buildings. For then the inexperienced would not be unpunished when they go about the work; but those with the highest subtlety of learning in their prudence would profess architecture without doubt; and fathers of households would not be led into unbounded outpourings of expense, such that they are cast out of their estates; and the architects themselves, constrained by fear of the penalty, more diligently reasoning the amount of the expense, would bring it about that the fathers of households could complete their buildings with what they had prepared, or with only a little more added. For those who can prepare four hundred for a work, if they add a hundred, are held by the hope of completion and by their delights; but those who are burdened with an addition of half or more expense, their hope being lost, and the outlay abandoned, with their things and their spirits broken, are forced to desist. §2
Not only this defect in buildings, but also in the games that are given by magistrates, of gladiators at the forum and of the stages of games, in which no delay nor waiting is conceded, but necessity compels to finish in a set time, that is, the seats of the shows and the drawing of awnings, and all those things which by stage-customs through machination are prepared for the views of the people. In these, indeed, there is need of a diligent prudence and the thought of most learned talent, because nothing of these is brought to pass without machination and the varied and dexterous vigor of studies. §3
Therefore, since these things have been so handed down and established, it does not seem alien that with caution and with the highest diligence, before works are set up, their reasonings be expedited. Therefore since neither a law nor an institution of customs can compel this, and yearly praetors and aediles must prepare machines for the games, it has seemed to me, Imperator, not alien, since of buildings in prior volumes I have set forth, in this, which has the highest completion of the body established, to unfold what the principles of machines, ordered by precepts, may be. §4
A machine is a continuous joining of material, having the greatest forces for the motions of loads. It is moved by the art of the rotundities of circles, which the Greeks call κυκλικὴν κίνησιν. There is one kind, the scansory, which in Greek is called ἀκροβατικόν; another, the spirabile (breathing), which among them is called πνευματικόν; the third, the tractory, which the Greeks call βαρουλκόν. The scansory is when machines are so placed that, timbers set up to the height and cross-pieces bound together, ascent may be made without danger for the inspection of the display. The spirabile is when breath, driven by pressings, so express blows and voices ὀργανικῶς (as if instrumentally). §5
The tractory is when loads are dragged with machines so as to be placed when lifted on high. The scansory reasoning glories not in art but in audacity. It is held together by fastenings, cross-pieces, braided bindings, and props of struts. What, however, takes approaches by the power of breath, pursues elegant effects by the subtleties of the art. The tractory has larger and magnificence-filled opportunities for use, and in acting with prudence, the highest virtues. §6
Of these there are some which are moved μηχανικῶς, others ὀργανικῶς. Between machines and instruments this seems to be the distinction: that machines are made, by the work of several men and by greater force, to have effects (as ballistae and the levers of wine-presses); but instruments, by the skilled touch of one workman, accomplish what is proposed (as the scorpion or the turnings of anisocycli). Therefore both instruments and the reasoning of machines are necessary for use, without which no thing can be without hindrance. §7
All machination is produced by the nature of things, and is instituted by the preceptress and mistress, the turning of the world. For let us observe and behold first the continuous nature of the sun, the moon, and the five stars, which, unless they were turned by machination, we should not have daylight at times nor the ripenings of fruits. When therefore the ancients observed these things to be so, from the nature of things they took exemplars, and imitating them they were led, by divine matters, to perfect the conveniences of life. Therefore they contrived, so as to be more ready, some by machines and their turnings, others by instruments, and so the things they observed to be useful in use, by the studies of the arts instituted, they took care to increase by learning step by step. §8
Let us attend first to the invention from necessity, as clothing, in which the arrangement of woof and warp by the instrumental administrations of looms not only, by covering, protects bodies, but adds also the honor of adornment. Of food, moreover, we should not have abundance, unless yokes and plows had been invented for oxen and every kind of beast. The preparation of windlasses, presses, and levers, if it had not been made for wine-presses, we could have had neither the brightness of oil nor the fruit of the vine for pleasantness; and their carriage would not be if the machinations of wagons or trucks by land, and of little boats by water, had not been invented. §9
The invention of the balance and the trial by weight of scales wards off life from inequity with just manners. And the kinds of machination are innumerable, of which it does not seem necessary to discuss, since they are to hand daily, as mills, smiths' bellows, wheels, carriages, lathes, and the rest which have convenience for use by common customs. Therefore we will begin to unfold those things that come rarely to hand, so that they may be known. §10
And first we will set forth those things which, by necessity, are prepared for the perfection of sacred temples and of public works, which are made thus. Two timbers are prepared, proportioned to the magnitude of loads. At the top, joined by a clamp, and at the bottom spread apart, they are raised, with ropes placed at their heads and disposed around so that, being erected, they are held. At the top a block is bound, which some also call rechamus. Into the block are put two sheaves (orbiculi) turning on little axles. Through the top sheave a drawing rope is sent across; then it is lowered and drawn around a sheave of the lower block. It is carried back to the lower sheave of the upper block, and so descends to the lower, and is tied in its hole. The other part of the rope is carried back to the bottom parts of the machine. §11
In the posterior squares of the timbers, in the place where they spread apart, are fixed sockets (chelonia), in which the ends of windlasses are thrown so that their axles may easily turn. These windlasses near the ends have two pairs of holes, so tempered that levers may fit in them. To the bottom rechamus iron forceps are bound, whose teeth are fitted into holed stones. When the rope has its end tied to the windlass, and levers, pulling it, turn it, the rope, winding itself round the windlass, stretches and so lifts loads up to the height and the placements of the works. §12
This reasoning of machination, because it revolves through three sheaves, is called trispastos. But when in the lower block are two sheaves and in the upper three, it is called pentaspaston. But if machines are to be prepared for greater loads, timbers of ampler lengths and thicknesses must be used, and by the same reasoning fastenings at the top, at the bottom the turning of windlasses. These being unfolded, the forestaying ropes be placed loose in front; restraining ropes be disposed far over the shoulders of the machine; and if there be not where to tie them, stakes reversed be dug in and solidified round by rammers, to which the ropes may be tied. §13
A block be held at the topmost head of the machine by a rope, and from it a rope be drawn to the stake and to the block tied on the stake. Round its sheave let the rope be thrown, and carried back to that block which will be tied at the head of the machine. Round the sheave, the rope, thrown over from the top, shall descend and return to the windlass that is at the bottom of the machine, and there be tied. Then, the windlass being turned by levers, it will, of itself, without danger, erect the machine. So, with ropes disposed about and restrainers fastened to stakes, the machine will be placed in more ample manner. The blocks and drawing ropes are expedited as written above. §14
But if loads be colossal in amplitude and weights in the works, the task is not to be entrusted to the windlass, but, as the windlass is held by sockets, so let an axle be enclosed having in the middle an ample drum (which some call a wheel; the Greeks call it ἀμφίεσιν, others περιθήκιον). §15
In these machines the blocks are prepared not in the same but in another manner. For they have at the bottom and at the top double rows of sheaves. Thus the drawing rope is thrown through a hole of the lower block, so that the two ends of the rope be equal when it has been stretched; and there, next to the lower block, a little cord being wound round and woven, holds together both parts of the rope, that they cannot go forth either to the right or to the left. Then the ends of the rope are carried back to the upper block on the outer side, and are thrown down around the lower sheaves, and return to the bottom, and are thrown into the sheaves of the lowest block from the inner side, and carried back to right and left, and return to the head round the top sheaves. §16
Thrown over from the outer side, they are carried to right and left to a drum on an axle, and there bound so that they cling. Then another rope, wound about the drum, is carried to the ergata (capstan); and it, driven round, winds about the drum and axle together, stretching them, and so lifts the loads gently without danger. But if a greater drum be placed, whether in the middle or at one outer part, without a capstan, men treading it will have more ready effects of the work. §17
There is another kind of machine, sufficiently artful and ready for the use of quickness, but in it none can give work except the skilled. There is a timber which is erected and held by restraints on four sides. Under the restraints two sockets are fixed; a block is bound with ropes above the sockets; under the block a rule is placed about two feet long, six inches broad, four thick. Blocks having three rows of sheaves in breadth are placed. Thus three drawing ropes are bound to the machine at the top. Then they are carried to the bottom block, and thrown through its top sheaves from the inner side; then they are carried to the upper block, and thrown from the outer to the inner side through the bottom sheaves. §18
When they have descended to the bottom, from the inner side they are led through the second sheaves to the outer, and are carried back to the top to the second sheaves; thrown across they return to the bottom; from the bottom they are carried to the top, and thrown across through the top return to the bottom of the machine. In the root of the machine is placed a third block; the Greeks call this ἐπαγόντα, our people artemon. This block is bound to the root of the machine, having three sheaves, through which the ropes thrown are given to the men for pulling. Thus three rows of men, pulling without a capstan, quickly bring the load to the top. §19
This kind of machine is called polyspaston, because, by many circuits of sheaves, it furnishes the highest facility and quickness. And a single setting-up of the timber has this advantage, that it can set down the load in front as far as one wishes, and to the right and to the left by inclining the side. Of all these machinations above written, the reasonings are prepared not only for these matters but also for loading and unloading ships, some standing upright, others flat placed on turning cranes. No less, without the raising of timbers, on a flat by the same reasoning and with tempered ropes and blocks, the hauling up of ships is effected. §20
It is not alien also to set forth the ingenious reasoning of Chersiphron. For he, when he wished to carry the shafts of columns from the quarries to the shrine of Diana at Ephesus, not trusting in carts (lest the wheels be swallowed up) on account of the magnitude of the loads and the soft plains of the roads, thus attempted. Of wood he prepared two beams of four-inch thickness, with two cross-pieces interposed, of the whole length of the shaft, and fitted them; and he leaded-in iron pivots (cnodaces) as dovetails into the ends of the shaft, and fixed into the wood rings to surround the pivots; likewise with tin bands bound the ends. The pivots, enclosed in the rings, had free rotation. So, with oxen yoked to the beams, the shaft, turning by the pivots and rings, was rolled without end. §21
When they had thus carried all the shafts, and the transport of the architraves was at hand, the son of Chersiphron, Metagenes, transferred the same method from the shaft-carriage to the conveyance of architraves. For he made wheels about twelve feet in diameter, and enclosed the ends of the architraves in the middle of the wheels. By the same reasoning he fixed pivots and rings in the ends. Thus, when the beams were drawn by oxen, the pivots, enclosed in the rings, turned the wheels, and the architraves, enclosed as axles in wheels by the same reasoning as the shafts, without delay reached the work. An example of it is how in the palaestrae cylinders level the walks. This could not have been done unless first the neighborhood had been near. For it is not more than eight miles from the quarries to the shrine, nor is there any slope but a continuous plain. §22
In our memory, however, when the base of the colossal Apollo in his shrine had been broken by age, and, fearing lest that statue fall and be broken, they contracted that a base be cut from the same quarries. A certain Paeonius took the contract. This base, moreover, was twelve feet long, eight feet wide, six feet high. Paeonius, relying on glory, did not carry it as Metagenes did, but resolved, by another kind, by the same reasoning, to make a machine. §23
For he made wheels about fifteen feet in diameter, and in these wheels enclosed the ends of the stone; then round the stone he fitted six-inch spindles, from wheel to wheel, according to the compasses, so that spindle was not distant from spindle by more than a foot. Then round the spindles he wound a rope, and with oxen yoked he drew the rope. So, as it unwound, it turned the wheels; but he could not draw them in a straight line to the road, but went out to one side. So it was necessary to lead them back again. Thus Paeonius, leading and leading back, wasted his money so that he had nothing left to pay. §24
Let me go forth a little, and set forth how these quarries were discovered. Pixodarus had been a shepherd. He used to turn about in these places. But when the citizens of Ephesus thought of making the shrine of Diana of marble, and decreed that from Paros, Proconnesus, Heraclea, Thasos, the marble should be sought, Pixodarus, driving his sheep, was feeding his flock in that place; and there two rams, running against each other, each missed the other, and with impact, one struck the rock with its horns, from which a crust of the whitest color had been broken off. So Pixodarus is said to have left his sheep on the mountains, and to have carried the crust at a run to Ephesus, when most of all that matter was being debated. So at once they decreed honors for him, and changed his name so that instead of Pixodarus he was called Evangelus. And to this day, every month, a magistrate goes to that place and performs a sacrifice for him, and if he does not, he is held to the penalty. §25
Of the reasonings of tractory works which I thought necessary I have briefly set forth. Of the motion and force of them, two different and unlike things, agreeing, bring forth as principles those perfect effects: one of the extended line (which the Greeks call εὐθεῖαν), the other of rotundity (which the Greeks call κυκλωτήν); but truly, neither without rotundity can the motions of the straight-line, nor without the extended line can the turnings of rotation, effect the liftings of loads. §26
That this may be understood I will set forth. Little axles, as centers, are put into sheaves and placed in blocks, through which sheaves the rope, drawn around by straight pulls and placed upon the windlass, by the turnings of levers makes the liftings of loads on high. The pivots of this windlass, as centers, straight out in the sockets, and, the levers enclosed in its holes with their heads turned round in the compasses like on a lathe, by turning make the liftings of loads. As an iron lever too, when it is applied to a load which a multitude of hands cannot move, with a straight projection placed as a center (which the Greeks call ὑπομόχλιον), and the tongue thrust under the load, its head being pressed by the strength of one man, lifts up that load. §27
This, because the shorter front part of the lever enters under the load from the pressure which is the center, and the head, which is at a greater distance from that center, is drawn down, by making that motion of turning, compels the weight of the greatest load to be balanced by a few hands. Likewise if the little tongue of the iron lever be placed under the load, and its head, not by pressing down, but, on the contrary, be lifted upwards, the tongue, supported on the floor of the ground, will have that floor as the load, and the angle of the load itself as the pressure. So, not so easily as by pressing down, but in the contrary direction, nonetheless that weight of the load will be raised. Therefore if the tongue of the lever placed above the hypomochlion go further under the load, and its head have the pressures nearer the center, it will not be able to lift the load, unless, as has been written above, the leverage of the long lever by drawing down its head be made. §28
This one may consider from the weighing-scales which are called staterae. For when the handle, near the head whence the little scale hangs, is placed there as a center, and the counterpoise on the other side of the beam, wandering through the points, as far or even to the end is brought, with a little and unequal weight it makes a most ample weighing equal by the balancing of the beam. So receding farther from the center, the counterpoise's shortness, becoming weaker, draws down the greater force of weight by its moment, compelling it without violence gently from the bottom upwards to go forth. In the same way also the helmsman of the largest merchant ship, holding the handle of the helm which by the Greeks is called οἴαξ, with one hand, moving it by reasoning of the art through the center by pressings, turns the ship, laden with the most ample and immense weights of merchandise and provisions. §29
And the sails, when they are hanging at the middle height of the mast, the ship cannot have a swift course; but when they are drawn up to the topmost peak of the sailyard, then it advances with a more vehement onset, because not next to the heel of the mast (which is the place of the center) but at the top, advancing further from it, the sails receive the wind into themselves. §30
Therefore as a lever placed under a load, if it is pressed through the middle, is harder and does not bend; but when its head at the top is drawn down, easily lifts the load, similarly sails, when they are tempered through the middle, have less force; but those which are placed on the top of the mast, departing further from the center, by no sharper but by the same blast, by the pressure of the peak, more vehemently compel the ship to advance. Also oars, bound by thongs round the tholes, when pushed by the hands and drawn back, with the extremities going on from the center, by the palms on the waves of the salt sea, with vehement blow thrust on the stretched ship, the prow cutting the rareness of the liquid. §31
Now the greatest weights of loads, when they are borne by six or four bearers, are balanced by the very middle centers of the phalangae (carrying poles), so that, the solid weight of the load being divided by a certain reasoning of division, the single workmen may carry equal parts on their necks. For the middle parts of the phalangae, where the straps of the four-bearers are brought in, are bounded by pegs, lest they slip to one side. For when they are moved beyond the end of the center, they press that place to which they have come nearer, as in a steelyard the weight, when by the balancing it advances to the ends of the weighings. §32
By the same reasoning beasts of burden, when their yokes with the subyoke straps are tempered through the middle, equally pull loads. But when their strengths are unequal, and the one being stronger presses the other, by the strap shifted, one part of the yoke is made longer, which aids the weaker beast. So in phalangae and yokes, when the thongs are not placed in the middle but on one part, by the space the thong goes from the middle, one part is made shorter, the other longer. By this reasoning, if through that center, at the place to which the thong is brought, both ends be turned round, the longer part will make a larger, the shorter a smaller, circumference. §33
Just as smaller wheels have harder and more difficult motions, so the phalangae and yokes, in whatever parts they have smaller intervals from the center to their heads, press harshly on the necks; but where they have longer spaces from the same center, they ease the carrying and drawing. Since these things, by projections and circlings, receive motions to the center, then indeed also wagons, carriages, drums, mills, screws, scorpions, ballistae, wine-presses, and the rest of machines, by the same reasonings, through a projected center and the rotation of the compasses, by turning make effects to the proposed purpose. §34
Now I shall set forth by what kinds the instruments, invented for drawing water, are prepared, and first I shall speak of the tympanum. This does not lift water high, but exhausts a great multitude swiftly. An axle is made by the lathe or compasses, its ends ironed with plates, having in the middle, around it, a drum of boards joined together. It is placed on supports having beneath the heads of the axle iron plates. In the hollow of this drum eight boards are interposed, crosswise, touching the axle and the outer circumference of the drum, which divide the drum into equal spaces. §35
Round its front are fixed boards, half-foot openings being left, for taking in water. Likewise, along the axle, pigeon-holes are cut, excavated in the single spaces on one side. When this has been pitched in the manner of ships, it is turned by men treading it, and, drawing through the openings which are in the fronts of the drum, gives back through the pigeon-holes along the axle, with a wooden basin placed beneath having a channel joined to it. Thus an abundance of water is furnished to gardens for irrigating, or to salt-works for tempering. §36
But when it must be lifted higher, the same reasoning will be changed thus. A wheel shall be made around an axle of such magnitude as can answer the height needed. Round the outer side of the wheel shall be fixed squared buckets solidified by pitch and wax. So when the wheel is turned by those treading, the buckets, full, lifted to the top, returning again to the bottom, themselves, of themselves, pour into the reservoir what they have raised. §37
But if to higher places it must be furnished, on the axle of the same wheel shall be wound a double iron chain, let down to the lowest level, having little bronze bowls hanging, of a congius capacity. So the turning of the wheel, by winding the chain on the axle, will lift the bowls to the top, which, when they are carried over the axle, will be forced to be inverted, and to pour into the reservoir the water they had lifted. §38
There are also wheels made in rivers by the same reasoning as above written. Round their fronts are fixed paddles, which, when struck by the onset of the river, compel the wheel, advancing, to turn; and so, drawing water with buckets and bringing it to the top, without the treading of workmen, by the impulse of the river itself they turned, they furnish what is needed for use. §39
By the same reasoning also water-mills are turned, in which all is the same, except that at one end of the axle is enclosed a toothed drum. This, placed perpendicular to the axle, turns on its edge, together with the wheel. Next to this drum a greater, likewise toothed flat, is placed, by which are contained so that the teeth of the drum enclosed on the axle, by striking the teeth of the flat drum, compel the millstones' circulation. In this machine a hopper hanging above supplies the millstones with grain, and by the same turning the flour is produced. §40
There is also the reasoning of the screw (cochlea), which lifts a great force of water, but not so high as a wheel. Its reasoning is expedited thus. A timber is taken, of which the ratioed length is as many feet, so many digits are fixed for its thickness. It is rounded to the compasses. At the ends the circumferences are divided by the compasses by quadrants and octants into eight parts, and those lines are so placed that, with the timber lying flat, the lines of either end by level correspond among themselves; and as great as is the eighth part of the circumference of the timber, such spaces be cut off in length. Likewise, the timber being laid flat, lines from one end to the other be drawn equally by level. So both in the rounding and in the length equal spaces shall be made. Thus at the place where the lines which are in length are described, by intersecting they will make crossings and fixed points at the crossings. §41
These being so correctly described, a thin willow rule, or one cut from agnus castus, is taken, which, anointed with liquid pitch, is fixed at the first point of crossing. Then it is drawn obliquely to the following crossings of the length and of the circumference, likewise in sequence going on past the single points, and, winding round, it is placed at the single crossings, and so it comes and fixes at that line, receding from the first to the eighth point, on which its first part is fixed. So as much as it advances obliquely through space and through eight points, so much also in length it advances to the eighth point. By the same reasoning, through all the space of length and rotundity, the rules fixed obliquely at the single crossings through the eight divisions of the thickness make involute channels, and a just and natural imitation of the screw. §42
Thus by that tracing, others over others are fixed, anointed with liquid pitch; and these are heaped up until the top thickness be an eighth part of the length. Above these, boards are wound round and fixed, to cover that involution. Then these boards are saturated with pitch and bound with iron bands, that they may not be dissolved by the force of the water. The ends of the timber are ironed. On the right and on the left of the screw are placed timbers at the ends, having on both sides cross-pieces fastened. In these, iron holes are included, and into these are put pins; and so the screws are made to turn by men treading. §43
Its erection to the inclination shall be so placed that, as a Pythagorean right-angled triangle is described, so may it have its correspondence; that is, let the length be divided into five parts; of them three lift the head of the screw. So from the perpendicular to its lowest nostrils will be the space of four of those parts. How it ought to be, at the end of the book is described in the very place. What instruments are made of material for drawing water, by what reasonings they are perfected, and by what they, receiving motions, furnish boundless utilities by turnings, that they may be better known, as openly as I could I have written. §44
Now follows to show the Ctesibian machine, which lifts water to the height. It is made of bronze, whose at the bottom are made twin little drums a little apart, having pipes of fork-like shape joined together, running into a middle basin. In that basin are placed round valves (asses) fitted by subtle joining to the upper nostrils of the pipes, which, by closing beforehand the openings of the nostrils, do not allow what has been forced into the basin by the air to return. §45
Above the basin a hood like an inverted funnel is fitted, and fastened to the basin by a clasp with a wedge driven through, lest the force of the inflating water compel it to be raised. Above, a pipe, which is called the tuba, fitted in, stands erect. The little drums have, below the lower nostrils, valves placed above their holes which are in the bottoms. §46
Thus from above in the little drums, male pistons polished on the lathe and oiled, enclosed by rods and levers, mill whatever air with water may be there; and, the valves closing the holes, they by inflating press and thrust the water through the nostrils of the pipes into the basin, out of which the hood, receiving the breaths, presses it through the pipe to the height; and so, from the lower place, with a castellum placed for leaping, the water is supplied. §47
Yet not this reasoning alone of Ctesibius is reported as discovered; but many and of various kinds, by the breath compressed by him by the pressures of liquid, are shown to bring forth effects borrowed from nature: as the voices of blackbirds by the motion of water, and angobatae (little figures mounted), drinking and moving figures, and the rest which, by the delights of the eyes and the use of the ears, flatter the senses. §48
Of these, which I most judged useful and necessary I have selected, and in the preceding volume I have spoken of sundials, in this of the expressings of water, I have thought needed to be said. The rest, which are not for necessity but for the pleasure of delights, those who shall be more eager for its subtlety may find in the commentaries of Ctesibius himself. §49
Concerning the water-organs (hydraulae), however, what reasonings they have, as briefly and nearly as I can, and by writing pursue, I shall not omit. On a compact base of material, a chest is placed, fabricated of bronze. Above the base are raised rules on right and left, compacted in the form of a ladder, in which bronze drums are enclosed, with movable bottoms subtly wrought on the lathe, having fixed in the middle iron elbows joined by pivots with levers, and enveloped with woolly skins. Likewise on the topmost plane are holes of about three digits. In these holes, bronze dolphins, placed by pivots close by, have cymbals hanging by chains, lowered beneath the holes of the drums. §50
Within the chest, in the place where the water is held, there is a pnigeus like an inverted funnel, under which little dice about three digits high, placed beneath, balance the space between the lowest lips of the pnigeus and the bottom of the chest. Above its little neck a little chest joined holds the head of the machine, which in Greek is called κανὼν μουσικός. In its length are channels, if tetrachordal, four; if hexachordal, six; if octachordal, eight. §51
In the single channels are enclosed single stopcocks, with iron handles placed. These handles, when turned, open the nostrils from the chest into the channels. From the channels, however, the canon has holes arranged transversely, corresponding to the nostrils that are in the top board, which board in Greek is called πίναξ. Between the board and the canon, rules are interposed, likewise holed and oiled so that they may easily be thrust and again drawn back inside, which close those holes and are called plinthides. Their going and returning closes some, opens others, the borings. §52
These rules have iron furnishings fixed and joined with keys, by whose touch the motions of the rules are continuously effected. Above the holes of the board, whence the breaths have exit from the channels, are rings fastened, in which the tongues of all the organ-pipes are enclosed. From the drums, continuous pipes are joined to the necks of the pnigeus and reach to the nostrils which are in the little chest. In them are valves wrought on the lathe and there placed, which, when the chest has received breath, will not suffer the breath, by closing the holes, to return. §53
Thus, when the levers are raised, the elbows draw the bottoms of the drums to the bottom; and the dolphins, enclosed on pivots, lowering into them cymbals, fill the spaces of the drums with air; and the elbows, raising the bottoms within the drums, with a vehement frequency of blow, and the cymbals closing the upper holes, compel the air that is enclosed there, pressed, into the pipes, through which it runs together into the pnigeus, and through its neck into the little chest. By a more vehement motion of the levers, the frequent breath, compressed, flows in through the openings of the stopcocks, and fills the channels with breath. §54
So when the keys, touched by hands, drive forth and draw back continuously the rules, closing alternately some holes and opening others, from the musical arts with manifold varieties of modules, sounding voices are raised. As much as I could strive to announce, by writing, an obscure matter clearly, I have done my best; but this reasoning is not easy, nor ready for understanding to all except those who have exercise in these kinds. If anyone has understood little from writings, when he recognizes the thing itself, he will certainly find all carefully and subtly ordered. §55
Now the thought of writing is transferred to a reasoning not useless, handed down by the ancestors with the highest skill, by which, sitting in a cart on the road or sailing the sea, we may know how many miles' journey we have made. This will be so: let the wheels that are in the cart be broad through the middle diameter of four feet and a sixth, so that when the wheel has a fixed point in itself, and, beginning thence to go forward on the ground of the road, to make its turn, arriving at the limit from which it began to turn, it shall have completed a fixed measure of space of twelve and a half feet. §56
These things being so prepared, then in the nave of the wheel, on the inner side, a drum be enclosed firmly, having outside the surface of its rounding one projecting little tooth. Over that, to the body of the cart, let a little case be firmly fixed, having an adjustable drum placed on its edge and enclosed on a little axle, in the front of which drum let there be worked out teeth equally divided, in number four hundred, fitting the little tooth of the lower drum. Also on the upper drum, to the side, be fixed another little tooth, projecting beyond the teeth. §57
Above, an upper drum, toothed in the same manner, is placed enclosed in another little case, with its teeth fitting the little tooth that was fixed on the side of the second drum. And in this drum let holes be made, as many as the number of miles of the day's journey the cart may complete. It hinders nothing, whether a little less or more. In all these holes let round pebbles be placed, and in the case of that drum, or the little receptacle, let one hole be made, with a little channel, by which the pebbles, which were placed in that drum, when they come to that place, can fall into the body of the cart and into a bronze vessel placed beneath one by one. §58
Thus when the wheel, advancing, drives the lowest drum with itself, and its little tooth compels, by its push, the single turnings to go past the single teeth of the upper drum, it will bring to pass that when the lowest has been turned four hundred times, the upper drum shall be turned once, and the little tooth that is fixed to its side shall drive forth one tooth of the flat drum. When therefore by four hundred turnings of the lowest drum, the upper shall have turned once, the advance will effect a space of five thousand feet, that is, a thousand paces. From this, the pebbles that have fallen will warn, by the sound, of single miles completed. The number of pebbles, collected from below, will indicate the sum of the miles of the day's journey. §59
For ships' journey, by the same reasoning with a few things changed, the same reasonings are brought about. For through the sides of the walls is passed an axle, having ends projecting beyond the ship, in which are enclosed wheels of four and one sixth feet in diameter, having fixed round their fronts paddles touching the water. Likewise, in the middle of the ship, an axle in the middle has a drum with one little tooth projecting beyond its rotundity. At that place is placed a little case having enclosed within itself a drum with 400 equalized teeth fitted to the little tooth of the drum that is enclosed on the axle; besides, fixed to the side projecting beyond the rotundity, another one tooth. §60
Above, in another little case fixed with it, enclosed is a flat drum toothed in the same way, with its teeth fitting the little tooth that is fixed on the side to the drum that is placed on its edge, so that, the single teeth of the flat drum, one at a time, pushing by the tooth by a single turning, shall turn the flat drum in a circle. In the flat drum, holes are made, in which holes are placed round pebbles. In its case, or little receptacle, one hole is hollowed out, having a little channel, by which the pebble, freed from its hindrance, falls into a bronze vessel and signifies by its sound. §61
Thus, when the ship has its course either by oars or by the blast of winds, the paddles that are on the wheels, touching the water facing them and, by a vehement push backward, forced, shall turn the wheels; these, winding themselves, drive the axle; and the axle, the drum, whose tooth, turned by the single turnings, drives the single teeth of the second drum, making measured circuits. So, when 400 have been turned by the paddles of the wheel, the drum, turned once, shall drive, by the tooth that is fixed to its side, a tooth of the flat drum. Therefore whenever the circling of the flat drum shall bring the pebbles to the hole, it shall emit through the little channel. Thus both by sound and by number it will indicate the miles' spaces of the sail. What, in times peaceful and without fear, must be prepared for use and delight, and how they ought to be made, I have carried through. §62
Now what, for the defenses of danger and the necessity of safety, have been invented, that is, the reasonings of scorpions and ballistae, with what symmetries they can be prepared, I will set forth. All their proportions of these instruments are reasoned from the proposed length of the arrow which that instrument ought to send. Of its ninth part is made the size of the hole in the capitals, through which are stretched the twisted sinews that hold the arms. §63
The height and breadth of these holes of the capital should then be shaped. The boards which are at the top and the bottom of the capital, which are called peritretoi, let them be made of the thickness of one hole, of the breadth of one and three-quarters of it, at the extremes of one and a half. The side pieces (parastaticae), on right and left, beside the pivots, tall four holes, thick one and a quarter holes, the pivots half a hole. From the side piece to the hole, a space of three-quarters of a hole; from the hole to the middle side piece, likewise three-quarters of a hole. The breadth of the middle side piece, one hole and a three-eighths; the thickness, one hole. §64
The interval where the arrow is placed in the middle side piece, a fourth part of the hole. The four angles that are round, on the sides and fronts, let be fastened by iron plates or bronze pins with nails. The channel (which in Greek is called σῦριγξ), the length, nineteen holes. Of the rules (which some call bucculae) which are fixed to the right and left of the channel, the length, nineteen holes; height and thickness, one hole. And two rules are fastened, into which is set the windlass, having the length of three holes, the breadth of half a hole. The thickness of the buccula which is fastened, also called scamillum (or as some call it little receptacle), fixed with dovetail pivots, one hole; the height, half a hole. The windlass's length, (here the text has a numeral), the thickness, a ninth of a hole. §65
The length of the epitoxis, half a hole; the thickness, a third. Likewise of the chelonium. The cheles (or manucula), the length, three holes; the breadth and thickness, half. The length of the floor of the channel, sixteen holes; the thickness, one hole; the height, half. The base of the little column on the ground, eight holes; the breadth on the plinth, in which the little column is set, a half and a fifth hole; the thickness (with fractional marks). The length of the little column to the pivot, twelve holes; the breadth, half a hole; the thickness, two hundredths. Of its struts, three, whose length, nine holes; breadth, half; thickness, a seventh. The length of the pivot, one hole; the length of the head of the little column, one and nine-tenths. §66
The breadth of the antefixum, one and three-quarters of a hole; the thickness, one. The rear smaller column, which in Greek is called ἀντίβασις, of eight holes; the breadth of a hole and a half; the thickness (fraction). The subiectio of twelve holes; of the same breadth and thickness as that smaller column. Above the smaller column, a chelonium (or cushion), of two and a half holes in height; of breadth, one and three-quarters. The scutulae of the cherolabae, of two and one-fifth holes; the thickness of a hole and a half; the breadth one and a half. The length of the transversaria with pivots, nine holes; the breadth one and a half, and the thickness of the arm the length is (one and a half) of seven holes; the thickness at the root, one hole and a half; at the top, two-thirds; the curvature, eight holes. §67
These are prepared by these proportions, or by additions and deductions. For if the capitals be made higher than their width (which are called anatona), one takes from the arms, so that, by how much softer the tension by the height of the capital, by so much the brevity of the arms makes the blow more vehement. If the capital be lower (which is called catatonum), on account of the vehemence the arms shall be a little longer, so that they may be easily drawn. For as a lever, when of five feet length, lifts a load of four men; when of ten, lifts it for two; in the same manner arms, the longer they are, the more softly, the shorter the more hardly, they are drawn. Of the reasonings of catapults, from what members and proportions they are composed, I have said. §68
The reasonings of ballistae are various and different, prepared for the sake of one effect. Some are turned by levers and windlasses, some by polyspasta, some by capstans; some also by the reasonings of drums. But nevertheless no ballista is perfected except to the proposed magnitude of weight of stone which that instrument ought to send. Therefore of their reasoning it is not easy for all, except for those who, by geometrical reasonings, have numbers and multiplications noted. §69
For the holes made in the capitals, through whose spaces cords twisted, especially of women's hair, or of sinew, are stretched, are taken proportional in size to the weight of the stone that that ballista ought to send, and by the reasoning of gravity, as in catapults from the lengths of arrows. Therefore, that those too who do not know geometry may have it ready, lest in war's danger they be detained by reflection, what I have myself known for certain by doing, and what I have received in part from teachers, definite I will set forth, and by what things the Greek weighings have reasoning of modules, I will hand down, unfolded, that they may also correspond to our weights. §70
For a ballista that ought to send a two-pound stone, the hole in its capital will be five digits; if of four pounds, of six digits and [a half]; of ten pounds, of eight digits; of twenty pounds, of ten digits; of forty pounds, of twelve and a half; of sixty pounds, of thirteen and an eighth; of eighty pounds, of fifteen digits; of one hundred twenty pounds, one and a half and one and a half more; of 160, two feet; of 180, of a foot and five digits; of 200 pounds, a foot and six digits; of 210, a foot and a half and six digits; of 360, a foot and a half. §71
When the size of the hole has been established, let a scutula be described (which in Greek is called περίτρητος), whose length is of (some) holes, breadth of two and a sixth. Let the middle of the described line be divided, and when it has been divided let the extreme parts of that form be contracted, that it have an oblique shape of a sixth part in length, a fourth in breadth at the turn. Where the curvatures are, in which shall run out the peaks of the angles, and the holes turned, and the contraction of the breadth to return inwards by a sixth part, the hole, however, be oblong by as much as the epizygis has thickness. When it has been shaped, let the end be planed off, that it have its curvature gently turned round. §72
Let the thickness of its hole be established at one and a half holes. The modioli (two holes, breadth one and a half, thickness besides what is put in the hole half a hole; at the extreme, breadth of a third of a hole). The length of the parastatae, six and three-quarters of a hole; curvature half a hole; thickness two hundred and sixtieths of a hole. Is added, however, to the middle breadth as much as is near the hole made in the description, of breadth and thickness five holes, height a fourth. §73
The length of the rule which is on the table, eight holes; the breadth and thickness, half a hole. The pivots, two and three-sevenths; the thickness of a hole, one (with fractions). Curvature of the rule, (numerals). The breadth and thickness of the exterior rule likewise; its length, what the very curvature of the deformation and the side piece's breadth to its curvature give. The upper rules shall be equal to the lower. §74
The cross-piece of the table of 300 and a quarter. The length of the scapi of the climacis (ladder), thirteen holes; thickness one and a quarter; the breadth of the middle interval, one hole and a quarter; the thickness, an eighth and a quarter. The upper part of the climacis, which is next to the arms and joined to the table, let the whole length be divided into five parts. Of these, let two be given to that member which the Greeks call χελώνιον: breadth two-sevenths, thickness one-ninth, length three and a half holes, projection of the chela half a hole, plentigomatos one-seventh and a twentieth. What, however, is at the axon (which is called the front of the cross-piece), three holes. §75
The breadth of the interior rules, one-seventh of a hole, the thickness one twenty-fourth. The chelonium's replum (which is the cover) is enclosed by a dovetail at one-twelfth, the scapi of the climacis, breadth twelve thirty-sixths, thickness of the hole twelve-twelfths. The thickness of the square that is on the climacis, a hole; at the extremes, one-twelfth; and the diameter of the round axle shall be equal to the chela, at the little pegs less by a sixteenth. §76
The length of the anterides of (certain) holes, the breadth at the bottom of one-third of a hole, at the top thickness one-seventh. The base (which is called ἐσχάρα), of (certain) holes, the antibasis of four, of each the thickness and breadth of a hole. They are put together however at half the height. The column, breadth and thickness one and a half. The height, however, has no proportion of the hole, but will be what shall be required for use. The length of the arm, six holes, thickness at the root one, at the ends a third. Of ballistae and catapults I have set forth the symmetries which I thought most expedient. How they are tempered by tensions of cords twisted of sinew and hair, as much as I can comprehend in writing, I will not pass over. §77
The largest timbers in length are taken; above, chelonia are fixed, in which the windlasses are enclosed. Through the middle spaces of the timbers, forms are cut and excised, in which excisions are enclosed the capitals of the catapults, and are distinguished by wedges lest they be moved in the tensions. Then bronze modioli are enclosed in those capitals, and in them iron little wedges are placed (which the Greeks call ἐπιζυγίδας). §78
Then the ends of the cords are passed through the holes of the capitals, and across to the other side; then they are thrown into the windlasses and wound, so that when they are stretched by the levers, when they are touched by the hands, they have an equal sound in both. Then they are enclosed by the wedges at the holes, so that they cannot relax. Thus passed across to the other side, by the same reasoning they are stretched by the levers through the windlasses, until they sound equally. Thus by the enclosings of wedges, by sound, by musical hearings, the catapults are tempered. Of these things, what I could, I have said. It remains for me, of siege-matters, how by machinations both leaders may be victors and states may be defended, to speak. §79
First, for sieges, the ram is reported to have been thus invented. The Carthaginians set a camp for attacking Gades. When they had first taken a fortress, they tried to demolish it. When they had no iron tools for demolition, they took a timber, and holding it with their hands, and with its head striking the topmost wall continuously, threw down the topmost rows of stones; and so by degrees, from the top down, they scattered the whole fortification. §80
Afterwards a certain Tyrian workman, by name Pephrasmenus, by reasoning led by that invention, set up a mast, and from it suspended another crosswise like the beam of a balance, and so, drawing back and thrusting with vehement blows, threw down the wall of the Gaditani. But Geras of Chalcedon first made a base of material with wheels beneath, and above built uprights and yokes, forks, and on these hung a ram and covered it with ox-hides, that those placed in that machine for striking the wall might be safer. Because it had slow beginnings, he began to call it the testudo arietaria (ram-tortoise). §81
These first steps being then set to that kind of machination, afterwards when Philip son of Amyntas besieged Byzantium, Polyidus the Thessalian unfolded it in more kinds and more easily. From him Diades and Charias, who served with Alexander, received the teaching. So Diades, in his writings, shows that he invented movable towers, which, even dissolved, he used to carry about with the army; besides a borer, and an ascending machine by which transit could be made to the wall on a level foot; also the raven-demolisher, which some call the crane. §82
No less did he use the wheeled ram, whose reasonings he left in writing. He says the smallest tower should be made not less than sixty cubits high, seventeen in breadth, its topmost contraction a fifth of the lowest part; its uprights at the foot of the tower nine inches, at the top half a foot. He says this tower must be made of ten stories, each part in it having windows. §83
The greater tower a hundred and twenty cubits high, twenty-three and a half in width, contraction also by a fifth; uprights at the bottom a foot, at the top six digits. This magnitude of tower he made of twenty stories, with each story having a circuit of three cubits; but he covered it with raw hides, that they might be safe from every blow. §84
The preparation of the ram-tortoise was perfected by the same reasoning. It had an interval of thirty cubits, a height besides the pediment of thirteen; but the pediment's height from the floor to the top, sixteen cubits. The pediment went out aloft, above the middle roof, not less than two cubits; and above, a little turret of three stories was raised, on which top story were set scorpions and catapults; on the lower stories, a great abundance of water was heaped for extinguishing if any force of fire were sent in. But in it was established a ram-engine, which in Greek is called κριοδόχη, in which was placed a rope perfected on the lathe; on which, set above, the ram by the pullings and pullings-back of ropes effected great effects of work. It was covered with raw hides, like the tower. §85
Of the borer he unfolded these reasonings in writing. The machine itself, like a tortoise having in the middle a channel placed on uprights, as is wont to be done in catapults or ballistae, fifty cubits long, a cubit high, in which was placed a transverse windlass. At the head, on right and left, two blocks, through which was moved that which was within that channel, a timber with an iron head. Beneath it, in the very channel, closed-in frequent tubes made its motions swifter and more vehement. Above it, that timber that was there, arches were raised to the channel frequently, to support the raw hide with which that machine was wrapped. §86
Of the raven, he thought nothing should be written, because he observed that machine to have no virtue. Of the ascent (which in Greek is called ἐπιβάθρα), and of the sea-machinations by which approaches could be had through ships, I have observed that he only much promised, and did not unfold their reasonings. What have been written by Diades of machines and with what preparations, I have set forth. Now, as I received from my teachers, and as seems to me useful, I will set forth. §87
A tortoise which is prepared for the filling of ditches, and by which also approach to the wall can be had, must be made thus. Let a base be compacted (which in Greek is called ἐσχάρα), squared, having on each side twenty-one feet long and four cross-pieces. Let these be held by two others thick four-ninths, broad three-fourths; and let the cross-pieces stand apart from one another about three and a half feet, and under the single intervals of them let little trees be placed (which in Greek are called ἁμαξόποδες), in which the axles of the wheels, enclosed in iron plates, turn. Let these little trees be so tempered that they have pivots and holes, by which levers thrown across may expedite their turnings, so that either forward or backward, or to the right or left side, or obliquely at the corners, if needed, by these turned little trees it may advance. §88
Above the base let two timbers be laid, projecting six feet on each side; at whose projections let two other projected timbers be fixed in front, twelve feet long, thick and broad as those written in the base. Above this compaction let joined uprights be raised, besides the pivots nine feet in height, thick each way a palm and a half-foot, having intervals between them of a foot and a half. Let them be enclosed above by crossing beams with dovetails. Above the beams let rafters be placed, enclosed with pivots one into another, raised to a height of twelve feet. Above the rafters let a squared timber be placed, by which the rafters are joined. §89
The rafters themselves are held by lath-pieces fixed around, and covered with boards, chiefly of holm-oak; if not, of any other material which can have the greatest virtue, except pine or alder, for these are fragile and readily take fire. Round the boards, let frames be placed of thin rods most closely woven, and especially of fresh ones. With double raw hides sewn, stuffed with seaweed or straw soaked in vinegar, let the whole machine be covered. So from these shall be thrown off the blows of ballistae and the onsets of fires. §90
There is another kind of tortoise also, which has everything else as above written, except the rafters; but it has round a breastwork and pinnacles of boards sloping down from the top, and above is bound firmly by boards and hides. Also above it, clay kneaded with hair is laid to such a thickness that fire cannot harm that machine at all. These machines, if need be, can be of eight wheels, if the nature of the place requires so to temper it. Those tortoises which are prepared for digging are called in Greek ὀρυκτίδες; they have everything else as above written, but their fronts are made like the angles of triangles, so that when weapons are cast upon them from the wall, they may not receive the blows on flat fronts but, gliding from the sides, they may protect those who are digging inside, without danger. §91
Nor does it seem to me alien to set forth, of the tortoise which Hegetor of Byzantium made, by what reasonings it was made. For the length of its base was 63 feet, breadth 42. The uprights which were above the compaction, four in number, were compacted from two timbers each, each in height 36 feet, a palm and a half in thickness, a foot and a half in breadth. Its base had eight wheels, by which it was moved. Their height was six and a half feet, their thickness three feet. They were so fabricated of triple material, joined alternately with dovetails, and bound by iron bands drawn cold; these in the little trees (or as they are called hamaxopodes) had their turnings. §92
Also above the plane of the cross-pieces that was above the base, uprights were raised of eighteen feet, breadth of three-quarters, thickness of two-thirds, standing apart one and one-eighth. Above them beams enclosed round about held the whole compaction, a foot wide, three-fourths thick; above them rafters were raised of twelve feet in height; above the rafters, a timber placed joined the junctions of the rafters. Likewise they had fixed lath-pieces across, on which above a flooring round about covered the lower parts. §93
It had moreover a middle flooring above the little cross-beams, where scorpions and catapults were placed. Two compact uprights were erected of 45 feet, a foot and a half thick, three-quarters broad, joined at the ends by a dovetailed cross-beam, and by another middle one, dovetailed between the two shafts and bound by iron plates. Above was placed material alternately between the shafts and cross-pieces, passed through, firmly enclosed with sockets and elbows. In that material had been made on the lathe two little axles, from which ropes bound held the ram. §94
Above the heads of those who held the ram, a breastwork was set, adorned with the likeness of a turret, so that two soldiers, standing safely without danger, could look out and report what things the adversaries were attempting. The whole ram was 180 feet long, at the bottom a palm and a foot wide, one foot thick, contracting at the head in breadth one foot, thickness half a foot. §95
This ram had of hard iron a beak, as long ships are wont to have; and from the beak four iron plates, about fifteen feet, were fixed on the material. From the head to the lowest heel of the timber, three ropes were held, in thickness eight digits, so bound as in a ship from stern to prow continuously; and these ropes were bound by transverse girdings, having between them palm-and-a-half intervals. Above, the whole ram was wrapped with raw hides. Of the ropes from which it hung, the ends had been made of quadruple iron chains, and these themselves were wrapped with raw hides. §96
Also its projection had a chest compacted and fixed, in which a net with larger cords stretched, through whose roughnesses, the feet not slipping, easily reached the wall. And that machine was moved by six motions: forward, backward, likewise to the right side and the left, with extension no less lifted up in height, and by inclination lowered to the depth. The machine was raised in height for knocking down the wall about 100 feet; likewise from the side, right and left, in going forward, skimmed not less than 100 feet. It was governed by 100 men, having a weight of 4000 talents, which makes 480,000 pounds. §97
Of scorpions and catapults and ballistae, also of tortoises and towers, those which seemed to me most fit, and by whom they were invented and how they ought to be made, I have unfolded. But of ladders and cranes (carchesia) and those whose reasonings are weaker, I have not thought it necessary to write. These, soldiers are wont to make of themselves. Nor can these themselves be useful in all places or by the same reasonings, because fortifications are unlike fortifications, and the courage of nations differs. For by one reasoning are machinations to be prepared against the bold and rash, differently against the diligent, otherwise against the timid. §98
So if any one shall wish to attend to these prescriptions, and, choosing their variety, to bring them into one preparation, he will not be in need of helps, but whatever matters from reasonings or places shall be needed, without doubt he will be able to unfold. Of defensive matters, however, it is not to be unfolded by writings. For the enemy does not prepare his besieging matters to our writings, but their machinations are often overturned, extempore, by the dexterous swiftness of counsels, without machines. This is reported to have befallen also the Rhodians. §99
Diognetus had been a Rhodian architect, and from the public each year a fixed fee was paid to him, for the dignity of art, as honor. At that time a certain architect from Arados, by name Callias, coming to Rhodes, gave a public lecture and produced an exemplar of a wall and above it a machine on a turning crane, with which, when a helepolis was coming to the walls, he seized and transferred it within the wall. When the Rhodians saw this exemplar, marveling, they took away from Diognetus what had been yearly established for him, and transferred that honor to Callias. §100
Meanwhile King Demetrius, who, on account of the persistence of his mind, was called Poliorcetes, preparing war against Rhodes, brought with him Epimachus, a noble Athenian architect. He had prepared a helepolis with immense expenses, industry, and the highest labor, whose height was 135 feet, breadth 60 feet. He made it firm with goat-hair cloths and raw hides, so that it could bear the blow of a stone sent from a ballista of 360 pounds; the machine itself had been 360,000 pounds. When Callias was asked by the Rhodians that he prepare a machine against that helepolis, and that he, as he had promised, transfer it within the wall, he denied he could. §101
For not all things can be done by the same reasonings; but there are some which, by small exemplars, similarly made great, have effects; others cannot have exemplars, but are set up of themselves; some are like to truth in exemplars, but when they begin to grow they fall apart. As we can also here observe. A hole is bored by a half-digit bit, by a digit, by a digit and a half. If by the same reasoning we should wish to make one of a palm, it has no unfolding; of half-a-foot or greater, not even to be thought of at all. Thus in some exemplars it is seen. §102
As in the smallest they seem to be done, not equally in the same manner in greater. Thus by the same reasoning the Rhodians, deceived, committed injury with contumely against Diognetus. So after they saw the enemy persistently hostile, with the danger of slavery, with the machination prepared for taking the city, the devastation of the state impending, they prostrated themselves before Diognetus, begging him to aid his country. He at first denied he would do it. §103
After well-born maidens and ephebi with priests came to entreat, then he promised, on these terms, that if he should take that machine, it would be his. With these things so established, in the region where the machine was about to approach, he pierced the wall, and ordered all publicly and privately, whatever anyone had of water, dung, mud, through that window, through the channels going out, to pour before the wall. When there was poured forth at night a great mass of water, mud, dung, on the next day the helepolis, approaching, before it drew near the wall, settled in the moist hole, and could not afterwards advance or retreat. So Demetrius, when he saw that he had been deceived by Diognetus's wisdom, with his fleet departed. §104
Then the Rhodians, freed from the war by Diognetus's skill, publicly gave thanks, and adorned him with all honors and ornaments. Diognetus led that helepolis back into the city, and placed it in public, and inscribed: 'Diognetus gave this gift to the people from the spoils.' So in defensive matters not only machines but above all counsels are to be prepared. §105
No less at Chios, when the enemy had prepared sambuca-machines above their ships, by night the Chians heaped earth, sand, and stones into the sea before the wall. So they, on the next day, when they wished to approach, their ships settled upon the heap that was under the water, and could neither approach the wall nor retreat backwards; but there, pierced by firebrands, they were consumed by fire. At Apollonia too, when it was besieged, and the enemy thought to penetrate within the walls by digging tunnels unsuspected, and this was reported to the Apollonians by spies, disturbed by the news, on account of fear and lacking counsels, they wavered in their spirits, because they could not know the time nor the certain place at which the enemy were to make their emergence. §106
Then indeed Trypho of Alexandria was there as architect. He designed several tunnels within the wall, and, by digging the earth, advanced outside the wall only so far as the shot of an arrow; and in all of them he hung bronze vessels. From these, in one digging that was opposite the enemy's tunnel, the hanging vessels began to sound at the blows of the iron tools. So it was understood from this, in what region the adversaries, driving the tunnels, were meditating to penetrate within. Thus, the line being known, he tempered bronze cauldrons of boiling water and pitch, and, from above, against the heads of the enemy, of human dung and of baked glowing sand. Then at night he pierced frequent holes, and through them, suddenly breaking through, killed all the enemies who were in that work. §107
Likewise when Massilia was besieged, and they drove more than thirty tunnels, the Massilians, suspicious, deepened by a deeper digging the whole ditch which was before the wall. Thus all the tunnels had their exits into the ditch. But where the ditch could not be made, within the wall a barathrum, of the amplest length and amplitude, they made like a piscina, opposite the place where the tunnels were driven, and filled it from wells and from the harbor. So when the tunnel was suddenly opened at the nostrils, the vehement force of water let in undermined the supports; and those who were within were overwhelmed, both by the multitude of water and by the ruin of the tunnel. §108
Also when a mound was being prepared against the wall against them, and, trees being cut and placed, the place was being heaped up by works, with ballistae they sent iron glowing bars into it, and compelled the whole fortification to blaze. And the ram-tortoise, when it had approached to strike the wall, they let down a noose and, that ram being constrained, by a drum turning a capstan, with its head suspended, they did not suffer it to touch the wall; then they scattered the whole machine with glowing firebrands and the blows of ballistae. Thus, by that victory, the states were freed not by machines but, against the reasoning of machines, by the dexterity of architects. What reasonings I could unfold of machines, and which I thought most useful in times of peace and war, in this volume I have brought to completion. In the prior nine books, on the single kinds and parts I have compared, so that the whole body of all the members of architecture might be unfolded in ten volumes. §109