M. VITRUVII POLLIONIS
DE ARCHITECTURA
LIBER DECIMUS ULTIMUSQUE
M. VITRUVIUS POLLIO
ON ARCHITECTURE
BOOK TEN AND LAST
P.1 P.2 P.3 P.4 1.1 1.2 1.3 1.4 1.5 1.6 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 5.1 5.2 6.1 6.2 6.3 6.4 7.1 7.2 7.3 7.4 7.5 8.1 8.2 8.3 8.4 8.5 8.6 9.1 9.2 9.3 9.4 9.5 9.6 9.7 10.1 10.2 10.3 10.4 10.5 10.6 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.1 12.2 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 14.1 14.2 14.3 15.1 15.2 15.3 15.4 15.5 15.6 15.7 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 16.12
P.1 P.2 P.3 P.4 1.1 1.2 1.3 1.4 1.5 1.6 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 5.1 5.2 6.1 6.2 6.3 6.4 7.1 7.2 7.3 7.4 7.5 8.1 8.2 8.3 8.4 8.5 8.6 9.1 9.2 9.3 9.4 9.5 9.6 9.7 10.1 10.2 10.3 10.4 10.5 10.6 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.1 12.2 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 14.1 14.2 14.3 15.1 15.2 15.3 15.4 15.5 15.6 15.7 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 16.12
[1] Nobili Graecorum et ampla civitate Ephesi lex vetusta dicitur a maioribus dura condicione sed iure esse non iniquo constituta. Nam architectus, cum publicum opus curandum recipit, pollicetur, quanto sumptui adsit futurum. Tradita aestimatione magistratui bona eius obligantur, donec opus sit perfectum.
[1] In the noble and ample city of the Greeks, Ephesus, an ancient law is said by our elders to have been established, with a hard condition but by a right not inequitable. For the architect, when he undertakes a public work to be cared for, promises for what expense it will be. Upon the estimation being delivered to the magistrate, his goods are obligated, until the work is perfected.
But when it is completed, if the expenditure matches what was stated, he is adorned with decrees and honors. Likewise, if not more than a quarter is consumed in the work, it is to be added to the estimate, it is furnished from the public treasury, and he is held by no penalty. But when more than a quarter is consumed in the work, money is exacted from his goods for completing it.
[2] Utinam dii inmortales fecissent, ea lex etiam P
[2] Would that the immortal gods had brought it about that that law had been established also for the R
[3] Nec solum id vitium in aedificiis, sed etiam in muneribus, quae a magistratibus foro gladiatorum scaenicisque ludorum dantur, quibus nec mora neque expectatio conceditur, sed necessitas finito tempore perficere cogit, id est sedes spectaculorum velorumque inductiones sunt et ea omnia, quae scaenicis moribus per machinationem ad spectationis populo conparantur. In his vero opus est prudentia diligens et igenii doctissimi cogitata, quod nihil eorum perficitur sine machinatione studiorumque vario ac sollerti vigore.
[3] And not only does that fault occur in edifices, but also in the munera, which are given by magistrates for the forum of gladiators and for the scenic games, to which neither delay nor waiting is conceded, but necessity compels completion within a fixed time—that is, the seats of the spectacles, the deployments of the awnings, and all those things which, according to scenic customs, are provided to the people’s viewing by machinery. In these, truly, there is need of diligent prudence and the devised plans of most learned ingenuity, since none of them is brought to completion without machinery and the varied and skillful vigor of studies.
[4] Igitur quoniam haec ita sunt tradita et constituta, non videtur esse alienum, uti caute summaque diligentia, antequam instituantur opera, eorum expediantur, rationes. Ergo quoniam neque lex neque morum institutio id potest cogere et quotannis et praetores et aediles ludorum causa machinationes praeparare debent, visum mihi est, imperator, non esse alienum, quoniam de aedificiis in prioribus voluminibus exposui, in hoc, quod finitionem summam corporis habet constitutam, quae sint principia machinarum, ordinata praeceptis explicare.
[4] Therefore, since these things have been transmitted and constituted in this way, it does not seem alien that, cautiously and with the utmost diligence, before the works are instituted, their plans be set forth. Therefore, since neither law nor the institution of customs can compel this, and since every year both the praetors and the aediles, for the sake of the games, must prepare machinations, it has seemed to me, Emperor, not to be alien, since I have expounded about buildings in the prior volumes, in this one, which has the ultimate finishing of the body established, to explain, ordered by precepts, what the principles of machines are.
[1] Machina est continens e materia coniunctio maximas ad onerum motus habens virtutes. Ea movetur ex arte circulorum rutundationibus, quam Graecicyclicen cinesin appellant. Est autem unum genus scansorium, quod graece acrobaticon dicitur; alterum spirabile, quod apud eos pneumaticon appellatur; tertium tractorium, id autem Graeci baru ison vocitant.
[1] A machine is a coherent conjunction out of material, having the greatest powers for the motions of burdens. It is moved by the art through the rotundations of circles, which the Greeks callcyclicen cinesin. There is, moreover, one climbing kind, which in Greek is called acrobaticon; another air-driven kind, which among them is called pneumaticon; a third tractive kind, which the Greeks term baru ison.
[2] Tractorium vero, cum onera machinis pertrahuntur, ut ad altitudinem sublata conlocentur. Scansoria ratio non arte sed audacia gloriatur; ea catenationibus [et transversariis et plexis conligationibus] et erismatum fulturis continentur. Quae autem spiritus potestate adsumit ingressus, elegantes artis subtilitatibus consequetur effectus.
[2] As for the hauling-gear, it is used when loads are dragged by machines, so that, once lifted to a height, they may be set in place. The climbing method boasts not of art but of audacity; these are held together by chainings [and by crosspieces and by plaited bindings] and by the props of erismata (shores). But those which take on motions by the power of air will achieve elegant effects through the subtleties of art.
[3] Ex his sunt quaemechanicos alia organicos moventur. Inter machinas et organa id videtur esse discrimen, quod machinae pluribus operis ut vi maiore coguntur effectus habenti, uti ballistae torculariorumque prela; organa autem unius operae prudenti tactu perficiunt quod est propositum, uti scorpionis seu anisocyclorum versationes. Ergo et organa et machinarum ratio ad usum sunt necessaria, sine quibus nulla res potest esse non impedita.
[3] Of these, there are those which are moved asmechanical, others as organical. Between machines and organs this seems to be the discrimination: that machines, by several labors, are driven so as, with greater force, to have an effect—such as ballistae and the presses of the wine-pressers; but organs, by the prudent touch of a single operation, accomplish what is proposed—such as the turnings of the scorpion or of the anisocycles. Therefore both organs and the rationale of machines are necessary for use, without which nothing can be unimpeded.
[4] Omnis autem est machinatio rerum natura procreata ac praeceptrice et magistra mundi versatione instituta. Namque ni advertamus primum et aspiciamus continentem solis, lunae, quinque etiam stellarum, natura machinata versarentur, non habuissemus interdum lucem nec fructûm maturitatis. Cum ergo maiores haec ita esse animadvertissent, e rerum natura sumpserunt exempla et ea imitantes inducti rebus divinis commodas vitae perfecerunt explicationes.
[4] Every machination is procreated by the nature of things and instituted by the revolution of the world, its preceptress and mistress. For unless we were to notice first and look upon the continuous revolution of the sun, the moon, and even the five stars, machinated by nature as they are revolved, we would not at times have light nor the fruit of maturity. Therefore, when the elders had observed that these things are so, from the nature of things they took examples, and imitating them, being induced by divine matters, they perfected explications commodious for life.
[5] Attendamus enim primum inventum de necessitate, ut vestitus, quemadmodum telarum organicis administrationibus conexus staminis ad subtemen non modo corpora tegendo tueatur, sed etiam ornatus adiciat honestatem. Cibi vero non habuissemus abundantiam, nisi iuga et aratra bubus iumentisque omnibus essent inventa. Sucularumque et prelorum et vectium si non fuisset torcularîs praeparatio, neque olei nitorem neque vitium fructum habere potuissemus ad iucunditatem, portationesque eorum non essent, nisi plostrorum seu serracorum per terram, navicularum per aquam inventae essent machinationes.
[5] For let us attend, first, to invention out of necessity: clothing—how, by the organic administrations of looms, the connection of the warp to the weft not only protects bodies by covering, but also adds respectability to adornment. Indeed, we would not have had an abundance of food, unless yokes and ploughs had been invented for oxen and all draught beasts. And as for screws, presses, and levers, if there had not been the preparation of the press, we could have had neither the sheen of oil nor the fruit of the vines for delight; and their transport would not exist, unless the machinations of wagons or carts over land, and of little ships over water, had been invented.
[6] Trutinarum vero librarumque ponderibus examinatio reperta vindicat ab iniquitate iustis moribus vitam. Non minus quae sunt innumerabili modo rationes machinationum, de quibus non necesse videtur disputare, quando sunt ad manum cotidianae, ut sunt molae, folles fabrorum, raedae, cisia, torni ceteraque, quae communes ad usum consuetudinibus habent opportunitates. Itaque incipiemus de îs, quae raro veniunt ad manus, ut nota sint, explicare.
[6] The examination by weights of steelyards and balances, once discovered, vindicates life from iniquity by just mores. No less the countless kinds of mechanisms, about which it does not seem necessary to discuss since they are everyday and at hand, such as millstones, the bellows of smiths, coaches, gigs, lathes, and the rest, which by customary usages have common conveniences for use. Therefore we shall begin to explain those things which rarely come to hand, so that they may be known.
[1] Primumque instituemus de is, quae aedibus sacris ad operumque publicorum perfectionem necessitate comparantur. Quae fiunt ita. Tigna duo ad onerum magnitudinem ratione expediuntur.
[1] And first we will set forth concerning those things which, from sacred buildings, by necessity are acquired for the perfection of public works. These are done thus. Two beams are made ready, by plan, to the magnitude of the burdens.
Joined at the head by a clasp and spread apart at the bottom, they are raised upright; with ropes placed on the heads and disposed around, the erected frame is retained. At the top a troclea is fastened, which some also call a rechamum. Into the troclea are inserted little wheels <two>, having revolutions by means of small axles.
Through the <summum> little wheel (sheave) the hauling-rope is passed, then it is let down and led around the little wheel of the lower pulley. It is carried back to the lowest little wheel of the upper pulley, and thus descends to the lower one and is tied fast in its hole. The other part of the rope is carried back among the lowest parts of the machine.
[2] In quadris autem tignorum posterioribus, quo loci sunt divaricata, figuntur chelonia, in quae coiciuntur sucularum capita, ut faciliter axes versentur. Eae suculae proxime capita habent foramina bina ita temperata, ut vectes in ea convenire possint. Ad rechamum autem imum ferrei forfices religantur, quorum dentes in saxa forata accommodantur.
[2] But on the rear quadrants of the beams, where they are splayed apart, chelonia are fastened, into which the heads of the windlasses are inserted, so that the axles may turn easily. These windlasses have, close to their heads, twin holes so calibrated that levers can fit into them. And to the lowest rechamum iron shears are tied, whose teeth are fitted into the bored stones.
[3] Haec autem ratio machinationis, quod per tres orbiculos circumvolvitur, trispastos appellatur. Cum vero in ima troclea duo orbiculi, in superiore tres versantur, id pentaspaston dicitur. Sin autem maioribus oneribus erunt machinae comparandae, amplioribus tignorum longitiudinibus et crassitudinibus erit utendum; eadem ratione in summo fibulationibus, in imo sucularum versationibus expediendum.
[3] But this method of machination, because it is wound around through three little wheels, is called a trispastos. When, however, two little wheels are turned in the lower pulley-block and three in the upper, that is called a pentaspaston. But if machines are to be prepared for greater loads, more ample lengths and thicknesses of beams must be used; in the same manner it must be set up—with fibulations at the top, with the turnings of windlasses at the bottom.
With these things explained, let the anterior ropes be placed slack in front; let the retinacula be laid out far over the shoulders of the machine, and if there will not be a place where they may be tied, let stakes laid back be sunk and solidified all around by fistucation, to which the ropes may be bound.
[4] Troclea in summo capite machinae rudenti contineatur, et ex eo funis perducitur ad palum et quae est in palo trocleam inligata. Circa eius orbiculum funis indatur et referatur ad eam trocleam, quae erit ad caput machinae religata. Circum autem orbiculum ab summo traiectus funis descendat et redeat ad suculam, quae est in ima machina, ibique religetur.
[4] Let the troclea at the top head of the machine be held by a cable, and from it the rope is led to the stake and to the troclea which is fastened on the stake. Around its little wheel (orbiculum) the rope is to be placed and carried back to that troclea which will be tied to the head of the machine. But the rope, having been passed around the little wheel from the top, should descend and return to the sucula (windlass) which is at the bottom of the machine, and there be fastened.
Moreover, the windlass, forced by levers, will be turned and will raise the machine by itself without danger. Thus, with the ropes laid around and the retinacula (guy-ropes) holding fast in the stakes, the machine will be set in place in a more ample manner. The trochleae (pulleys) and the draught-ropes, as has been written above, are made ready.
[5] Sin autem colossicotera amplitudinibus et ponderibus onera in operibus fuerint, non erit suculae committendum, sed quemadmodum sucula chelonîs retinetur, ita axis includatur habens in medium tympanum amplum, quod nonnulli rotam appellant, Graeci autemamphieren, alii perithecium vocant.
[5] But if in works the loads are of more colossal amplitudes and weights, it must not be entrusted to the windlass; rather, just as the windlass is held in the tortoise, so let an axle be enclosed, having in the middle a large drum, which some call a wheel, but the Greeks callamphieren, others call perithecium.
[6] In his autem machinis trocleae non eodem sed alio modo comparantur. Habent enim et in imo et in summo duplices ordines orbiculorum. Ita funis ductarius traicitur in inferioris trocleae foramen, uti aequalia duo capita sint funis, cum erit extensus, ibique secundum inferiorem trocleam resticula circumdata et contenta utraeque partes funis continentur, ut neque
[6] In these machines, however, the pulleys are arranged not in the same but in another way. For they have double rows of little wheels at both the bottom and the top. Thus the hauling-rope is passed through the aperture of the lower pulley, so that, when it is stretched, there may be two equal ends of the rope; and there, next to the lower pulley, a little cord having been wound around and tightened, both parts of the rope are held fast, so that they can move out neither
Then the ends of the rope are carried to the upper pulley on the outer side and are led down around the lowest sheaves, and they return to the bottom and are threaded into the lowest pulley at the sheaves on the inner side, and are led back to the right and to the left; to the head they return around the topmost sheaves.
[7] Traiecti autem ab exteriore parte feruntur dextra sinistra tympanum in axe ibique, ut haereant, conligantur. Tum autem circa tympanum involutus alter funis refertur ad ergatam, et is circumactus tympanum et axem. Se involvendo pariter extendunt, et ita leniter levant onera sine periculo.
[7] Having been passed through from the exterior side, they are borne right and left to the drum on the axle, and there, so that they may adhere, they are bound fast. Then moreover another rope, wound around the drum, is carried back to the windlass, and by being turned it makes the drum and the axle revolve. By wrapping themselves they are extended equally, and thus they gently lift the loads without danger.
[8] Est autem aliud genus machinae satis artificiosum et ad usum celeritatis expeditum, sed in eo dare operam non possunt nisi periti. Est enim tignum, quod erigitur et distenditur retinaculis quadrifariam. Sub retinaculo chelonia duo figuntur, troclea funibus supra chelonia religatur, sub troclea regula longa circiter pedes duos, lata digitos sex, crassa quattuor supponitur.
[8] Moreover, there is another kind of machine quite artificious and expeditious for the use of celerity, but in it none can apply themselves unless they are skilled. For it is a beam, which is raised and stretched with guy-ropes in four directions. Under the guy-rope two chelonia are fixed; a pulley is fastened with ropes above the chelonia; beneath the pulley a bar is placed, about two feet long, six digits wide, and four thick.
[9] Cum descenderint ad imum, ex interiore parte et per secundos orbiculos traducuntur in extremum et referuntur in summum ad orbiculos secundos; traiecti redeunt ad imum et per imum referuntur ad caput; traiecti per summos redeunt ad machinam imam. In radice autem machinae conlocatur tertia troclea; eam autem Graeciepagonta nostri artemonem appellant. Ea troclea religatur ad trocleae radicem habens orbiculos tres, per quos traiecti funes traduntur hominibus ad ducendum.
[9] When they have descended to the bottom, from the inner side and through the second sheaves they are led across to the end and are carried back up to the second sheaves; having been passed through, they return to the bottom and along the bottom are carried back to the head; having been passed through the topmost, they return to the lowest machine. But at the root of the machine a third pulley is placed; the Greeks call itepagonta, our people call it artemon. That pulley is tied to the root of the pulley, having three sheaves, through which the passed-through ropes are handed over to the men for hauling.
[10] Hoc genus machinae polyspaston appellatur, quod multis orbiculorum circuitionibus et facilitatem summam praestat et celeritatem. Una autem statutio tigni hanc habet utilitatem, quod ante quantum velit et dextra ac sinistra a latere proclinando onus deponere potest.
[10] This kind of machine is called a polyspaston, because with many circuits of little wheels it affords the greatest facility and celerity. But a single erection of the timber has this utility, that forward as far as one wishes, and by inclining to the right and to the left from the side, it can set down the load.
Harum machinationum omnium, quae supra sunt scriptae, rationes non modo ad has res, sed etiam ad onerandas et exonerandas naves sunt paratae, aliae erectae, aliae planae in carchesîs versatilibus conlocatae. Non minus sine tignorum erectionibus in plano etiam eadem ratione et temperatis funibus et trocleis subductiones navium efficiuntur.
Of all these machinations which have been written above, the methods are prepared not only for these purposes, but also for loading and exonerating ships, some set up upright, others level, placed on versatile carchesii. No less, without erections of beams, even on the level, by the same method and with adjusted ropes and pulleys, haulings of ships are effected.
[11] Non est autem alienum etiam Chersiphronos ingeniosam rationem exponere. Is enim scapos columnarum e lapidicinis cum deportare vellet Ephesi ad Dianae fanum, propter, magnitudinem onerum et viarum campestrem mollitudinem non confisus carris, ne rotae devorarentur, sic est conatus. De materia trientali scapos quattuor, duos transversarios interpositos, quanta longitudo scapi fuerit, complectet et conpeget et ferreos cnodacas uti subscudes in capitibus scaporum inplumbavit et armillas in materia ad cnodacsas circumdandos infixit; item bucculis tigneis capita religavit; cnodaces autem in armillis inclusi liberam habuerunt versationem tantam; ita, cum boves ducerent subiuncti, scapi versando in cnodacibus et armillis sine fine volvebantur.
[11] Moreover, it is not alien to set forth also Chersiphron’s ingenious method. For when he wished to convey the shafts of the columns from the stone‑quarries to the fane of Diana at Ephesus, not trusting in carts on account of the magnitude of the burdens and the softness of the level roads, lest the wheels be devoured, he attempted as follows. From third‑measure timber he made four beams, with two crosspieces interposed, enclosing and pinning together a frame as long as the length of the shaft; and iron cnodaces, to serve as dowel‑pivots, he set in with lead at the ends of the shafts, and he fixed rings in the timber to encircle the cnodaces; likewise with wooden cheek‑blocks he bound the ends; but the cnodaces, enclosed in the rings, had so free a revolution; thus, when oxen, yoked beneath, drew, the shafts, by turning on the cnodaces and rings, rolled without end.
[12] Cum autem scapos omnes ita vexerunt et instabant epistyliorum vecturae, filius Chersiphronos Metagenes transtulit ex scaporum vectura etiam in epistyliorum deductione. Fecit enim rotas circiter pedum duodenûm et epistyliorum capita in medias rotas inclusit; eadem ratione cnodaces et armillas in capitibus inclusit: ita cum trientes a bubus ducerentur, in armillis inclusi cnodaces versabant rotas, epistylia vero inclusa uti axes in rotis eadem ratione, qua scapi, sine mora ad opus pervenerunt. Exemplar autem erit eius, quemadmodum in palaestris cylindri exaequant ambulationes.
[12] But when they had thus conveyed all the shafts and the haulage of the epistyles was pressing, Chersiphron’s son Metagenes transferred from the conveyance of the shafts also to the bringing-down of the epistyles. For he made wheels of about 12 feet, and enclosed the ends of the epistyles in the middles of the wheels; by the same method he enclosed the cnodaces and armillae at the ends: thus, when the trientes (timber-frames) were drawn by the oxen, the cnodaces, enclosed in the armillae, made the wheels revolve, while the epistyles, enclosed like axles in the wheels by the same method as the shafts, arrived at the work without delay. A model of this, moreover, will be how in the palaestrae cylinders level the walkways.
[13] Nostra vero memoria cum colossici Apollinis in fano basis esset a vetustate diffracta, et metuentes, ne cederet ea statua et frangeretur, locaverunt ex eisdem lapidicinis basim excidendam. Conduxit quidam Paconius. Haec autem basis erat longa pedes duodecim, lata pedes VIII, alta pedes sex.
[13] But in our own memory, when the base of the colossal Apollo in the fane had been shattered by age, and fearing lest that statue should give way and be broken, they let out by contract that a base be hewn from the same quarries. A certain Paconius undertook it. Now this base was 12 feet long, 8 feet wide, 6 feet high.
[14] Rotas enim circiter pedum XV fecit et in his rotis capita lapidis inclusit, deinde circa lapidem fusos sextantales ab rota ad rotam ad circinum compegit, ita uti fusus a fuso non distaret pedem esse unum. Deinde circa fusos funem involvit et bubus iunctis funem ducebant. Ita cum explicaretur, volvebat rotas, sed non poterat ad lineam via recta ducere, sed exibat in unam partem.
[14] For he made wheels of about 15 feet and enclosed the ends of the stone in these wheels; then, around the stone, he fastened spindles of a sextans-measure from wheel to wheel, by the compass, so that spindle from spindle was one foot distant. Then he wound a rope around the spindles, and with oxen yoked they were drawing the rope. Thus, as it was unwound, it was rolling the wheels; but he could not guide it in a straight line, and it kept going off to one side.
[15] Pusillum extra progrediar et de his lapidicinis, quemadmodum sint inventae, exponam. Pixodarus fuerat pastor. Is in his locis versabatur.
[15] I will advance a little further and will expound about these stone-quarries, how they were discovered. Pixodarus had been a shepherd. He used to frequent these places.
When the citizens of the Ephesians were considering to make the temple of Diana out of marble and were decreeing that marble be sought from Paros, Proconnesus, Heraclea, and Thasos, Pixodarus, after driving his sheep forward, was pasturing the flock in that same place; and there two rams, charging one another, passed each the other, and, an attack having been made, one struck a rock with his horns, from which a crust of the most gleaming white color was knocked off. Thus Pixodarus is said to have left the sheep in the mountains and to have quickly carried the crust to Ephesus, at the very time when that matter was being transacted. So immediately they decreed honors for him and changed his name: instead of Pixodarus he should be called Evangelus.
[1] De tractoriis rationibus quae necessaria putavi, breviter exposui. Quorum motus et virtutes duae res diversae et inter se dissimiles uti congruentes uti principia pariunt eos perfectus: una porrecti, quam Graecieutheiam vocitant, altera rutunditatis, quam Graeci cycloten appellant. Sed vero neque sine rutunditate motus porrecti nec sine porrecto rotationis versationes onerum possunt facere levationes.
[1] On traction methods I have briefly set forth what I considered necessary. Their motions and powers—two things diverse and mutually dissimilar, yet congruent as principles—produce them perfected: one of straight extension, which the Greeks calleutheiam, the other of roundness, which the Greeks call cycloten. But in truth neither can the motions of straight advance effect the elevations of loads without roundness, nor can the rotations of turning do so without straight advance.
[2] Id autem ut intellegatur, exponam. Inducuntur uti centra axiculi in orbiculos et in trocleis conlocantur, per quos orbiculos funis circumactus directis ductionibus et in sucula conlocatus vectium versationibus onerum facit egressus in altum. Cuius suculae cardines uti centra porrecti in cheloniis, foraminibusque eius vectes conclusi capitibus ad circinum circumactis torni ratione versando faciunt oneris elationes.
[2] So that this may be understood, I will set it forth. The centers of the little axles are introduced and placed into little wheels and into trochleae (pulleys), through which little wheels a rope, having been led around in straight draughts and set upon the windlass, by the turnings of the levers makes the burdens go out upward into the height. The pivots of this windlass, as elongated centers, are set in the chelonia (bearing-blocks), and with the levers enclosed in its holes, their heads rotated to the circle, by the method of the lathe in turning they produce the elevations of the load.
[3] Id autem quod brevior pars prior vectis ab ea pressione, quod est centrum, subit sub onus, et quo longius ab eo centro distans caput eius deducitur. Per id faciundo motus circinationis cogit pressionibus examinare paucis manibus oneris maximi pondus. Item si sub onus vectis ferrei lingula subiecta fuerit neque eius caput pressione in imum, sed adversus in altitudinem extolletur, lingula fulta in areae solo habebit eam pro onere, oneris autem ipsius angulum pro pressione.
[3] And as to this: that the shorter, front part of the lever goes under the load from that pressing-point which is the center, and that the farther its head, being distant from that center, is drawn down. By doing this, the motion of circination compels, by pressures, to examine (to weigh) with few hands the weight of a very great burden. Likewise, if under the load the little tongue of an iron lever has been placed, and its head is not by pressure driven downward, but contrariwise is raised upward into height, the little tongue, propped on the floor of the area, will have that for the load, but the corner of the load itself for the pressing-point.
Thus not so easily as by oppression (downward pressure), but nevertheless in the opposite direction, it will be exerted against the weight of the load. Therefore, if the little tongue of the lever, placed above the hypomochlion (fulcrum), has gone farther in under the load and its head has had pressures nearer to the center, it will not be able to elevate the load, unless, as written above, an examination of the lever’s length through the head and by tractions has been made.
[4] Id autem ex trutinis, quae staterae dicuntur, licet considerare. Cum enim ansa propius caput, unde lancula pendet, ibi ut centrum est conlocata et aeqipondium in alteram partem scapi, per puncta vagando quo longius aut etiam ad extremum perducitur, paulo et inpari pondere amplissimam pensionem parem perficit per scapi librationem, et examinatio longius ab centro recedens ita inbecillior. Aequipondii brevitas maiorem vim ponderis momento deducens sine vehementia molliter ab imo susum versum egredi cogit futurum.
[4] But this may be considered from balances, which are called steelyards. For when the handle is placed nearer the head, whence the little pan hangs, there it is set as the center; and the equiponderant on the other part of the shaft, by roaming through the points, the farther—indeed even to the extremity—it is brought, with a small and unequal weight accomplishes an equal poise of a very large burden through the libration of the shaft; and the pointer (examen), receding farther from the center, is thereby weaker. The shortness of the equiponderant, drawing down the greater force of the weight by its moment, compels that which is to be raised to go forth gently, from below upward, without vehemence.
[5] Quemadmodum etiam navis onerariae maximae gubernator ansam gubernaculi tenens, quioiax a Graecis appellatur, una manu momento per centrum ratione pressionibus artis agitans, versat eam amplissimis et inmanibus mercis et pinus ponderibus oneratam. Eiusque vela cum sunt per altitudinem mediam mali pendentia, non potest habere navis celerem cursum, cum autem in summo cacumine antemnae subductae sunt, tunc vehementiore progreditur impetu, quod non proxime calcem mali, quod est loco centri, sed in summo longius et ab eo progressa recipiunt in se vela ventum.
[5] Just as also the helmsman of a very great cargo ship, holding the handle of the rudder, which is calledoiax by the Greeks, with one hand, by a moment through the center, moving it by the method and pressures of the art, turns it, though laden with the very large and immense weights of merchandise and pine timbers. And its sails, when they are hanging along the middle height of the mast, the ship cannot have a swift course; but when at the topmost summit the yards have been drawn up, then it advances with a more vehement impetus, because the sails receive the wind into themselves not near the heel of the mast, which is in the place of the center, but at the top, farther from it and moved away from it.
[6] Itaque uti vectis sub onere subiectus, si per medium premitur, durior est neque incumbit, cum autem caput eius summum deducitur, faciliter onus extollit, similiter vela, cum sunt per medium temperata, minorem habent virtutem, quae autem in capite mali summo conlocantur discedentia longius a centro, non acriore sed eodem flatu, pressione cacuminis vehementius cogunt progredi navem. Etiam remi circa scalmos strophis religati, cum manibus inpelluntur et reducuntur, extremis progredientibus a centro parmis maris undis spumam impulsu vehementi protrudunt porrectam navem, secante prora liquoris raritatem.
[6] And so, just as a lever placed under a load, if it is pressed at the middle, is harder and does not bear down; but when its top end is drawn down, it more easily lifts the load—so likewise sails, when they are trimmed through the middle, have less virtue; but those which are set at the very head of the mast, withdrawing farther from the center, not with a sharper but with the same blast, by the pressure of the summit more vehemently force the ship to advance. Also the oars, tied around the thole-pins with loops, when they are driven and drawn back by the hands, as their extremities progress from the center, with their broad blades upon the waves of the sea they thrust the foam forward with vehement impulse, sending the outstretched ship ahead, the prow cutting the thinness of the liquid.
[7] Onerum vero maxima pondera, cum feruntur a phalangariis hexaphoris et tetraphoris, examinantur per ipsa media centra phalangarum, uti in diviso oneris solido pondere certa quadam divisionis ratione aequas partis collis singuli ferant operarii. Mediae enim partes phalangarum, quibus lora tetraphororum invehuntur, clavis sunt finitae, nec labuntur in unam partem. Cum enim extra finem centri promoventur, premunt eum locum, ad quem propius accesserunt, quemadmodum in statera pondus, cum examine progreditur ad fines ponderationum.
[7] But the greatest weights of burdens, when they are carried by phalangarii in hexaphores and tetraphors, are balanced through the very middle centers of the phalanxes, so that, in the divided solid weight of the load, by a certain method of division, the necks of the individual workers may bear equal parts. For the middle parts of the phalanxes, on which the straps of the tetraphors are set, are limited by pins, and do not slip to one side. For when they are moved beyond the boundary of the center, they press upon that spot to which they have approached more closely, just as in a steelyard the weight, when the index-beam (examen) advances, tends toward the extremes of the graduations.
[8] Eadem ratione iumenta, cum iuga eorum subiugiis loris per medium temperantur, aequaliter trahunt onera. Cum autem inpares sunt eorum virtutes et unum plus valendo premit alterum, loro traiecto fit una pars iugi longior, quae inbecilliori auxiliatur iumento. Ita in phalangis et iugis cum in medio lora non sunt conlocata sed in una parte, qua progreditur lorum ab medio, unam breviorem,
[8] By the same method the draught-animals, when their yokes are adjusted by the sub-yoke straps through the middle, draw the loads equally. But when their strengths are unequal and the one, by being stronger, bears down the other, by shifting the strap one part of the yoke is made longer, which assists the weaker beast. Thus in the poles and in the yokes, when the straps are not placed in the middle but on one side, namely toward the side to which the strap advances from the middle, it makes one part shorter, and
[9] Quemadmodum vero minores rotae duriores et difficiliores habent motus, sic phalangae et iuga, in quibus partibus habent minora a centro ad capita intervalla, premunt duriter colla, quae autem longiora habent ab eodem centro spatia, levant oneribus et trahentes et ferentes. Cum haec ita ad centrum porrectionibus et circinationibus reciperent motos, tunc vero etiam plostra, raedae, tympana, rotae, cocleae, scorpionis, ballistae, prela ceteraeque machinae isdem rationibus per porrectum centrum et rotationem circini versantum faciunt ad propositum effectus.
[9] And just as smaller wheels have tougher and more difficult motions, so the phalanges and yokes, in those parts in which they have shorter intervals from the center to the ends, press the necks hard; but those which have longer spans from the same center lighten the burdens for both pullers and bearers. Since these, thus, by extensions toward the center and by circlings take on motions, then indeed carts, chariots, drums, wheels, screws, the scorpion, ballistae, presses, and the other machines, by the same principles, through the extended center and the rotation of the turning compass, produce effects suited to the intended purpose.
[1] Nunc de organis, quae ad hauriendam aquam inventa sunt, quemadmodum variis generibus conparentur, exponam. Et primum dicam de tympano. Id autem non alte tollit aquam, sed exhaurit expeditissime multitudinem magnam.
[1] Now I will expound about the machines which have been invented for drawing water, how they are prepared in various kinds. And first I will speak about the tympanum. This, however, does not lift the water to a great height, but most expeditiously draws off a great quantity.
An axis, fashioned on the lathe or by the compass, with the ends shod with iron laminae, having around its middle a tympanum made from boards joined together, is set upon posts which have within them, beneath the heads of the axis, iron plates. In the cavity of this tympanum eight transverse boards are inserted, touching the axis and the outer circumvolution of the tympanum, which divide the spaces in the tympanum into equal parts.
[2] Circa frontem eius figuntur tabulae, relictis semipedalibus aperturis ad aquam intra concipiendam Item secundum axem columbaria fiunt excavata in singulis spatiis ex una parte. Id autem cum est navali ratione picatum, hominibus calcantibus versatur et hauriendo per aperturas, quae sunt in frontibus tympani, reddit per columbaria secundum axem supposito labro ligneo habente una secum coniunctum canalem. Ita hortis ad inrigandum vel ad salinas ad temperandum praebetur aquae multitudo.
[2] Around its front boards are fastened, with half‑foot apertures left for the water to be taken in within. Likewise, along the axle columbaria are made, excavated in each compartment on one side. And when it has been pitched in naval fashion, it is revolved by men treading, and, drawing through the apertures which are on the fronts of the drum, it delivers through the columbaria along the axle into a wooden lip placed beneath, which has a channel joined together with it. Thus a multitude of water is furnished to gardens for irrigating, or to salt‑works for tempering.
[3] Sic rota fiet circum axem eadem magnitudine, ut ad altitudinem, quae opus fuerit, convenire possit. Circum extremum latus rotae figentur modioli quadrati pice et cera solidati. Ita cum rota a calcantibus versabitur, modioli pleni ad summum elati rursus ad imum revertentes infundent in castellum ipsi per se quod extulerint.
[3] Thus a wheel will be made around the axle of equal magnitude, so that it can be suited to whatever height may be required. Around the outer side of the wheel there will be fixed square buckets, made solid with pitch and wax. Thus, when the wheel is turned by the treaders, the filled buckets, lifted to the top and returning again to the bottom, will pour into the cistern, of their own accord, what they have raised.
[4] Sin autem magis altis locis erit praebendum, in eiusdem rotae axe involuta duplex ferrea catena demissaque ad imum libramentum conlocabitur, habens situlos pendentes aereos congiales. Ita versatio rotae catenam in axem involvendo efferet situlos in summum, qui
[4] But if it must be supplied in places that are rather higher, a double iron chain, wound upon the axle of the same wheel and let down to the lowest level, will be set in place, having bronze hanging buckets of congius capacity. Thus the turning of the wheel, by winding the chain onto the axle, will carry the buckets up to the top; which,
[1] Fiunt etiam in fluminibus rotae eisdem rationibus, quibus supra scriptum est. Circa earum frontes adfiguntur pinnae, quae, cum percutiuntur ab impetu fluminis, cogunt progredientes versari rotam, et ita modiolis haurentis et in summum referentes sine operarum calcatura ipsius fluminis inpulsu versatae praestant, quod opus est ad usum.
[1] Wheels are also made in rivers by the same methods as have been written above. Around their faces vanes are fastened, which, when they are struck by the impulse of the river, compel the wheel, as they advance, to turn; and thus, with little buckets drawing and carrying to the top, being turned by the very impulse of the river without the treading of laborers, they furnish what work is needed for use.
[2] Eadem ratione etiam versantur hydraletae, in quibus eadem sunt omnia, praeterquam quod in uno capite axis tympanum dentatum est inclusum. Id autem ad perpendiculum conlocatur in cultrum versatur cum rota pariter. Secundum id tympanum maius item dentatum planum est conlocatum, quo continetur.
[2] By the same method the hydraletae are likewise set in motion, in which all things are the same, except that in one end of the axle a toothed drum is enclosed. This, moreover, is set vertically on a pivot and is turned together with the wheel. Next to it a larger, likewise toothed, flat drum is placed, with which it is engaged.
[1] Est autem etiam cocleae ratio, quae magnam vim haurit aquae, sed non tam alte tollit quam rota. Eius autem ratio sic expeditur. Tignum sumitur, cuius tigni quanta rata est pedum longitudo, tanta digitorum expeditur crassitudo.
[1] There is also the principle of the cochlea, which draws a great quantity of water, but does not raise it as high as the wheel. Its method is thus set forth. A beam is taken, and for that beam the fixed ratio is this: as many feet as its length is, so many digits is its thickness prescribed.
It is rounded by the compass. At the ends, with the compass, their circumductions are divided by quarterings and eighthings into eight parts, and those lines are so placed that, the beam being set on a plane, at both ends the lines answer to each other to the level; and as large as the eighth part of the circination of the beam is, so large spaces are cut off in the length. Likewise, the beam being placed level, lines are led from one end to the other end, agreeing to the level.
[2] His ita emendate descriptis sumitur salignea tenuis aut de vitice secta regula, quae uncta liquida pice figitur in primo decusis puncto. Deinde traicitur oblique ad insequentes longitudinis et circumitionis decusis, item ex ordine progrediens singula puncta praetereundo et circum involvendo conlocatur in singulis decusationibus, et ita pervenit et figitur ad eam lineam recedens a primo in octavum punctum, in qua prima pars est eius fixa. Eo modo quantum progreditur oblique spatium et per octo puncta, tantundem et longitudine procedit ad octavum punctum.
[2] With these thus accurately described, a slender willow rule, or a rule cut from a withy, is taken, which, smeared with liquid pitch, is fixed at the first decussation-point. Then it is carried obliquely to the following decussations of the length and of the circuit, likewise proceeding in order, passing over individual points and winding around, it is set at the several decussations; and so it reaches and is fixed at that line, withdrawing from the first to the eighth point, on which its first part is fastened. In this way, as far as it advances obliquely a span and through eight points, by just so much it also proceeds in length to the eighth point.
[3] Ita per id vestigium aliae super alias figuntur unctae pice liquida, et exaggerantur ad id, uti longitudinis octava pars fiat summa crassitudo. Supra eas circumdantur et figuntur tabulae, quae pertegant eam involutionem. Tunc eae tabulae pice saturantur et lamminis ferreis conligantur, ut ab aquae vi ne dissolvantur.
[3] Thus along that vestige others are fixed upon others, smeared with liquid pitch, and they are built up to the point that the total thickness becomes an eighth part of the length. Above them planks are wrapped around and fastened, which cover over that involution. Then those planks are saturated with pitch and are bound together with iron plates, so that by the force of the water they may not be dissolved.
[4] Erectio autem eius ad inclinationem sic erit conlocanda, uti, quemadmodum Pythagoricum trigonum orthogonium describitur, sic id habeat responsum, id est uti dividatur longitudo in partes V, earum trium extollatur caput cocleae; ita erit ab perpendiculo ad imas naris spatium earum partium IIII. Qua ratione autem oporteat id esse, in extremo libro eius forma descripta est in ipso tempore.
[4] Moreover, the erection of it at an inclination shall be arranged thus, that, just as the Pythagorean orthogonal (right-angled) triangle is described, so it may have a correspondence; that is, the length is to be divided into 5 parts, and by 3 of them the head of the screw is to be raised; thus from the perpendicular to the lowest openings the distance will be 4 of those parts. By what method it ought to be, its form is described in the last book in its proper place.
[1] Insequitur nunc de Ctesibica machina, quae in altitudinem aquam educit, monstrare. Ea si ex aere. Cuius in radicibus modioli fiunt gemelli paulum distantes, habentes fistulas furcillae figura similiter cohaerentes, in medium catinum concurrentes.
[1] It follows now to show about the Ctesibian machine, which leads water up into height. If it is of bronze. At the bases of its small cylinder there are made twins a little separated, having pipes, of the figure of a little fork, similarly joining, converging into the middle basin.
[2] Supra catinum paenula ut infundibulum inversum est attemperata et per fibulam cum catino cuneo traiecto continetur, ne vis inflationis aqua eam cogat elevari. Insuper fistula, quae tuba dicitur, coagmentata in altitudine fit erecta. Modioli autem habent infra nares inferiores fistularum asses interpositos supra foramina eorum, quae sunt in fundis.
[2] Above the basin a paenula, adjusted as an inverted funnel, is arranged, and it is held together with the basin by a fibula, a wedge having been passed through, lest the force of inflation by the water compel it to be raised. On top a fistula, which is called the tuba, coagmented to height, is set upright. The modioli, moreover, have below the lower nostrils of the pipes asses interposed above their openings, which are in the bottoms.
[3] Ita de supernis in modiolis emboli masculi torno politi et oleo subacti conclusique regulis et vectibus conmoliuntur. Qui erit aer ibi cum aqua, assibus obturantibus foramina cogent. Extrudent inflando pressionibus per fistularum nares aquam in catinum, e quo recipiens paenula spiritu exprimit per fistulam in altitudinem, et ita ex inferiore loco castello conlocato ad saliendum aqua subministratur.
[3] Thus, from above, in the little casings (modioli), the male plungers (emboli), polished on the lathe and worked with oil, shut in with guides and levers, are set in motion. The air that will be there together with the water, the openings being stopped by the discs (asses), will drive it: by inflating pressures they will extrude the water through the nostrils of the pipes into the basin (catinum), from which the receiving cloak-funnel (paenula) expresses it by the breath through the pipe upward; and thus, with the castellum set in a lower place, water is furnished for leaping (spouting).
[4] Nec tamen haec sola ratio Ctesibii fertur exquisita, sed etiam plures et variis generibus ab eo liquore pressionibus coactae spiritus efferre ab natura mutuatos effectus ostendentur, uti merularum aquae motu voces atqueangubatae, bibentiaque et eadem moventia sigilla ceteraque, quae delectationibus oculorum et aurium usu sensus eblandiantur.
[4] Nor, however, is this the only method of Ctesibius said to be exquisite, but several others too, and of various kinds, by that liquid forced by pressures, are shown to emit air producing effects borrowed from nature, such as the voices of blackbirds by the motion of water and theangubatae, and little figures that drink and, the same, move, and the rest which, by the delights of the eyes and ears in their use, coax the senses.
[5] E quibus quae maxime utilia et necessaria iudicavi selegi, et in priore volumine de horologiis, in hoc de expressionibus aquae dicendum putavi. Reliqua quae non sunt ad necessitatem sed ad deliciarum voluntatem, qui cupidiores erunt eius subtilitatis, ex ipsius Ctesibii commentariis poterunt invenire.
[5] From these I have selected those which I judged most useful and necessary, and in the former volume I thought it right to speak about horologes, in this one about the expressions of water. The remaining things, which pertain not to necessity but to the will for delights, those who are more desirous of that subtlety will be able to find in Ctesibius’s own commentaries.
[1] Dehydraulicis autem, quas habeant ratiocinationes, quam brevissime proximeque attingere potero et scriptura consequi, non praetermittam. De materia conpacta basi, ara in ea ex aere fabricata conlocatur. Supra basim eriguntur regulae dextra ac sinistra scalari forma conpactae, quibus includuntur aerei modioli, fundulis ambulatilibus ex torno subtiliter subactis habentibus fixos in medio ferreos ancones et verticulis cum vectibus coniunctos, pellibusque lanatis involutis.
[1] As for thehydraulic organs, what ratiocinations they have, I will not omit to touch upon as briefly and as closely as I can and to attain by writing. Upon a base of compacted material, an altar fabricated of bronze is set upon it. Above the base there are raised rails on the right and on the left, compacted in ladder-form, within which are enclosed bronze modioli, with little running sockets very finely worked on the lathe, having iron ancones fixed in the middle and joined to little pivots with levers, and wrapped with woolly skins.
[2] Intra aram, quod loci aqua sustinetur, inest pnigeus uti infundibulum inversum, quem subter taxilli alti circiter digitorum ternûm suppositi librant spatium imum una inter labra pnigeos et arae fundum. Supra autem cervicula eius coagmentata arcula sustinet caput machinae, qui graececanon musicus appellatur. In cuius longitudine canales, si tetrachordos est, fiunt quattuor, si hexachordos, sex, si octochordos, octo.
[2] Inside the altar, in that place where water is held, there is the pnigeus, like an inverted funnel; beneath which little blocks about three fingers high, set underneath, keep level the lowest gap uniformly between the lips of the pnigeus and the bottom of the altar. Above, moreover, a small little box, jointed onto its little neck, supports the head of the machine, which in Greek is called thecanon musicus. Along its length the channels are made: if it is tetrachord, four; if hexachord, six; if octachord, eight.
[3] Singulis autem canalibus singula epitonia sunt inclusa, manubriis ferreis conlocata. Quae manubria, cum torquentur, ex arca patefaciunt nares in canales. Ex canalibus autem canon habet ordinata in transverso foramina respondentia naribus, quae sunt in tabula summa, quae tabula graecepinax dicitur.
[3] In the individual channels, individual epitonia are enclosed, furnished with iron handles. Which handles, when they are twisted, open from the chest the “nostrils” into the channels. Moreover, from the channels the canon has foramina arranged transversely, corresponding to the nostrils, which are in the top board, which board in Greek is calledpinax.
[4] Haec regulae habent ferrea choragia fixa et iuncta cum pinnis, quarum pinnarum tactus motiones efficit regularum continenter. Supra tabulam foramina quae ex canalibus habent egressum spiritus. Sunt anuli adglutinati, quibus lingulae omnium includuntur organorum.
[4] These sliders have iron gearings fixed and joined with vanes, the touch of which vanes continuously effects motions of the sliders. Above the board are the holes which have the egress of the breath from the channels. There are annuli glued on, by which the little tongues of all the organ-pipes are enclosed.
And from the little hubs (modioli) there are connecting pipes joined to the necks of the pnigeis and reaching to the nostrils, which are in the little chest (arcula). In these there are asses, turned on the lathe and set there, which, when the little chest receives breath, by stopping up the holes do not allow the spirit/air to return back.
[5] Ita cum vectes extolluntur, ancones deducunt fundos modiolorum ad imum delphinique, qui sunt in verticulis inclusi, calantes in eos cymbala, aere implent spatia modiolorum, atque ancones extollentes fundos intra modiolos vehementi pulsus crebritate et obturantes foramina cymbalis superiora, aera, qui est ibi clusus, pressionibus coactum in fistulas cogunt, per quas in pnigea concurrit et per eius cervices in arcam. Motione vero vectium vehementiore spiritus frequens compressus epitoniorum aperturis influit et replet animae canales.
[5] Thus, when the levers are lifted up, the ancones draw down the bottoms of the modioli to the lowest point, and the dolphins, which are enclosed in the little pivots, letting the cymbals drop into them, fill with air the spaces of the modioli; and the ancones, raising the bottoms within the modioli with a vehement frequency of strokes and stopping the upper openings with the cymbals, force the air, which is shut in there, constrained by pressures, into the tubes, through which it runs together into the pnigea and through its necks into the little chest. But with a more vigorous motion of the levers the frequent breath, compressed, flows in through the apertures of the epitonia and fills the channels of the breath.
[6] Itaque cum pinnae manibus tactae propellunt et reducunt continenter regulas alternis opturando foramina alternis aperiundo, e musicis artibus multiplicibus modulorum varietatibus sonantes excitant voces.
[6] And so, when the keys, touched by the hands, continually propel and draw back the sliders, by turns obturating holes and by turns opening them, they, by the musical arts with manifold varieties of modulations, sounding, arouse voices.
Quantum potui niti, ut obscura res per scripturam dilucide pronuntiaretur, contendi, sed haec non est facilis ratio neque omnibus expedita ad intellegendum praeter eos, qui in his generibus habent exercitationem. Quodsi qui parum intellexerit ex scriptis, cum ipsam rem cognoscet, profecto inveniet curiose et subtiliter omnia ordinata.
As far as I was able to strive, that the obscure matter might be declared clearly through writing, I contended; but this is not an easy method nor ready for understanding to all, except to those who have exercise in these kinds. But if anyone should understand too little from the writings, when he comes to know the thing itself, he will surely find all things arranged carefully and subtly.
[1] Transfertur nunc cogitatio scripturae ad rationem non inutilem sed summa sollertia a maioribus traditam, qua in via raeda sedentes vel mari navigantes scire possimus, quot milia numero itineris fecerimus. Hoc autem erit sic. Rotae, quae erunt in raeda, sint latae per medium diametrum pedum quaternûm [et sextantes], ut, cum finitum locum habeat in se rota ab eoque incipiat progrediens in solo viae facere versationem, perveniendo ad eam finitionem, a qua coeperit versari, certum modum spatii habeat peractum pedes XII s
[1] The thought of the treatise is now transferred to a method not useless but handed down by our elders with the highest skill, by which, sitting in a carriage on the road or sailing on the sea, we may know how many miles in number of the journey we have made. But this will be thus. Let the wheels that will be on the carriage be broad across the middle diameter of 4 feet [and a sixth], so that, since the wheel has within itself a defined limit and, starting from it, as it advances on the surface of the road makes a revolution, by arriving at that boundary from which it began to turn, it will have a fixed measure of distance accomplished: 12 feet and a half.
[2] His ita praeparatis tunc in rotae modiolo ad partem interiorem tympanum stabiliter includatur habens extra frontem suae rutundationis extantem denticulum unum. Insuper autem ad capsum raedae loculamentum firmiter figatur habens tympanum versatile in cultro conlocatum et in axiculo conclusum, in cuius tympani frontem denticuli perficiantur aequaliter divisi numero quadringenti convenientes denticulos tympani inferioris. Praeterea superiori tympano ad latus figatur alter denticulus prominens extra dentes.
[2] With these things thus prepared, then in the wheel’s modiolus (hub), toward the inner side, let a tympanum be securely enclosed, having one denticle projecting beyond the face of its roundness. Moreover, above, to the case of the raeda, let a little compartment be firmly fastened, having a revolving tympanum set on a knife-edge and enclosed on a little axle-pin, on the face of which tympanum let denticles be fashioned, equally divided, in the number four hundred, to meet the denticle of the lower tympanum. Furthermore, on the side of the upper tympanum let another denticle be fixed, projecting beyond the teeth.
[3] Super autem, planum eadem ratione dentatum inclusum in alterum loculamentum conlocetur, convenientibus dentibus denticulo, qui in secundi tympani latere fuerit fixus, in eoque tympano foramina fiant, quantum diurni itineris miliariorum numero cum raeda possit exire. Minus plusve rem nihil inpedit. Et in his foraminibus omnibus calculi rotundi conlocentur, inque eius tympani theca, sive id loculamentum est, fiat foramen unum habens canaliculum, qua calculi, qui in eo tympano inpositi fuerint, cum ad eum locum venerint, in raedae capsum et vas aeneum, quod erit suppositum, singuli cadere possint.
[3] Above, moreover, a flat plate, dentate by the same method, is to be enclosed and placed in another little compartment, its teeth fitting the little tooth which has been fixed on the side of the second drum; and in that drum let holes be made, as many as the number of miles of a day’s journey that can be covered with the carriage. Less or more does not hinder the matter. And in all these holes let round pebbles be placed; and in the case of that drum, or whatever that compartment is, let there be made one hole having a little channel, through which the pebbles that shall have been set upon that drum, when they shall have come to that place, may be able, one by one, to fall into the carriage’s chest and into a brazen vessel which will be set beneath.
[4] Ita cum rota progrediens secum agat tympanum imum et denticulum eius singulis versationibus tympani superioris denticulos inpulsu cogat praeterire, efficiet,
[4] Thus, when the wheel, advancing, carries along with it the lowest drum and its little tooth, with each rotation forces the denticles of the upper drum to pass by with an impulse, it will bring it about,
[5] Navigationibus vero similiter paucis rebus commutatis eadem ratione efficiuntur. Namque traicitur per latera parietum axis habens extra navem prominentia capita, in quae includuntur rotae diametro pedum quaternûm et s
[5] But for navigations likewise, with a few things changed, they are effected by the same method. For an axle is passed through the side-walls, having ends projecting outside the ship, into which are fitted wheels with a diameter of 4.5 feet, having fins affixed around their faces, projecting and touching the water. Likewise, the middle axle in the middle of the ship
[6] Insuper in altero loculamento cum eo confixo inclusum tympanum planum ad eundem modum dentatum, quibus dentibus
[6] Moreover, in another little compartment, fastened together with it, there is enclosed a flat tympanum, toothed in the same way; with these teeth the denticle that is fixed to the side of the tympanum which is set on a knife-edge engages, so that, by driving, with each single revolution a single tooth, it may turn the flat tympanum round in a circle. But in the flat tympanum holes are to be made, in which round calculi will be placed. In the theca of that tympanum, or if it is a little compartment, let one hole be hollowed out having a little channel, by which a calculus, once freed from the obstruction, when it has fallen into a bronze vessel, may indicate the sound.
[7] Ita navis cum habuerit impetum aut remorum aut ventorum flatu, pinnae, quae erunt in rotis, tangentes aquam adversam vehementi retrorsus inpulsu coactae versabunt rotas; eae autem involvendo se agent axem, axis vero tympanum, cuius dens circumactus singulis versationibus singulos secundi tympani dentes inpellendo modicas efficit circuitiones. Ita cum CCCC ab pinnis rotae fuerint versatae, semel tympanum circumactum inpellet dente, qui est ad latus fixus, plani tympani dentem. Igitur circuitio tympani plani quotienscumque ad foramen perducet calculos, emittet per canaliculum.
[7] Thus, when the ship has an impulse either from the oars or from the blast of the winds, the fins/vanes that will be on the wheels, touching the opposing water, compelled by a vehement backward push, will turn the wheels; and these, by rolling themselves, will drive the axle, and the axle in turn the drum, whose tooth, carried around, by each single turning driving single teeth of the second drum, produces modest circuits. Thus, when 400 turns by the fins of the wheel have been made, once the rotated drum will, with the tooth which is fixed at the side, strike the tooth of the flat drum. Therefore the revolution of the flat drum, as often as it shall bring the little stones to the opening, will send them out through the little channel.
[1] Nunc vera quae ad praesidia periculi et necessitatem salutis sunt inventa, id est scorpionum et ballistarum rationes, quibus symmetriis comparari possint, exponam.
[1] Now the true things which have been found for protections against danger and the necessity of safety, that is, the designs of scorpions and ballistae, and by what symmetries they can be assembled, I will expound.
[2] Eorum foraminum capituli deformatur altitudo et latitudo. Tabulae, quae sunt in summo et in imo capituli, peritreta quae vocantur, fiant crassitudine unius foraminis, latitudine unius et eius dodrantis, in extremis foraminis unius et eius 
, a foramine ad medianam parastaticam item foraminis . Latitudo parastados mediae unius foraminis et eius 
, crassitudo foraminus unius.
[2] The height and breadth of the head-piece’s holes are shaped. The boards which are on the top and on the bottom of the head-piece, called peritreta, should be made with a thickness of one hole, a width of one and its three-quarters, and at the extremities of one and its , and from the hole to the middle parastatica likewise a hole . The breadth of the middle parastasis is one hole and its , the thickness of the holes one.
[3] Intervallum, ubi sagitta conlocatur in media parastade, foraminis partis quartae. Anguli quattuor, qui sunt circa, in lateribus et frontibus lamnis ferreis aut stylis aereis et clavis configantur. Canaliculi, qui graecesyrinx dicitur, longitudo foraminum XVIIII.
[3] The interval, where the arrow is placed in the middle parastade, is one fourth of a foramen. The four corners, which are around, on the sides and on the fronts, should be fastened with iron plates or bronze pins and nails. The little channel, which in Greek is calledsyrinx, has a length of 19 foramina.
. Suculae longitudo foraminum 
, crassitudo suculae foraminis VIIII.
Of the rules (which some call cheeks), which are fastened to the channel on the right and on the left, <length> of 19 holes, the height of one hole and the thickness. And two rules are affixed, into which the windlass is inserted, having a length of 3 holes, a width of half a hole. The thickness of the cheek which is affixed (it is called a camillum or, as some, a compartment), fixed with safety-latched hinges, of 1 hole, the height of the hole . The windlass’s length of holes , the thickness of the windlass of 9 holes.
[4] Epitoxidos longitudo foraminis, crassitudo 
. Item chelonii. Chelae, sive manucla dicitur, longitudo foraminum trium, latitudo et crassitudo 
. Canalis fundi longitudo foraminis XVI, crassitudo foraminis 
, altitudo . Columellae basis in solo foraminum VIII, latitudo in plinthide, in qua statuitur columella, foraminis 
crassitudo 
, columellae longitudo ad cardinem foraminum XII, latitudo foraminis crassitudo 
. Eius capreoli tres, quorum longitudo foraminum VIIII, latitudo dimidium foraminis, crassitudo 
. Cardinis longitudinis foraminis; columellae capitis longitudo 
; antefixa latitudo foraminis 
, crassitudo I.
[4] The epitoxis’s length is of a hole, the thickness . Likewise for the chelone. The chela, or it is called the manicle, has a length of 3 holes, the width and thickness . The channel’s bottom has a length of 16 holes, a thickness of a hole , a height . The base of the columella on the ground is of 8 holes; the width on the plinth, on which the columella is set, of a hole thickness ; the columella’s length up to the hinge is of 12 holes, width of a hole thickness . Its capreoles 3, whose length is of 9 holes, width half of a hole, thickness . The hinge’s length is of a hole; the length of the head of the columella ; the antefix’s width of a hole , thickness 1.
[5] Posterior minor columna, quae graece diciturantibasis, foraminum VIII, latitudo foraminis 
, crassitudinis . Subiecto foraminum XII, latitudinis et crassitudinis eiusdem, cuius minor columna illa. Supra minorem columnam chelonium, sive pulvinus dicitur, foraminum II s<emissisque>, altitudinis II s<emissisque>, latitudinis 
. Cherolabae sucularum foraminum II , crassitudo foraminis 
, latitudo I s<emissisque>. Transversariis cum cardinibus longitudo foraminum , latitudo I s<emissisque> et crassitudo. Bracchi<i> longitudo [ I s<emissisque> ] foraminum VII, crassitudo ab radice foraminis , in summo foraminis 
; curvaturae foraminis VIII.
[5] The posterior lesser column, which in Greek is called theantibasis, of 8 holes, with a width of and a thickness of . The substructure of 12 holes, of the same width and thickness as that lesser column. Above the lesser column a chelonium, or it is called a cushion, of 2 and a half holes, with a height of 2 and a half, with a width of . The cherolabae of the suculae of 2 holes, thickness of , width 1 and a half. With the crosspieces together with the hinges, a length of holes, a width of 1 and a half, and thickness. Bracchi length [ 1 and a half ] of 7 holes, thickness from the root of , at the top of ; of the curvature 8 holes.
[6] Haec his proportionibus aut adiectionibus aut detractionibus comparantur. Nam si capitula altiora, quam erit latitudo, facta fuerint, quae anatona dicuntur, de bracchiis demetur, ut, quo mollior est tonus propter altitudinem capituli, bracchii brevitas faciat plagam vehementiorem.
[6] These are adjusted by these proportions, either by additions or by subtractions. For if the head-pieces are made higher than their breadth will be, which are called anatona, something will be taken off from the arms, so that, because the tone is softer on account of the height of the head-piece, the shortness of the arm may make the stroke more vehement.
[1] Catapultarum rationes, e quibus membris ex portionibus conponantur, dixi. Ballistarum autem rationes variae sunt et differentes unius effectus causa conparatae. Aliae enim vectibus suculis, nonnullae polyspastis, aliae ergastis, quaedam etiam tympanorum torquentur rationibus.
[1] I have spoken of the principles of catapults, from what members they are composed in their proportions. But the principles of ballistas are various and different, contrived for the sake of a single effect. For some are worked by levers and windlasses, some by polyspasts, others by winches, and certain even are turned by the methods of drums.
[2] Nam quae fiunt in capitibus foramina, per quorum spatia contenduntur capillo maxime muliebri vel nervo funes, magnitudine ponderis lapidis, quem debet ea ballista mittere, ex ratione gravitatis proportione sumuntur, quemadmodum catapultis de longitudinibus sagittarum. Itaque ut etiam qui geometrice non noverunt, habeant expeditum, ne in periculo bellico cogitationibus detineantur, quae ipse faciundo certa cognovi quaeque ex parte accepta praeceptoribus, finita exponam, et quibus rebus Graecorum pensiones ad modulos habeant rationem, ad eam ut etiam nostris ponderibus respondeant, tradam explicata.
[2] For the holes that are made in the heads, through whose spaces the cords—made of hair, most especially womanly, or of sinew—are stretched, are taken by proportion from the magnitude of the weight of the stone which that ballista ought to send, just as for catapults they are taken from the lengths of the arrows. And so, that even those who do not know geometrically may have it ready, lest in the peril of war they be detained by deliberations, I will set forth the determinate points which I myself have ascertained as certain by doing, and which in part I have received from preceptors, and, having explained them, I will hand down how the Greeks’ assessments according to modules have a rationale, so that they may also correspond to our weights.
[3] Nam quae ballista duo pondo saxum mittere debet, foramen erit in eius capitulo digitorum V; si pondo IIII, digitorum sex, VI, digitorum VII; decem pondo digitorum VIII; viginti pondo digitorum X; XL pondo digitorum XII s
; LX pondo digitorum XIII et digiti octava parte; LXXX pondo digitorum XV; CXX pondo I pedis et sesquidigiti; C et LX pedis 
; C et LXXX pe<di>s et digiti V; CC pondo pedis et digitorum VI; CC et X pedis et digitorum VI; CCCLX, pedis I s<emissisque>.
[3] For a ballista that ought to hurl a stone of 2 pounds, the opening in its head will be 5 fingers; if of 4 pounds, 6 fingers; 6, 7 fingers; 10 pounds, 8 fingers; 20 pounds, 10 fingers; 40 pounds, 12 and a half fingers s; 60 pounds, 13 fingers and the eighth part of a finger; 80 pounds, 15 fingers; 120 pounds, 1 foot and a digit-and-a-half; 160, of a foot ; 180 pe<di>s and 5 fingers; 200 pounds, of a foot and 6 fingers; 210 pedis and 6 fingers; 360, of 1 foot s<emissisque>.
[4] Cum ergo foraminis magnitudo fuerit instituta, describatur scutula, quae graeceperitretos appellatur, cuius longitudo foraminum VIII, latitudo duo et sextae partis. Dividatur medium lineae discriptae et, cum divisum erit, contrahantur extremae partes eius formae, ut obliquam deformationem habeat longitudinis sexta parte, latitudinis, ubi est versura, quartam partem. In qua parte autem est curvatura, in quibus procurrunt cacumina angulorum, et foramina convertuntur, et contractura latitudinis redeat introrsus sexta parte, foramen autem oblongius sit tanto, quantam epizygis habet crassitudinem.
[4] Therefore, when the magnitude of the hole has been established, let a plate be delineated, which in Greek is calledperitretos, whose length is 8 hole-diameters, its width two and a sixth. Let the middle of the described figure be divided by a line, and, when it has been divided, let the end parts of that form be contracted, so that it may have an oblique deformation by a sixth part of the length, and, of the width—where the turning is—a fourth part. Moreover, in that part where the curvature is, where the tips of the angles run forward, and the holes are turned, let the contraction of the width go back inward by a sixth part; and let the hole be more oblong by as much as the epizygis has in thickness.
[5] Crassitudo eius foraminis
constituatur. Modioli foraminum duo, latitudo 
, crassitudo praeterquam quod in foramine inditur foraminis 
, ad extremum autem latitudo foraminis 
. Parastatarum longitudo foraminis 
; curvatura foraminis pars dimidia; crassitudo foraminis 
et partis LX. Adicitur autem ad mediam latitudinem, quantum est prope foramen factum in descriptione, latitudine et crassitudine foraminis V, altitudo parte IIII.
[5] Let the thickness of that aperture be established at. Of the hub, two holes; breadth ; thickness, except for what is inserted into the hole, of the hole ; but at the end the breadth of the hole . Of the parastatae, the length of the hole ; the curvature of the hole a half part; the thickness of the hole and a 60th part. Moreover, there is added to the middle breadth, as much as is made near the hole in the description, the breadth and thickness of the hole 5, the height by the 4th part.
[6] Regulae, quae est in mensa, longitudo foraminum VIII; latitudo et crassitudo dimidium foraminis. Cardines
, crassitudo foraminis 
. Curvatura regulae 
. Exterioris regulae latitudo et crassitudo tantundem; longitudo, quam dederit ipsa versura deformationis et parastaticae latitudo ad suam curvaturam . Superiores autem regulae aequales erunt inferioribus . Mensae transversarii foraminis 
.
[6] The rule, which is on the table: length 8 of the hole-units; width and thickness half of the hole. Pivots, thickness of the hole . Curvature of the rule . Of the outer rule, the width and thickness are the same; the length, as the very turning of the deformation shall have given, and the width of the parastatic to its own curvature . Moreover, the upper rules will be equal to the lower . The table’s transverse member: of the hole .
[7] Climacidos scapi longitudo foraminum XIII, crassitudo I, intervallûm mediûm latitudo foraminis et parte quarta, crassitudo pars VIII . Climacidos superioris pars quae est proxima bracchiis, quae coniuncta est mensae, tota longitudine dividatur in partes V. Ex his dentur duae partes ei membro, quod Graeci chelen vocant latitudo 
, crassitudo 
, longitudo foraminum III et semis<sis> ; extantia cheles foraminis s<emissisque> pterygomatos foraminis 
et sicilicus. Quod autem est ad axona, quod appellatur frons transversarius, foraminum trium.
[7] The length of the shafts of the climacides is 13 openings; thickness 1; the middle interval has the width of an opening and a quarter part, thickness one-eighth . The part of the upper climacis which is nearest to the arms, which is joined to the table, is to be divided through its whole length into 5 parts. Of these, let two parts be given to the member which the Greeks call chelen width , thickness , length 3 openings and a half et semis<sis> ; the projection of the chele [is] of an opening s<emissisque>; of the pterygoma, of an opening and a sicilicus. But what is toward the axones, which is called the transverse front, [is] of three openings.
[8] Interiorum regularum latitudo foraminis
, crassitudo 
. Cheloni replum, quod est operimentum, securiculae includitur scapo climacidos latitudo 
crassitudo foraminis XII . Crassitudo quadrati, quod est ad climacida, foraminis 
, in extremis , rutundi autem axis diametros aequaliter erit cheles, ad claviculas autem minus parte sexta decuma .
[8] The width of the inner rules is of the hole, the thickness . The replum of the chelon, which is the covering, is enclosed for the little-axe to the shaft of the ladder: width , thickness of the hole 12 . The thickness of the square, which is at the ladder, is of the hole , at the extremities ; but the diameter of the round axle will be equal to the cheles, and at the little-keys it will be less by the sixteenth part .
[9] Anteridon longitudo foraminum IIII s, in summo crassitudo . Basis, quae appelatur eschara, longitudo foraminum 
, antibasis foraminum IIII, utriusque crassitudo et latitudo foraminis 
. Conpingitur autem dimidia altitudinis columna, latitudo et crassitudo I s<emissque>. Altitudo autem non habet foraminis proportionem, sed erit quod opus erit ad usum. Bracchii longitudo foraminum VI, crassitudo in radice foraminis, in extremis 
.
[9] The length of the anterides is 4 and a half in holes, the width at the bottom is in holes, at the top the thickness is . The base, which is called the eschara, has a length of in holes; the antibase 4 in holes; the thickness and the width of each are in holes. A column of half the height is fitted on; its width and thickness are 1 and a half. The height, however, does not have the proportion of the hole, but will be whatever is needed for use. The length of the arm is 6 in holes; the thickness at the root is of a hole, at the extremities .
[1] Sumuntur tigna amplissima longitudine; supra figuntur chelonia, in quibus cluduntur suculae. Per media autem spatia tignorum insecantur exciduntur formae, in quibus excisionibus cluduntur capitula catapultarum, cuneisque distinentur, ne in contentionibus moveantur. Tum vero modioli aerei in ea capitula includuntur et in eos cuneoli ferrei, quasepizygidas Graeci vocant, conlocantur.
[1] Very long beams are taken; above, tortoises are fastened, in which sows are enclosed. Through the middle spaces of the beams, openings are incised and hewn out, and in these cut-outs the heads of the catapults are enclosed and are braced with wedges, lest they be moved under tensions. Then indeed bronze hubs are inserted into those heads, and into them little iron wedgelets, which the Greeks callepizygidas, are set.
[2] Deinde ansae rudentum induntur per foramina capitulorum, in alteram partem traiciuntur, deinde in suculas coiciuntur involvuntur, uti vectibus per eas ext
[2] Then the loops of the ropes are inserted through the foramina of the head-pieces, passed across to the other side, then cast onto and wound around the windlasses, so that, the ropes stretched through them by levers, when they are touched with the hands, they may have an equal sound in response on both sides. Then they are secured at the foramina with wedges, so that they cannot relax. Thus, carried across to the other side, by the same method they are stretched by levers over the windlasses until they sound equally.
[1] Primum ad oppugnationis aries sic inventus memoratur esse. Carthaginienses ad Gadis oppugnandas castra posuerunt. Cum autem castellum ante cepissent, id demoliri sunt conati.
[1] First, the battering ram for siege is recounted to have been invented in this way. The Carthaginians pitched camp to besiege Gades. But when they had earlier captured a small fort, they tried to demolish it.
[2] Postea quidam faber Tyrius nomine Pephrasmenos hac ratione et inventione inductus malo statuto ex eo alterum transversum uti trutinam suspendit et in reducendo et inpellendo vementibus plagis deiecit Gaditanorum murum. Ceras autem Carchedonius de materia primum basim subiectis rotis fecit supraque compegit arrectariis et iugis varas et in his suspendit arietem coriisque bubulis texit, uti tutiore essent, qui in ea machinatione ad pulsandum murum essent conlocati. Id autem, quod tardos conatus habuerat, testudinem arietariam appellare coepit.
[2] Afterwards a certain Tyrian craftsman named Pephrasmenos, induced by this method and invention, with a mast set up suspended from it another beam crosswise like a steelyard-balance, and by drawing it back and driving it forward with vehement blows he cast down the wall of the Gaditanians. But Ceras the Carthaginian made first out of timber a base with wheels placed underneath, and above he fastened together uprights and, with yokes, forked timbers, and in these he suspended the ram; and he covered it with bulls’ hides, so that those who were stationed in that machination for pounding the wall might be safer. And because it had slow efforts, he began to call it a ramming tortoise.
[3] His tunc primis gradibus positis ad id genus machinationis, postea cum Philippus, Amyntae filius, Byzantios oppugnaret, Polydios Thettalos pluribus generibus et facilioribus explicavit, a quo receperunt doctrinam Diades et Charias, qui cum Alexandro militaverunt.
[3] With these first steps then having been set toward that kind of machination, afterwards, when Philip, son of Amyntas, was assaulting the Byzantines, Polydius the Thessalian unfolded more numerous and more facile kinds; from him Diades and Charias, who served with Alexander, received the doctrine.
Therefore Diades, in his writings, shows that he discovered ambulatory towers, which he was even accustomed to carry about disassembled in the army; besides, the drill, and an ascending machine by which passage to the wall could be made with level foot, and also the demolishing corvus, which some call a crane.
[4] Non minus utebatur ariete subrotato, cuius rationes scriptas reliquit. Turrem autem minimam ait oportere fieri ne minus altam cubitorum LX, latitudinem XVII, contracturam autem summam imae partis quintam, arrectaria in turris in imo dodrantalia in summo semipedalia. Fieri autem ait oportere eam turrem tabulatorum decem, singulis partibus in ea fenestratis.
[4] He used likewise a wheeled battering-ram, of which he left written specifications. Moreover, he says that the smallest tower ought to be made not less than 60 cubits in height, 17 in breadth, and that the top should be contracted to a fifth of the lower part; the uprights of the tower at the bottom three-quarter-foot, at the top half-foot. He says, furthermore, that that tower ought to be made of 10 stories, with each part in it provided with windows.
[5] Maiorem vero turrem altam cubitorum CXX, latam cubitorum XXIII
[5] But a larger tower he made 120 cubits high, 23 and a half cubits wide, the taper likewise by a fifth part, the uprights a foot thick at the bottom, at the top six digits. This size of tower he made of 20 floors, each floor having a circuit-walk of 3 cubits. He covered it with raw hides, so that they might be safe from every stroke.
[6] Testudinis arietariae comparatio eadem ratione perficiebatur. Habuerat autem intervallum XXXII, altitudinem praeter fastigium XVI, fastigii autem altitudo ab strato ad summum cubita XVI. Exibat autem in altum et supra medium tectum fastigium non minus cubita duo, et supra extollebatur turricula cubitorum quattuor tabulatorum III, quo tabulato summo statuebantur scorpionis et catapultae, inferioribus congerebatur aquae magna multitudo ad extinguendum, si qua vis ignis inmitteretur.
[6] The preparation of the battering‑ram tortoise was accomplished by the same method. It had a span of 32, a height, apart from the gable, of 16, and the height of the gable from the paved floor to the top was 16 cubits. Moreover, the gable rose up on high and above the middle roof by not less than 2 cubits, and above there was raised a little turret of 4 cubits with 3 stories, on the topmost of which scorpions and catapults were set, while on the lower ones a great multitude of water was heaped up for extinguishing, if any force of fire should be sent in.
Moreover, upon it there was set up a battering-ram machine, which in Greek is called criodocis, in which a torus, perfected on the lathe, was placed; upon this, set above, the ram, by the leadings and re-leadings of ropes, produced great effects of the work. And it was covered with raw hides, just like the tower.
[7] De terebra has explicuit scriptis rationes. Ipsam machinam uti testudinem in medio habentem conlocatum in orthostatis canalem, quemadmodum in catapultis aut ballistis fieri solet, longitudine cubitorum L, altitudine cubiti, in quo constituebatur transversa sucula. In capite autem dextra ac sinistra trocleae duae, per quas movebatur quod inerat in eo canali capite ferrato tignum.
[7] About the drill he has explained these rationales in writings. The machine itself, having like a tortoise in the middle a channel set upon orthostats, as is wont to be made in catapults or ballistae, of a length of 50 cubits, of a height of 1 cubit, in which there was set a transverse windlass. At the head, moreover, on the right and on the left, two pulleys, through which the beam with an iron head that was within that channel was moved.
Under it, moreover, within the very channel, enclosed torsion-bundles, set at close intervals, made its motions swifter and more vehement. Above, moreover, upon the beam which was therein, arches were laid over to the channel at close intervals, so that they might support the raw hide with which that machine was wrapped.
[8] De corace nihil putavit scribendum, quod animadverteret eam machinam nullam habere virtutem. De accessu, quaeepibathra graece dicitur, et de marinis machinationibus, quae per navium aditus habere posset, scripsit tantum; pollicitum esse vehementer animadverti neque rationes eorum eum explicavisse.
[8] Concerning the corax he thought nothing should be written, because he observed that that machine had no efficacy. About the “approach,” which in Greek is calledepibathra, and about marine machinations which might have an entry by way of ships, he wrote only this much; I noticed that he had strongly promised, and that he did not explain their rationales.
[1] Testudo, quae ad congestionem fossarum paratur (eaque etiam accessus ad murum potest habere), sic erit facienda. Basis compingatur, quae graeceeschara dicitur, quadrata habens quoque versus latera singula pedum XXI et transversaria IIII. Haec autem contineantur ab alteris duobus crassi<tudini>s I s<emissisque>, lati<tudini>s s<emissisque>; distent autem transversaria inter se circiter pedes III s<emissemque>. Supponanturque in singulis intervallis eorum arbusculae, quae graece amaxopodes dicuntur, in quibus versantur rotarum axes conclusi lamnis ferreis.
[1] The testudo, which is prepared for the heaping-up of ditches (and it can also have an access to the wall), will be made thus. Let a base be fastened together, which in Greek is called aneschara, square, having on each side 21 feet, and with 4 crosspieces. And let these be held by two others of a thickness of 1 and a half feet, and a width of half a foot; and let the crosspieces be set apart from one another about 3 and a half feet. And in each of their intervals let little saplings be set underneath, which in Greek are called amaxopodes, in which the axles of the wheels turn, enclosed with iron plates.
And let those uprights be so adjusted as to have pivots and apertures, through which levers passed may expedite their rotations, so that, whether forward and back, or to the right or left side, or, if need be, obliquely toward the angles, by turning the uprights they may be able to advance accordingly.
[2] Conlocentur autem insuper basim tigna duo in utramque partem proiecta pedes senos, quorum circa proiecturas figantur altera proiecta duo tigna ante frontes pedes XII, crassa et lata uti in basi sunt scripta. Insuper hanc conpactionem exigantur postes compactiles praeter cardines pedum VIIII, crassitudine quoquoversus palmopedales, intervalla habentes inter se sesquipedes. Ea concludantur superne intercardinatis trabibus.
[2] Moreover, let two beams be placed above the base, projecting six feet to either side; around the projections of these, let two other beams, likewise projecting, be fastened in front, 12 feet, thick and broad as they are prescribed in the base. Above this compaction let jointable uprights be set up beside the pivots to 9 feet, with thickness in every direction of a palm‑and‑foot, having intervals between them of one‑and‑a‑half feet. Let them be closed in above with beams set between the pivots.
[3] Ipsi autem laterariis circa fixis contineantur teganturque tabulis maxime prinis, si non, ex cetera materia, quae maxime habere potest virtutem, praeter pinum aut alnum; haec enim sunt fragilia et faciliter recipiunt ignem. Circum tabulata conlocentur crates ex tenuibus virgis creberrime textae maximeque recentibus. Percrudis coriis duplicibus consutis, fartis alga aut paleis in aceto maceratis, circa tegatur machina tota.
[3] And they themselves, with side-boards fixed around, should be held together and covered with boards, chiefly of holm-oak; if not, from other material which can most possess strength, except pine or alder; for these are fragile and readily receive fire. Around the boarding let hurdles be placed, woven very closely from slender twigs and especially fresh ones. With very raw hides sewn double, stuffed with seaweed or straw soaked in vinegar, let the whole machine be covered around.
[1] Est autem et aliud genus testudinis, quod reliqua omnia habet, quemadmodum quae supra scripta sunt, praeter capreolos, sed habet circa pluteum et pinnas ex tabulis et superne subgrundas proclinatas, supraque tabulis et coriis firmiter fixis continentur. Insuper vero argilla cum capillo subacta ad eam crassitudinem inducatur, ut ignis omnino non possit ei machinae nocere. Possunt autem, si opus fuerit, eae machinae ex VIII rotis esse, sed ad loci naturam ita opus fuerit temperare.
[1] Moreover, there is another kind of testudo, which has all the rest just as those written above, except for the capreoli; but it has around the pluteus and pinnae made of boards, and above, slanted subgrundae; and on top they are held together by boards and hides firmly fastened. In addition, argilla worked with hair is to be applied to such a thickness that fire cannot at all harm that machine. They can also, if there is need, be of 8 wheels, but one must in this way adjust to the nature of the place.
But the tortoises for digging are prepared (they are called orynges in Greek); they have all the other features, as written above, but their fronts are made like the angles of triangles, so that, when missiles are sent at them from the wall, they do not receive the blows on flat fronts, but with them slipping off from the sides, and those inside, while digging, look out without danger.
[2] Non mihi etiam videtur esse alienum de testudine, quam Hagetor Byzantius fecit, quibus rationibus sit facta, exponere. Fuerat enim eius baseos longitudo pedum LX, latitudo XIII. Arrectaria, quae supra compactionem erant quattuor conlocata, ex binis tignis fuerant compacta, in altitudinibus singulo pedum XXXVI, crassitudine palmopedali, latitudine sesquipedali.
[2] Nor does it seem foreign to me to set forth about the tortoise which Hagetor the Byzantine made, by what methods it was fashioned. For the length of its base was 60 feet, the breadth 13. The uprights (arrectaria), which were four placed above the compaction, had been constructed from pairs of beams, each 36 feet in height, of a foot-and-a-palm in thickness, and a foot-and-a-half in width.
[3] Eae in arbusculis, sive amaxopodes dicuntur, habuerant versationes. Ita supra transtrorum planitiem, quae supra basim fuerat, postes erant erecti pedes XVIII
, latitudine , crassitudine , distantes inter se I . Supra eos trabes circumclusae continebant totam compactionem latae pede I 
, crassae . Supra eam capreoli extollebantur altitudine pedum XII; supra capreolos tignum conlocatum coniungebat capreolorum compactiones. Item fixa habuerant lateraria in transverso, quibus insuper contabulatio circumdata contegebat inferiora.
[3] On little uprights, or as they are called amaxopodes (“wagon-feet”), they had turnings. Thus, above the plane of the thwarts, which was above the base, posts were erected 18 feet, in width , in thickness , spaced from one another 1 . Above them, enclosing beams contained the whole compagination, 1 foot broad , and thick. Above that, rafters were raised to a height of 12 feet; above the rafters a beam set in place joined the compaginations of the rafters. Likewise they had lateral pieces fixed transversely, by which, above, a contabulation laid around covered the lower parts.
[4] Habuerat autem mediam contabulationem supra trabiculas, ubi scorpiones et catapultae conlocabantur. Et erigebantur arrectaria duo compacta pedum XXXXV, crassitudine sesquipedali, latitudine
, coniuncta capitibus transversario cardinato tigno et altero mediano inter duos scapos cardinato et lamnis ferreis religato. Quo insuper conlocata erat alternis materies inter scapos et transversarium traiecta e chelonîs et anconibus firmiiter inclusa.
[4] It had, moreover, a middle decking above the little beams, where scorpions and catapults were placed. And two upright-frames, assembled, 45 feet in height, a sesquipedalian (one-and-a-half-foot) thickness, and a width of, were raised, joined at their heads by a transversary, a hinged beam, and by another median one, hinged between the two shafts and bound with iron plates. Upon this, in addition, timbering was set, in alternating fashion run between the shafts and the transversary, and firmly enclosed with chelonîs and ancones.
[5] Supra caput eorum, qui continebant arietem, conlocatum erat pluteum turriculae similitudine ornatum, uti sine periculo duo milites tuto stantes prospicere possent et renuntiare, quas res adversarii conarentur. Aries autem eius habuerat longitudinem pedum CIV, latitudine in imo palmopedali, crassitudine pedali, contractum capite in latitudine pes crassitudine
.
[5] Above the heads of those who were holding the battering-ram, there had been placed a mantelet adorned in the likeness of a little turret, so that, without danger, two soldiers, standing safely, might be able to look out and report what things the adversaries were attempting. The ram moreover had had a length of 104 feet, with a width at the base of a palm-and-foot, a thickness of 1 foot, tapered at the head to a width of 1 foot, a thickness.
[6] Is autem aries habuerat de ferro duro rostrum, ita uti naves longae solent habere, et ex ipso rostro lamminae ferreae IIII circiter pedum XV fixae fuerant in materia. A capite autem ad imam calcem tigni contenti fuerunt funes III crassitudine digitorum VIII, ita relegati, quemadmodum navis a puppi ad proram continentur, eique funes praecinctura e transversis erant religati habentes inter se palmipedalia spatia. Insuper coriis crudis totus aries erat involutus.
[6] This battering-ram had had a rostrum of hard iron, just as long ships are accustomed to have, and from that very rostrum 4 iron laminae, about 15 feet long, had been fastened into the timber. From the head, moreover, to the lowest heel of the beam, there were 3 ropes, of a thickness of 8 fingers, held taut, thus belayed, as a ship is braced from stern to prow; and to these ropes a praecincture of crosspieces had been tied, having palmipedal spaces between them. On top of this the whole ram was wrapped in raw hides.
[7] Item habuerat protectura eius ex tabulis arcam conpactam et confÌxam, in qua rete rudentibus maioribus extentis, per quarum asperitates non labentibus pedibus, faciliter ad murum perveniebatur. Atque ea machina sex modis movebatur: progresso, item latere dextra et sinistra, porrectiones non minus in altitudinem extollebantur et in imum inclinatione dimittebantur. Erigebatur autem machina in altitudinem ad disiciendum murum circiter p
pondo.
[7] Likewise it had its protecture from planks, a coffer compacted and fastened with nails, in which a net, with larger ropes stretched out, by the roughnesses of which, the feet not slipping, one could easily arrive at the wall. And that machine was moved in six modes: by advancing, likewise to the right and left flank; the projections were raised into height and were sent down to the bottom by inclination. Moreover, the machine was erected in height for the breaking up of the wall to about p pounds.
[1] De scorpionibus et catapultis et ballistis etiamque testudinibus et turribus, quae maxime mihi videbantur idonea et a quibus essent inventa et quemadmodum fieri deberent, explicui. Scalarum autem et carchesiorum et eorum, quorum rationes sunt inbecilliores, non necesse habui scribere. Haec etiam milites per se solent facere.
[1] Concerning scorpions and catapults and ballistae and also tortoises and towers, which seemed to me most suitable, and by whom they were invented and how they ought to be made, I have explained. But about ladders and carchesia, and those whose contrivances are weaker, I have not had the necessity to write. These too the soldiers are accustomed to make by themselves.
[2] Itaque his praescriptionibus si qui adtendere voluerit ex varietate eorum eligendo in unam conparationem conferre, non indigebit auxiliis, sed quascumque res ex rationibus aut locis opus fuerit, sine dubitatione poterit explicare. De repugnatoriis vero non est scriptis explicandum. Non enirn ad nostra scripta hostes conparant res oppugnatorias, sed machinationes eorum ex tempore sollerti consiliorum celeritate sine machinis saepius evertuntur.
[2] Therefore, with these prescriptions, if anyone shall have wished to attend, by choosing from their variety and bringing them together into one comparison, he will not need assistance; but whatever things from the rationales or the locales there is need of, he will be able without hesitation to explicate. As for repugnatorial matters, it is not to be explicated in writings. For the enemies do not prepare oppugnatory resources according to our writings, but their machinations, ex tempore, by the ingenious rapidity of counsels, are more often overthrown without machines.
[3] Diognetus enim fuerat Rhodius architectus, et ei de publico quotannis certa merces pro arti tribuebatur ad honorem. Eo tempore quidam architectus ab Arado nomine Callias Rhodum cum venisset, acroasin fecit exemplaque protulit muri et supra id machinam in carchesio versatili constituit, qua helepolim ad moenia adcedentem corripuit et transtulit intra murum. Hoc exemplar Rhodii cum vidissent, admirati ademerunt Diogneto, quod fuerat quotannis constitutum, et eum honorem ad Calliam transtulerunt.
[3] For Diognetus had been a Rhodian architect, and from the public treasury a fixed wage was allotted to him each year for his art as an honor. At that time a certain architect from Arados, by name Callias, when he had come to Rhodes, gave a lecture and produced models of a wall, and above it he set a machine on a revolving carchesium, with which he seized the helepolis as it was approaching the walls and transported it within the wall. When the Rhodians saw this model, admiring it, they took away from Diognetus what had been established annually, and transferred that honor to Callias.
[4] Interea rex Demetrius, qui propter animi pertinaciam Poliorcetes est appellatus, contra Rhodum bellum conparando Epimachum Atheniensem nobilem architectum secum adduxit. Is autem comparavit helepolim sumptibus inmanibus industria laboreque summo, cuius altitudo fuerat p
[4] Meanwhile King Demetrius, who on account of pertinacity of spirit is called Poliorcetes, while preparing war against Rhodes brought with him Epimachus the Athenian, a noble architect. He, moreover, constructed the Helepolis at enormous expense and with the highest industry and labor, whose height was 125 feet, its width 60 feet. He so reinforced it with cilicia (haircloths) and raw hides that it could endure the stroke of a stone hurled by a ballista to a range of 360 feet; but the machine itself weighed 360,000 pounds. But when Callias was asked by the Rhodians to prepare a machine against that Helepolis, so that he might transfer it within the wall as he had promised, he said that it could not be done.
[5] Non enim omnia eisdem rationibus agi possunt, sed sunt alia, quae exemplaribus non magnis similiter magna facta habent effectus; alia autem exemplaria non possunt habere, sed per se constituuntur; nonnulla vero sunt, quae in exemplaribus videntur veri similia, cum autem crescere coeperunt, dilabantur. Ut etiam possumus hic animum advertere. Terebratur terebra foramen semidigitale, digitale, sesquidigitale.
[5] For not all things can be conducted by the same rational principles, but there are others which, from not-great exemplars, likewise, when made great, have their effects; others, however, cannot have exemplars, but are constituted on their own; and there are some, indeed, which in the exemplars appear verisimilar, but when they begin to grow, they fall apart. As we can also here turn our mind. A hole is bored by a drill half a digit, a digit, a sesqui-digit.
[6] Sic item in nonnullis exemplaribus videntur, quae ad modum in minimis fieri videntur, atque eodem modo in maioribus. Id eodem modo Rhodii eadem ratione decepti iniuriam cum contumelia Diogneto fecerunt. Itaque posteaquam viderunt hostem pertinaciter infestum, periculum servitutis, machinationem ad capiendam urbem conparatam, vastitatem civitatis expectandam, procubuerunt Diogneto rogantes, ut auxiliaretur patriae.
[6] Thus likewise, in some examples there are seen things which seem to occur, after a fashion, in the very smallest matters, and in the same way in greater ones. In the same way the Rhodians, deceived by the same rationale, did an injury with contumely to Diognetus. And so, after they saw the enemy stubbornly hostile, the danger of servitude, a machination prepared for taking the city, the devastation of the civitas to be expected, they prostrated themselves before Diognetus, begging that he would bring aid to the fatherland.
[7] Is primo negavit se facturum. Posteaquam ingenuae virgines et ephebi cum sacerdotibus venerunt ad deprecandum, tunc est pollicitus his legibus, uti, si eam machinam cepisset, sua esset. Is ita constitutis, qua machina accessura erat, ea regione murum pertudit et iussit omnes publice et privatim quod quisque habuisset aquae, stercoris, luti per eam fenestram per canales progredientes effundere ante murum.
[7] He at first denied that he would do it. After the freeborn virgins and the ephebes came with the priests to entreat, then he promised on these terms, that if he should seize that machine, it would be his own. With these terms thus established, in the region where the machine was going to approach, he pierced the wall and ordered everyone, publicly and privately, whatever each had of water, dung, mud, to pour it out in front of the wall through that window, proceeding through channels.
When there a great mass of water, mud, and dung had been poured out by night, on the next day the helepolis, approaching, before it came near to the wall, settled in the wet, a quagmire having been made, and thereafter could neither advance nor get out. Therefore Demetrius, when he saw that he had been deceived by the wisdom of Diognetus, departed with his fleet.
[8] Tunc Rhodii Diogneti sollertia liberati bello publice gratias egerunt honoribusque omnibus eum et ornamentis exornaverunt. Diognetus eam helepolim reduxit in urbem et in publico conlocavit et inscripsit 'Diognetus e manubiis id populo dedit munus'. Ita in repugnatoriis rebus non tantum machinae, sed etiam maxime consilia sunt comparanda.
[8] Then the Rhodians, liberated from the war by the ingenuity of Diognetus, gave public thanks and adorned him with all honors and ornaments. Diognetus led that helepolis back into the city and placed it in a public place and inscribed, 'Diognetus, from the spoils, gave this gift to the people.' Thus in defensive matters, not only machines, but most of all counsels are to be provided.
[9] Non minus Chio cum supra naves sambucarum machinas hostes conparavissent, noctu Chii terram, harenam, lapides progresserunt in mare ante murum. Ita illi postero die cum accedere voluissent, naves supra aggerationem, quae fuerat sub aqua, sederunt nec ad murum accedere nec retrorsus se recipere potuerunt, sed ibi malleolis confixae incendio sunt conflagratae. Apollonia quoque cum circumsederetur et specus hostes fodiendo cogitarent sine suspicione intra moenia penetrare, id autem a speculatoribus esset Apolloniatibus renuntiatum, perturbati nuntio propter timorem consiliis indigentes animis deficiebant, quod neque tempus neque certum locum scire poterant, quo emersum facturi fuissent hostes.
[9] No less at Chios, when the enemies had prepared sambuca-machines upon their ships, by night the Chians pushed out earth, sand, and stones into the sea before the wall. Thus, the next day, when they wished to approach, the ships settled upon the embankment which had been under water, and they could neither approach the wall nor retreat backward, but there, transfixed with fire-darts, they were consumed in a conflagration. Apollonia too, when it was being besieged and the enemies, by digging a tunnel, were planning to penetrate within the walls without suspicion, but this had been reported by the scouts to the Apolloniates; disturbed by the message, through fear, lacking counsels, their spirits were failing, because they could know neither the time nor the certain place at which the enemies were going to make their emergence.
[10] Tum vero Trypho Alexandrinus ibi fuerat architectus; intra murum plures specus designavit et fodiendo terram progrediebatur extra murum dumtaxat extra sagittae missionem et in omnibus vasa aenea suspendit. Ex his in una fossura, quae contra hostium specus fuerat, vasa pendentia ad plagas ferramentorum sonare coeperunt. Ita ex eo intellectum est, qua regione adversarii specus agentes intra penetrare cogitabant, Sic liniatione cognita temperavit aenea aquae ferventis et picis de superne contra capita hostium et stercoris humani et harenae coctae candentis.
[10] Then indeed Trypho the Alexandrian had been the architect there; within the wall he marked out several tunnels and, by digging the earth, advanced beyond the wall, only beyond the range of an arrow, and in all of them he hung up bronze vessels. From these, in one trench, which was opposite the enemies’ tunnel, the hanging vessels began to sound at the blows of the iron tools. Thus from that it was understood in what region the adversaries, driving their tunnel, were thinking to penetrate within. So, the lineation having been ascertained, he prepared bronze [vessels] of boiling water and of pitch to be poured from above against the heads of the enemy, and likewise of human dung and of baked, glowing-white sand.
[11] Item Massilia cum oppugnaretur et numero supra XXX speculatum agerent, Massilitani suspicati totam quae fuerat ante murum fossam altiore fossura depresserunt. Ita specus omnes exitus in fossam habuerunt. Quibus autem locis fossa non potuerat fieri, intra murum barathrum amplissima longitudine et amplitudine uti piscinam fecerunt contra eum locum, qua specus agebantur, eamque e puteis et e portu impleverunt.
[11] Likewise, when Massilia was being assaulted and, in a number exceeding 30, they were carrying on tunneling for reconnaissance, the Massilians, suspecting it, lowered the entire ditch which had been before the wall by a deeper digging. Thus all the galleries had their outlets into the ditch. But in those places where a ditch could not be made, within the wall they made a barathrum, of very great length and amplitude, like a piscina, opposite the place where the galleries were being driven, and they filled it from wells and from the harbor.
[12] Etiam cum agger ad murum contra eos conpararetur et arboribus excisis eoque conlocatis locus operibus exaggeraretur, ballistis vectes ferreos candentes in id mittendo totam munitionem coegerunt conflagrare. Testudo autem arietaria cum ad murum pulsandum accessisset, permiserunt laqueum et eo ariete constricto, per tympanum ergata circumagentes suspenso capite eius non sunt passi tangi murum. Denique totam machinam malleolis candentibus et ballistarum plagis dissipaverunt.
[12] Even when an agger up to the wall was being prepared against them, and, the trees having been cut down and set there, the place was being heaped up with works, by sending with the ballistae incandescent iron bars into it they compelled the whole fortification to conflagrate. Moreover, when the battering-ram testudo had come up to pound the wall, they let down a noose, and, the ram having been constricted by it, by a windlass-drum (tympanum) turning it round, with its head lifted they did not allow the wall to be touched. Finally, they shattered the entire machine with glowing malleoli (fire-darts) and with the blows of the ballistae.