Vitruvius: DE ARCHITECTVRA

[1] Nobilibus athletis, qui Olympia, Isthmia, Nemea vicissent, Graecorum maiores ita magnos honores constituerunt, uti non modo in conventu stantes cum palma et corona ferant laudes, sed etiam, cum revertantur in suas civitates cum victoria, triumphantes quadrigis in moenia et in patrias invehantur e reque publica perpetua vita constitutis vetigalibus fruantur. Cum ergo id animadvertam, admiror, quid ita non scriptoribus eidem honores etiamque maiores sint tributi, qui infinitas utilitates aevo perpetuo omnibus gentibus praestant. Id enim magis erat institui dignum, quod athletae sua corpora exercitationibus efficiunt fortiora, scriptores non solum suos sensus, sed etiam omnium, libris ad discendum et animos exacuendos praeparant praecepta.

[1] To noble athletes who had conquered at Olympia, the Isthmia, and the Nemea, the ancestors of the Greeks established such great honors, that not only, standing in the assembly with palm and crown, they should bear praises, but also, when they return into their own cities with victory, triumphing, they should be conveyed by quadrigas (four-horse chariots) into the walls and into their fatherlands, and should enjoy from the commonwealth a perpetual maintenance, with revenues established. Therefore, when I observe this, I marvel why the same honors, and even greater, have not been allotted to writers, who furnish infinite utilities to all nations for an everlasting age. For that was more worthy to be instituted, because athletes render their bodies stronger by exercises, whereas writers prepare books precepts for learning and for sharpening minds, not only their own senses but also those of all.

[2] Quid enim Milo Crotoniates, quod fuit invictus, prodest hominibus aut ceteri, qui eo genere fuerunt victores, nisi quod, dum vixerunt ipsi, inter suos cives habuerunt nobilitatem. Pythagorae vero praecepta, Democriti, Platonis, Aristotelis ceterorumque sapientium cotidiana perpetuis industriis culta non solum suis civibus, sed etiam omnibus gentibus recentes et floridos edunt fructus. E quibus qui a teneris aetatibus doctrinarum abundantia satiantur, optimos habent sapientae sensus, instituunt civitatibus humanitatis mores, aequa iura, leges, quibus absentibus nulla potest esse civitas incolumis.

[2] For what, indeed, does Milo of Croton, because he was undefeated, profit humankind, or the others who were victors in that kind, except that, while they themselves lived, they possessed renown among their own fellow citizens? But the precepts of Pythagoras, Democritus, Plato, Aristotle, and the rest of the wise, cultivated daily by perpetual industry, yield fresh and flourishing fruits not only to their own citizens but to all nations. Of these fruits, those who from tender ages are satiated by an abundance of doctrines have the best senses of sapience; they institute for commonwealths the mores of humanity, equal rights, laws—these being absent, no commonwealth can be intact.

[3] Cum ergo tanta munera ab scriptorum prudentia privatim publiceque fuerint hominibus praeparata, non solum arbitror palmas et coronas his tribui oportere, sed etiam decerni triumphos et inter deorum sedes eos dedicando iudicari.

[3] Since therefore such great munera from the prudence of writers have been prepared for men both privately and publicly, I judge that not only should palms and crowns be bestowed upon them, but even triumphs decreed, and that, by dedicating them among the seats of the gods, they be adjudged.

Eorum autem cogitata utiliter hominibus ad vitam explicandam e pluribus singula paucorum uti exempla ponam, quae recognoscentes necessario his tribui honores oportere homines confitebuntur.

Moreover, of their thoughts, useful to human beings for explaining life, from among the many I will set forth single examples of a few; and, recognizing these, men will necessarily confess that honors ought to be bestowed upon them.

[4] Et primum Platonis e multis ratiocinationibus utilissimis unam, quemadmodum ab eo explicata sit, ponam. Locus aut ager paribus lateribus si erit quadratus eumque oportuerit duplicare, quod opus fuerit genere numeri, quod multiplicationibus non invenitur, eo descriptionibus linearum emendatis reperitur. Est autem eius rei haec demonstratio.

[4] And first, from the many most useful ratiocinations of Plato I will set forth one, just as it was explained by him. If a place or field with equal sides shall be squared and it should be necessary to double it, the task, which belongs to the genus of number and is not discovered by multiplications, is discovered by corrected delineations of lines. But the demonstration of this matter is this.

Quadratus locus, qui erit longus et latus pedes denos, efficit areae pedes C. Si ergo opus fuerit eum duplicare, pedum CC, item e paribus lateribus facere, quaerendum erit, quam magnum latus eius quadrati fiat, ut ex eo CC pedes duplicationibus areae respondeant. Id autem numero nemo potest invenire. Namque si XIIII constituentur, erunt multiplicati pedes CXCVI, si XV, pedes CCXXV.

A square plot, which will be long and broad 10 feet, yields an area of 100 square feet. If therefore there is need to double it—to 200 feet—and likewise to make it with equal sides, it will have to be inquired how large the side of that square should be, so that from it 200 feet may answer to the duplication of the area. But no one can find that by number. For if 14 be set down, the multiplied feet are 196; if 15, 225 feet.

[5] Ergo quoniam id non explicatur numero, in eo quadrato, longo et lato pedes X quod fuerit, linea ab angulo ad angulum diagonios perducatur, uti dividantur duo trigona aequa magnitudine, singula area pedum quinquagenûm, ad eiusque lineae diagonalis longitudinem locus quadratus paribus lateribus describatur. Ita quam magna duo trigona in minores quadrato quinquagenûm pedum linea diagonio fuerint designata, eadem magnitudine et eodem pedum numero quattuor in maiore erunt effecta. Hac ratione duplicatio grammicis rationibus ab Platone, uti schema subscriptum est, explicata est in ima pagina.

[5] Therefore, since that is not explained by number, in that square which is ten feet long and wide, let a line be drawn from corner to corner, the diagonal, so that two triangles of equal magnitude may be divided, each with an area of fifty feet; and to the length of that diagonal line let a square with equal sides be described. Thus, as large as the two triangles in the smaller square of fifty feet were designated by the diagonal line, of the same magnitude and the same number of feet four will have been produced in the larger. By this method the duplication was explained by Plato with grammic (geometric) reasonings, as the schema written below is, at the bottom of the page.

[6] Item Pythagoras normam sine artificis fabricationibus inventam ostendit, et quam magno labore fabri normam facientes vix ad verum perducere possunt, id rationibus et methodis emendatum ex eius praeceptis explicatur. Namque si sumantur regulae tres, e quibus una sit pedes III, altera pedes IIII, tertia pedes V, eaeque regulae inter se compositae tangant alia aliam suis cacuminibus extremis schema habentes trigoni, deformabunt normam emendatam. Ad eas autem regularum singularum longitudines si singula quadrata paribus lateribus describantur, cum erit trium latus, areae habebit pedes VIIII, quod IIII, XVI quod V erit, XXV.

[6] Likewise Pythagoras showed a square (right-angle rule) discovered without the fabrications of a craftsman, and that which workmen, making a square with great labor, can scarcely bring to truth, is explained, corrected by reasons and methods, from his precepts. For if three rulers are taken, of which one is 3 feet, another 4 feet, a third 5 feet, and these rulers, fitted together so that each touches the other with their extreme tips, having the schema of a triangle, will fashion a corrected square. But to those several lengths of the individual rulers, if individual squares with equal sides are described: when the side is of 3, the area will have 9 feet; that of 4, 16; that of 5 will be 25.

[7] Ita quantum areae pedum numerum duo quadrata ex tribus pedibus longitudinis laterum et quattuor efficiunt, aeque tantum numerum reddidit unum ex quinque descriptum. Id Pythagoras cum invenisset, non dubitans a Musis se in ea inventione monitum, maximas gratias agens hostias dicitur his immolavisse. Ea autem ratio, quemadmodum in multis rebus et mensuris est utilis, etiam in aedificiis scalarum aedificationibus, uti temperatas habeant graduum librationis, est expedita.

[7] Thus, as many square-feet of area as the two squares with side-lengths of 3 feet and 4 produce, the single one described on 5 returned an equal number. When Pythagoras had discovered this, not doubting that he had been admonished by the Muses in that invention, giving the greatest thanks he is said to have sacrificed victims to them. Moreover, this ratio, just as it is useful in many matters and measures, is also readily applied in buildings, in the constructions of stairways, so that they may have a tempered libration of the steps.

[8] Si enim altitudo contignationis ab summa coaxatione ad imum libramentum divisa fuerit in partes tres, erit earum quinque in scalis scaporum iusta longitudine inclinatio. Quam magnae fuerint inter contignationem et imum libramentum altitudinis partes tres, quattuor a perpendiculo recedant et ibi conlocentur inferiores calces scaporum. Ita sic erunt temperatae; et graduum ipsarum scalarum erunt conlocationes.

[8] For if the height of the story, from the highest coagmentation down to the lowest level, be divided into three parts, the inclination in the stairs will be five of those parts, with the stringers of just length. However great the three parts of height between the flooring and the lowest level shall be, let four recede from the perpendicular, and there let the lower heels of the stringers be placed. Thus they will be well-tempered; and the placements of the steps themselves of the stairs will be arranged.

Item eius rei erit subscripta forma.

Likewise, there will be a subjoined form of this matter.

[9] Archimedis vero cum multa miranda inventa et varia fuerint, ex omnibus etiam infinita sollertia id, quod exponam, videtur esse expressum. Nimium Hiero enim Syracusis auctus regia potestate, rebus bene gestis cum auream coronam votivam diis inmortalibus in quodam fano constituisset ponendam, manupretio locavit faciendam et aurum ad sacomam adpendit redemptori. Is ad tempus opus manu factum subtiliter regi adprobavit et ad sacomam pondus coronae visus est praestitisse.

[9] But although the inventions of Archimedes were many, wondrous, and diverse, among them all, even with infinite cleverness, that which I will set forth seems to have been expressed. For Hiero at Syracuse, being greatly advanced in royal power, after successful affairs, when he had determined that a golden votive crown should be set up for the immortal gods in a certain fane, he let it out to contract for a set price and weighed out the gold to the contractor on the scale. He, at the appointed time, presented to the king the work made by hand, finely, and to the scale he seemed to have made good the weight of the crown.

[10] Posteaquam indicium est factum dempto auro tantundem argenti in id coronarium opus admixtum esse, indignatus Hiero se contemptum esse neque inveniens, qua ratione id furtum reprehenderet, rogavit Archimeden, uti in se sumeret sibi de eo cogitationem. Tunc is, cum haberet eius rei curam, casu venit in balineum, ibique cum in solium descenderet, animadvertit, quantum corporis sui in eo insideret, tantum aquae extra solium effluere. Itaque cum eius rei rationem explicationis ostendisset, non est moratus, sed exiluit gaudio motus de solio et nudus vadens domum verius significabat clara voce invenisse, quod quaereret; nam currens identidem graece clamabat:

[10] After evidence had been made that, with the gold taken off, just so much silver had been mixed into that crown-work, Hiero, indignant that he was being held in contempt and not finding by what method he might apprehend that theft, asked Archimedes to take upon himself the consideration of it. Then he, since he had the care of that matter, by chance came into a bath, and there, when he descended into a tub, he noticed that as much of his body as settled in it, so much water flowed out beyond the tub. And so, when he had shown the rationale of the explanation of that matter, he did not delay, but leapt, moved by joy, out of the tub, and going home naked he was more truly signifying with a clear voice that he had found what he was seeking; for, running again and again, he was shouting in Greek:

[11] Tum vero ex eo inventionis ingressu duas fecisse dicitur massas aequo pondere, quo etiam fuerat corona, unam ex auro et alteram ex argento. Cum ita fecisset, vas amplum ad summa labra implevit aquae, in quo dimisit argenteam massam. Cuius quanta magnitudo in vasum depressa est, tantum aquae effluxit.

[11] Then indeed, from that inception of the discovery he is said to have made two masses of equal weight, with which also the crown had been, one of gold and the other of silver. When he had done thus, he filled a large vessel with water to the very brim, into which he lowered the silver mass. And the amount of its bulk that was pressed into the vessel, just so much water flowed out.

Ita exempta massa quanto minus factum fuerat, refudit sextario mensus, ut eodem modo, quo prius fuerat, ad labra aequaretur. Ita ex eo invenit, quantum ad certum pondus argenti ad certam aquae mensuram responderet.

Thus, the mass having been removed, by as much as it had been made less, he poured back, measured by a sextarius, so that in the same way as it had been before it might be leveled to the brim. Thus from this he discovered how much, for a certain weight of silver, corresponded to a certain measure of water.

[12] Cum id expertus esset, tum auream massam similiter pleno vaso demisit et ea exempta, eadem ratione mensura addita invenit ex aquae numero non tantum esse: minore quanto minus magno corpore eodem pondere auri massa esset quam argenti. Postea vero repleto vaso in eadem aqua ipsa corona demissa invenit plus aquae defluxisse in coronam quam in auream eodem pondere massam, et ita ex eo, quod fuerit plus aquae in corona quam in massa, ratiocinatus reprehendit argenti in auro mittionem et manifestum furtum redemptoris.

[12] When he had tested that, then he likewise lowered a golden mass into the full vessel, and, it being taken out, with a measure added by the same method he found from the number of the water that it was not as much: smaller, inasmuch as the mass of gold, with the same weight, was a body less great than that of silver. Afterwards, indeed, the vessel having been refilled, in the same water, the crown itself being lowered, he found that more water had flowed off for the crown than for a golden mass of the same weight; and thus from the fact that there was more water for the crown than for the mass, by reasoning he detected an admixture of silver in the gold and the manifest theft of the contractor.

[13] Transferatur mens ad Archytae Tarentini et Eratosthenis Cyrenaei cogitata; hi enim multa et grata a mathematicis rebus hominibus invenerunt. Itaque cum in ceteris inventionibus fuerint grati, in eius rei concitationibus maxime sunt suspecti. Alius enim alia ratione explicaverunt, quod Delo imperaverat responsis Apollo, uti arae eius, quantum haberent pedum quadratorum, id duplicarentur, et ita fore uti, qui essent in ea insula, tunc religione liberarentur.

[13] Let the mind be transferred to the thoughts of Archytas the Tarentine and Eratosthenes the Cyrenaean; for these men discovered many and pleasing things for men from mathematical matters. And so, although in their other inventions they were grateful/thankworthy, in the agitations of this affair they are most suspect. For they explained by different reasoning what Apollo had commanded by his responses to Delos: that his altars, to whatever amount they had of square feet, should be doubled—and thus it would come to pass that those who were on that island would then be freed from religious scruple.

[14] Itaque Archytas cylindrorum descriptionibus, Eratosthenes organica mesolabi ratione idem explicaverunt. Cum haec sint tam magnis doctrinarum incunditatibus animadversa et cogamur naturaliter inventionibus singularum rerum considerantes effectus moveri, multas res attendens admiror etiam Democriti de rerum natura volumina et eius commentarium, quo scribiturcheirotometon; in quo etiam utebatur anulo signaturam optice est expertus.

[14] And so Archytas, by descriptions of cylinders, and Eratosthenes, by the organic mesolabe method, explained the same thing. Since these have been observed with so great delights of doctrines, and we are compelled by nature, when considering the effects of the inventions of individual things, to be moved, attending to many matters I also admire the volumes of Democritus On the Nature of Things and his commentary, in which thecheirotometon is written; in which also, employing a ring, he tested a signet optically.

[15] Ergo eorum virorum cogitata non solum ad montes corrigendos, sed etiam ad omnium utilitatem perpetuo sunt praeparata, athletarum autem nobilitates brevi spatio cum suis corporibus senescunt; [itaque neque cum maxime sunt] florentes neque posteritati hi, quemadmodum sapientium cogitata hominum vitae, prodesse possunt.

[15] Therefore the cogitations of those men have been prepared not only for correcting mountains, but also perpetually for the utility of all; but the nobilities (renowns) of athletes in a brief span grow old together with their bodies; [therefore neither when they are at their very peak] flourishing, nor can these benefit posterity, in the way that the cogitations of the wise can benefit the life of men.

[16] Cum vero neque moribus neque institutis scriptorum praestantibus tribuantur honores, ipsae autem per se mentes aeris altiora prospicientes memoriarum gradibus ad caelum elatae aevo inmortali non modo sententias sed etiam figuras eorum posteris cogunt esse notas. Itaque, qui litterarum iucunditatibus instinctas habent mentes, non possunt non in suis pectoribus dedicatum habere, sicuti deorum, sic Enni poetae simulacrum; Acci autem carminibus qui studios delectantur, non modo verborum virtutes sed etiam figuram eius videntur secum habere praesentem esse.

[16] But since honors are granted neither by morals nor by the institutions to preeminent writers, the minds themselves, on their own, looking out to the higher regions of the air, raised to heaven by the steps of memories, in immortal age compel not only their sentences but also their figures to be known to posterity. And so, those who have minds instigated by the delights of letters cannot but have in their own breasts, dedicated, just as the images of the gods, so the simulacrum of the poet Ennius; moreover, those who take studious delight in the poems of Accius seem to have with them present not only the virtues of his words but even his figure.

[17] Item plures post nostram memoriam nascentes cum Lucretio videbuntur velut coram de rerum naturam disputare, de arte vero rhetorica cum Cicerone, multi posterorum cum Varrone conferent sermonem de lingua latina, non minus etiam plures philologi cum Graecorum sapientibus multa deliberantes secretos cum his videbuntur habere sermones, et ad summam sapientium scriptorum sententiae corporibus absentibus vetustate florentes cum insunt inter consilia et disputationes, maiores habent, quam praesentium sunt, auctoritates omnes.

[17] Likewise, many born after our remembrance will seem, as if face-to-face, to dispute with Lucretius about the nature of things; indeed about the rhetorical art with Cicero; many of posterity will confer discourse with Varro on the Latin language; and no less, many philologists, deliberating many matters with the wise men of the Greeks, will seem to have private conversations with them; and, to sum up, the judgments of wise writers—though their bodies are absent, flourishing by antiquity—when they are present amid counsels and disputations, have, in all respects, authorities greater than those of persons present.

[18] Itaque, Caesar, his auctoribus fretus sensibus eorum adhibitis et consiliis ea volumina conscripsi, et prioribus septem de aedificiis, octavo de aquis, in hoc de gnomonicis rationibus, quemadmodum de radiis solis in mundo sunt per umbras gnomonis inventae quibusque rationibus dilantentur aut contrahantur, explicabo.

[18] Therefore, Caesar, relying on these authors, with their perceptions and counsels employed, I have composed those volumes: the preceding seven on buildings, the eighth on waters; and in this one I will explain the gnomonic methods—how, from the sun’s rays in the world, they have been discovered through the shadows of the gnomon, and by what principles they are dilated or contracted.

Caput Primum

Chapter One

[1] Ea autem sunt divina mente comparata habentque admirationem magnam considerantibus, quod umbra gnomonis aequinoctialis alia magnitudine est Athenis, alia Alexandriae, alia Romae, non eadem Placentiae ceterisque orbis terrarum locis. Itaque longe aliter distant descriptionis horologiorum locorum mutationibus. Umbrarum enim aequinoctialium magnitudinibus designantur analemmatorum formae, e quibus perficiuntur ad rationem locorum et umbrae gnomonum horarum descriptiones.

[1] These things, moreover, are arranged by a divine mind and arouse great admiration in those who consider them, namely that the equinoctial shadow of the gnomon is of one magnitude at Athens, another at Alexandria, another at Rome, not the same at Placentia and in the other places of the orb of lands. Therefore the descriptions of horologes vary greatly with changes of location. For by the magnitudes of the equinoctial shadows the forms of the analemmata are delineated, from which, according to the rationale of the places, both the shadows of the gnomons and the descriptions of the hours are brought to completion.

Analemma est ratio conquisita solis cursu et umbrae crescentis ad brumam observatione inventa, e qua per rationes architectonicas circinique descriptiones est inventus effectus in mundo.

Analemma is a rationale obtained by inquiry from the sun’s course and from observation of the shadow increasing toward the winter solstice, from which, through architectonic reasonings and compass-descriptions, the practical effect has been discovered in the world.

[2] Mundus autem est omnium naturae rerum conceptio summa caelumque sideribus conformatum. Id volvitur continenter circum terram atque mare per axis cardines extremos. Namque in his locis naturalis potestas ita architectata est conlocavitque cardines tamquam centra, unum a terra inmane in summo mundo ac post ipsas stellas septentrionum, alterum trans contra sub terra in meridianis partibus, ibique circum eos cardines orbiculos circum centra uti in torno perfecit, qui graeceapsides nominantur, per quos pervolitat sempiterno caelum.

[2] Moreover, the world is the supreme conception of all the things of nature, and the heaven configured with stars. It revolves continually around the earth and the sea by the extreme pivots of the axis. For in these places the natural power has so architected and has placed the pivots as centers: one at an immense distance from the earth, at the summit of the world and beyond the very stars of the north; the other opposite across, beneath the earth in the southern parts; and there around those pivots it has fashioned little circles around the centers, as on a lathe, which in Greek are calledapsides, through which the heaven flies about everlastingly.

Ita media terra cum mari centri loco naturaliter est conlocata.

Thus the middle earth together with the sea is naturally located in the place of the center.

[3] His natura dispositi ita, uti septentrionali parte a terra excelsius habeat altitudinem centrum, in meridiana autem parte in inferioribus locis subiectum a terra obscureter, tunc etiam per medium transversa et inclinata in meridiem circuli delata zona XII signis et conformata. Quae eorum species stellis dispositis XII partibus peraequatis exprimit depictam ab natura figurationem. Itaque lucentia cum mundo reliquisque sideribus ornatu circum terram mareque pervolantia cursus perficiunt ad caeli rotunditatem.

[3] Arranged by nature in this way: that in the septentrional part the center has a higher elevation from the earth, but in the meridional part, in lower places, it lies set beneath the earth more obscurely; then also, across the middle, a zone borne over the circle and inclined toward the south, fashioned and conformed with 12 signs. The appearance of these—its form with the stars disposed into 12 equalized parts—expresses a figuration painted by nature. And so the shining ones, together with the world and with the remaining stars as ornament, flying around the earth and the sea, complete their courses according to the rotundity of the heaven.

[4] Omnia autem visitata et invisitata temporum necessitate sunt constituta. Ex quis sex signa numero supra terram cum caelo pervagantur, cetera sub terram subeuntia ab eius umbra obscurantur. Sex autem ex his semper supra terram nituntur.

[4] But all things, both visited and unvisited, are constituted by the necessity of times. Of which, six signs in number roam above the earth with the sky; the rest, going down beneath the earth, are obscured by its shadow. Six, moreover, of these are always above the earth.

Quanta pars enim novissimi signi depressione coacta versatione subiacens sub terram occultatur, tantundem eius contraria e conversationis necessitate suppressa rotatione circumacta trans locis patentibus ex obscuris egreditur ad lucem; namque vis una et necessitas utrimque simul orientem et occidentem perficit.

For whatever portion of the last sign, compelled by depression and, lying under the turning, is concealed beneath the earth, just so much of its opposite, by the necessity of the revolution, carried around by a suppressing rotation, passes across the open places and goes out from the obscurities into the light; for one force and necessity on both sides together perfects the Orient and the Occident.

[5] Ea autem signa cum sint numero XII partesque duodecumas singula possideant mundi versenturque ab oriente ad occidentem continenter, tunc per ea signa contrario cursu luna, stella Mercuri, Veneris, ipse sol itemque Martis et Iovis et Saturni ut per graduum ascensionem percurrentes alius alia circuitionis magnitudine ab occidenti ad orientem in mundo pervagantur. Luna die octavo et vicesimo et amplius circiter hora caeli circuitionem percurrens, ex quo signo coeperit ire, ad id signum revertendo perficit lunarem mensem.

[5] Those signs, moreover, since they are in number 12 and each possesses a twelfth part of the world and they revolve continuously from east to west, then through those signs with a contrary course the Moon, the star of Mercury, of Venus, the Sun himself, and likewise of Mars and Jupiter and Saturn, running through by the ascension of degrees, each with a different magnitude of circuition, wander through the world from west to east. The Moon, traversing the circuit of the sky in the eight-and-twentieth day and, in addition, about an hour, from the sign from which she began to go, by returning to that sign completes the lunar month.

[6] Sol autem signi spatium, quod est duodecuma pars mundi, mense vertente vadens transit; ita XII mensibus XII signorum intervalla pervagando cum redit ad id signum, unde coeperit, perficit spatium vertentis anni. Ex eo, quem circulum luna terdecies in XII mensibus percurrit, eum sol eisdem mensibus semel permetitur. Mercuri autem et Veneris stellae circa solis radios uti per centrum eum itineribus coronantes regressus retrorsus et retardatione faciunt, etiam stationibus propter eam circinationem morantur in spatiis signorum.

[6] The Sun, however, advancing as the month turns, crosses the space of a sign, which is the twelfth part of the world; thus, in 12 months, by ranging through the intervals of the 12 signs, when it returns to that sign whence it began, it completes the span of the revolving year. Of that circle which the Moon traverses thirteen times in 12 months, the Sun in those same months passes through it once. But the stars of Mercury and of Venus, around the Sun’s rays, as if crowning him with their journeys through the center, produce retrograde returns and retardation, and, with stations too, on account of that circination, they linger in the spaces of the signs.

[7] Id autem ita esse maxime cognoscitur ex Veneris stella, quod ea, cum solem sequatur, post occasum eius apparens in caelo clarissimeque lucens vesperugo vocitatur, aliis autem temporibus eum antecurrens et oriens ante lucem lucifer appellatur. Ex eoque nonnumquam plures dies in signo commorantur, alias celerius ingrediuntur in alterum signum. Itaque quod non aeque peragunt numerum dierum in singulis signis, quantum sunt moratae prius, transiliendo celerioribus itineribus perficiunt [iustum cursum.

[7] But that this is so is most clearly recognized from the star of Venus, because when it follows the sun, appearing after his setting in the sky and shining most brightly, it is called the evening-star Vesperugo; but at other times, outpacing him and rising before light, it is called the light-bringer, Lucifer. And from this they sometimes stay for more days in a sign, at other times they more swiftly enter into another sign. And so, because they do not equally complete the number of days in individual signs, as much as they have delayed before, by leaping over with speedier journeys they make up [the just course.

Ita efficitur], uti, quod demorentur in nonnullis signis, nihilominus, cum eripiant se ab necessitate morae, celeriter consequantur iustam circumitionem.

Thus it is brought about], that, although they delay in some signs, nevertheless, when they free themselves from the necessity of delay, they swiftly attain the just circuit.

[8] Iter autem in mundo Mercuri stella ita pervolitat, uti trecentesimo et sexagensimo die per signorum spatia currens perveniat ad id signum, ex quo priore circulatione coepit facere cursum, et ita peraequatur eius iter ut circiter tricenos dies in singulis signis habeat numeri rationem.

[8] But the journey in the world of the star of Mercury flies through in such a way that, running through the spaces of the signs, on the 360th day it arrives at that sign from which in the prior circulation it began to make its course, and thus its path is so equalized that it has the reckoning of the number at about thirty days in each sign.

[9] Veneris autem, cum est liberata ab inpeditione radiorum solis, XXX diebus percurrit signi spatium. Quo minus quadragenos dies in singulis signis patitur, cum stationem fecerit, restituit eam summam numeri in uno signo morata. Ergo totam circinationem in caelo quadrigintesimo et octogensimo et quinto die permensa iterum in id signum, ex quo signo prius iter facere coepit.

[9] Venus, however, when she is freed from the impediment of the sun’s rays, runs through the space of a sign in 30 days. Wherefore she undergoes fewer than forty days in individual signs; when she has made a station, by lingering in one sign she restores that total of the count. Therefore, having measured the whole circination in the sky in 485 days, she returns again into that sign from which sign she had previously begun to make the course.

[10] Martis vero circiter sescentesimo octogensimo tertio siderum spatia pervagando pervenit eo, ex quo initium faciendo cursum fecerat ante, et in quibus signis celerius percurrit, cum stationem fecit, explet dierum numeri rationem. Iovis autem placidioribus gradibus scandens contra mundi versationem, circiter CCCLX diebus in singula signa permetitur, et consistit post annum XI et dies CCCXIII et redit in id signum, in quo ante XII annos fuerat. Saturni vero, mensibus undetriginta et amplius paucis diebus pervadens per signi spatium, anno nono et vicensimo et circiter diebus CLX, in quo ante tricensimo fuerat anno, in id restituitur, ex eoque, quo minus ab extremo distat mundo, tanto maiorem circinationem rotae percurrendo tardior videtur esse.

[10] But Mars, by ranging through the spaces of the stars, arrives back at that point from which, having begun, it had made its course before, in about 683 days; and in those signs which it runs through more swiftly, when it has made a station, it fills up the reckoning of the number of days. But Jupiter, ascending with more placid steps against the world’s rotation, is measured through about 360 days in each sign, and it takes its stand after 11 years and 313 days and returns into that sign in which it had been 12 years before. But Saturn, passing through the space of a sign in 29 months and a few days more, is restored, after the 29th year and about 160 days, into that in which it had been in the 30th year before; and from this, the less it is distant from the extreme world, by traversing the greater circination of the wheel, the slower it seems to be.

[11] Ei autem, qui supra solis iter circinationes peragunt, maxime cum in trigono fuerint, quod is inierit, tum non progrediuntur, sed regressus facientes morantur donique cum idem sol de eo trigono in aliud signum transitionem fecerit. Id autem nonnullis sic fieri placet, quod aiunt solem, cum longius absit abstantia quadam, non lucidis itineribus errantia per ea sidera obscuritatis morationibus inpedire. Nobis vero id non videtur.

[11] But those who complete circinations above the sun’s course, especially when they have been in the trigon which he has entered, then do not advance, but, making regressions, they linger, and this until the same sun has made a transition from that trigon into another sign. Some, however, are pleased to have it happen thus, because they say that the sun, when it is farther away, by a certain abstance, through paths not lucid, impedes the wanderers through those stars with delays of obscurity. To us, however, that does not seem so.

Solis enim splendor perspicibilis et patens sine ullis obscurationibus est per omnem mundum, ut etiam nobis appareant, cum facient eae stellae regressus et morationes. Ergo si tantis intervallis nostra species potest id animadvertere, quid ita divinationibus splendoribusque astrorum iudicamus obscuritatis obici posse?

For the sun’s splendor is perspicuous and open without any obscurations through the whole world, so that they even appear to us when those stars perform retrogradations and delays. Therefore, if at such vast intervals our sight can notice this, why then do we judge that obscurity can be cast in the way of the divinations and splendors of the stars?

[12] Ergo potius ea ratio nobis constabit, quod, fervor quemadmodum omnes res evocat et ad se ducit, ut etiam fructus e terra surgentes in altitudinem per calorem videmus, non minus aquae vapores a fontibus ad nubes per arcus excitari, eadem ratione solis impetus vehemens radiis trigoni forma porrectis insequentes stellas ad se perducit et ante currentes veluti refrenando retinendoque non patitur progredi, sed ad se regredi, in alterius trigoni signum esse.

[12] Therefore rather this rationale will stand for us: that, just as fervor calls forth all things and draws them to itself—as we even see fruits rising from the earth into height through heat, and no less the vapors of water are aroused from springs to the clouds along arches—by the same rationale the sun’s vehement impulse, with rays stretched out in triangular form, draws the stars that are following to itself, and those running ahead, as if by reining in and holding back, it does not allow to advance, but to return to itself, to be in the sign of the other triangle.

[13] Fortasse desiderabitur, quid ita sol quinto a se signo potius quam secundo aut tertio, quae sunt propiora, facit in his fervoribus retentiones. Ergo, quemadmodum id fieri videatur, exponam. Eius radii in mundo uti trigoni paribus lateribus formae liniationibus extenduntur.

[13] Perhaps it will be desired to know why the sun rather produces, in these fervors, retentions in the fifth sign from itself than in the second or third, which are nearer. Therefore, how this may seem to occur, I will set forth. Its rays in the world are extended by lineations in the form of a trigon with equal sides.

Id autem nec plus nec minus est ad quintum ab eo signo. Igitur si radii per omnem mundum fusi circinationibus vagarentur neque extentionibus porrecti ad trigoni formam liniarentur, propiora flagrarent. Id autem etiam Euripides, Graecorum poeta, animadvertisse videtur.

But this is exactly at the fifth sign from it. Therefore, if the rays, diffused through the whole world, were to wander by circinations and were not, by extensions stretched forth, delineated to the form of a trigon, the nearer things would blaze. And this too Euripides, a poet of the Greeks, seems to have observed.

Ait enim, quae longius a sole essent, haec vehementius ardere, propiora vero eum temperata habere. Itaque scribit in fabula Phaethonte sic:

For he says that those which were farther from the sun burn more vehemently, while he keeps the nearer ones tempered. And so he writes thus in the fable Phaethon:

[14] Si ergo res et ratio et testimonium poetae veteris id ostendit, non puto aliter oportere iudicari, nisi quemadmodum de ea re supra scriptum habemus.

[14] If therefore the matter and the rationale and the testimony of an ancient poet show this, I do not think it ought to be judged otherwise, except just as we have it written above concerning that matter.

Iovis autem inter Martis et Saturni circinationem currens maiorem quam Mars, minorem quam Saturnus pervolat cursum. Item reliquae stellae, quo maiore absunt spatio ab extremo caelo proxumamque habent terrae circinationem, celerius videntur, quod quaecumque earum minorem circinationem peragens saepius subiens praeterit superiorem.

Jupiter, however, running between the circuit of Mars and of Saturn, flies through a course greater than Mars’s, smaller than Saturn’s. Likewise the remaining stars, the greater the space they are distant from the outermost heaven and the more proximate a circuit to the earth they have, are seen to be swifter, because whichever of them, accomplishing a smaller circuit, by coming up more often, passes by the superior.

[15] Quemadmodum, si in rota, qua figuli utuntur, inpositae fuerint septem formicae canalesque totidem in rota facti sint circum centrum in imo adcrescentes ad extremum, in quibus hae cogantur circinationem facere, verseturque rota in alteram partem, necesse erit eas contra rotae versationem nihil minus adversus itinera perficere, et quae proximum centrum habuerit, celerius pervagari, quaeque extremum orbem rotae peragat, etiamsi aeque celeriter ambulet, propter magnitudinem circinationis multo tardius perficere cursum: similiter astra nitentia contra mundi cursum suis itineribus perficiunt circuitum, sed caeli versatione redundationibus referuntur cotidiana temporis circumlatione.

[15] Just as, if on the wheel which potters use seven ants were placed, and just so many canals were made in the wheel around the center, growing in depth at the bottom toward the edge, in which these are compelled to make a circination, and the wheel were turned in the other direction, it would be necessary that they, against the wheel’s turning, nonetheless complete their journeys in the opposite way; and the one which has the nearest position to the center would range more swiftly, while the one which traverses the outer rim of the wheel, even if it walks equally swiftly, on account of the magnitude of the circination completes its course much more slowly: similarly the shining stars, against the course of the world, perfect their circuit by their own itineraries, but by the turning of the heaven they are borne back by redundations through the daily circumlation of time.

[16] Esse autem alias stellas temperatas, alias ferventes, etiamque frigidas haec esse causa videtur, quod omnis ignis in superiora loca habet scandentem flammam. Ergo sol aethera, qui est supra se, radiis exurens effecit candentem, in quibus locis habet cursum Martis stella; itaque fervens ab ardore solis efficitur. Saturni autem, quod est proxima extremo mundo tangit congelatas caeli regiones; vehementer est frigida.

[16] That there are, moreover, some stars temperate, others fervent, and even cold, this seems to be the cause: that every fire has a flame climbing to the higher places. Therefore the sun, scorching with its rays the aether which is above itself, has made it incandescent, in the regions in which the star of Mars has its course; and thus it is made fervent by the sun’s ardor. But that of Saturn, because it is nearest to the extreme of the world, touches the congealed regions of the sky; it is exceedingly cold.

Ex eo Iovis, cum inter utriusque circuitiones habet cursum, a refrigeratione caloreque eorum medio convenientes temperatissimosque habere videtur effectus.

From this, Jupiter, since he has his course between the circuits of both, seems to have effects most temperate, consonant with the middle between their refrigeration and their heat.

De zona XII signorum et septem astrorum contrario opere ac cursu, quibus rationibus et numeris transeunt e signis in signa, et circuitum eorum, uti a praeceptoribus accepi, exposui; nunc de crescenti lumine lunae deminutioneque, uti traditum est nobis a maioribus, dicam.

Concerning the zone of the 12 signs and the seven stars, with contrary operation and course, by what reasons and numbers they pass from signs into signs, and their circuit, as I received from my preceptors, I have set forth; now of the waxing light of the moon and its diminution, as it has been handed down to us by our ancestors, I will speak.

Caput Secundum

Chapter Two

[1] Berosus, qui ab Chaldaeorum civitate sive natione progressus in Asia etiam disciplinam Chaldaicam patefecit, ita est professus:

[1] Berosus, who, having proceeded from the city or nation of the Chaldaeans, also laid open in Asia the Chaldaean discipline, has thus professed:

Pilam esse ex dimidia parte candentem, reliqua habere caeruleo colore. Cum autem cursum itineris sui peragens subiret sub orbem solis, tunc eam radiis et impetu caloris corripi convertique candentem propter eius proprietatem luminis ad lumen. Cum autem ea vocata ad solis orbem superiora spectent, tunc inferiorem partem eius, quod candens non sit, propter aeris similitudinem obscuram videri.

That the ball is candescent in half its portion, and the remainder has a cerulean color. But when, accomplishing the course of its journey, it goes beneath the orb of the sun, then it is seized by the rays and the impetus of heat and is turned candescent, on account of its property of light, toward the light. But when its upper parts, called toward the orb of the sun, look upward, then its lower part, because it is not candescent, appears dark by reason of its likeness to air.

Cum ad perpendiculum esset ad eius radios, totum lumen ad superiorem speciem retineri, et tunc eam vocari primam.

When it is at the perpendicular to its rays, all the light is retained upon the upper aspect, and then it is called the first.

[2] Cum praeteriens vadat ad orientis caeli partes, relaxari ab impetu solis extremamque eius partem candentiae oppido quam tenui linia ad terram mittere splendorem, et ita ex eo eam secundam vocari. Cotidiana autem versationis remissione tertiam, quartam in dies numerari. Septimo die, sol sit ad occidentem, [luna autem inter orientem et occidentem] medias caeli teneat regiones, quod dimidia parte caeli spatio distaret a sole, item dimidiam candentiae conversam habere ad terram.

[2] As, in passing, it goes to the eastern parts of the sky, it is relaxed from the impulse of the sun, and the outermost part of its candescence sends to the earth a splendor by a very thin line; and thus from this it is called the second. By the daily remission of its revolution the third and the fourth are numbered day by day. On the seventh day, the sun is toward the west, [but the moon, between east and west,] holds the middle regions of the sky, because by half the space of the sky it is distant from the sun; likewise it has half of its candescence turned toward the earth.

Inter solem vero et lunam cum distet totum mundi spatium et lunae orienti sol trans contra sit ad occidentem, eam, quo longius arsit, a radiis remissam XIIII die plena rota totius orbis mittere splendorem, reliquosque dies decrescentia cotidiana ad perfectionem lunaris mensis versationibus et cursu a sole revocationibus subire sub rotam radiosque eius et iam menstruas dierum efficere rationes.

But when the whole space of the world lies between the sun and the moon, and the sun stands over-against the moon’s rising toward the west, then, the farther it has burned, released from the rays, on the 14th day the full wheel of its whole orb sends forth brightness; and for the remaining days, with daily waning, by revolutions and by its course, with withdrawals from the sun, it goes under its disk and rays and now produces the monthly reckonings of the days.

[3] Uti autem Aristarchus Samius mathematicus vigore magno rationes varietatis disciplinis de eadem reliquit, exponam. Non enim latet lunam suum propriumque non habere lumen, sed esse uti speculum et ab solis impetu recipere splendorem. Namque luna de septem astris circulum proximum terrae in cursibus minimum pervagatur.

[3] But since Aristarchus the Samiote, the mathematician, with great vigor left reasonings of the variation in disciplines on the same subject, I will expound them. For it is not hidden that the moon does not have its own proper light, but is as a mirror and receives splendor from the sun’s impetus. For the moon, of the seven stars, wanders through the circle nearest to the earth, the least in its courses.

Ita quot mensibus sub rotam solis radiosque uno die, antequam praeterit, latens obscuratur. Cum est cum sole, nova vocatur. Postero autem die, quo numeratur secunda, praeteriens ab sole visitationem facit tenuem extremae rotundationis.

Thus, every month, beneath the sun’s wheel and rays, for one day, before it passes by, hidden it is darkened. When it is with the sun, it is called new. But on the following day, which is counted the second, passing by from the sun it makes a slight visitation of the extremity of its rotundity.

Cum triduum recessit ab sole, crescit et plus inluminatur. Cotidie vero discendens cum pervenit ad diem septimum, distans a sole occidente circiter medias caeli regiones, dimidia luce, et eius quae ad solem pars spectat, ea est inluminata.

When it has withdrawn from the sun for three days, it grows and is more illuminated. Indeed, descending daily, when it arrives at the seventh day, being distant from the setting sun by about the middle regions of the sky, it is in half-light, and the part of it which looks toward the sun is illuminated.

[4] Quarto autem decumo die, cum in diametro spatio totius mundi absit ab sole, perficitur plena et oritur, cum sol sit ad occidentem, ideo quod totum spatium mundi distans consistit contra et impetu solis totius orbis in se recipit splendorem. Septumo decumo die cum sol oriatur, ea pressa est ad occidentem. Vicensimo et altero die cum sol est exortus, luna tenet circiter caeli medias regiones, et id quod spectat ad solem, id habet lucidum reliquis obscura.

[4] But on the fourteenth day, when at a diameter’s distance across the space of the whole world it is away from the sun, it is perfected full and rises when the sun is at the west, because, with the whole expanse of the world lying between, it stands opposite and receives into itself splendor from the impetus of the sun of the whole orb. On the seventeenth day, when the sun rises, it is pressed toward the west. On the twenty-second day, when the sun has risen, the moon holds about the middle regions of the sky, and that which looks toward the sun, that part it has bright, the rest dark.

Item cotidie cursum faciendo circiter octavo et vicensimo die subit sub radios solis, et ita menstruas perficit rationes.

Likewise, by making its daily course, around the 28th day it goes beneath the rays of the sun, and thus it completes its monthly reckonings.

Nunc, ut in singulis mensibus sol signa pervadens auget et minuit dierum et horarum spatia, dicam.

Now, how in the several months the sun, pervading the signs, increases and diminishes the intervals of days and hours, I will speak.

Caput Tertium

Chapter Three

[1] Namque cum arietis signum iniit et partem octavam pervagatur, perficit aequinoctium vernum. Cum progreditur ad caudam tauri sidusque vergiliarum, e quibus eminet dimidia pars prior tauri, in maius spatium mundi quam dimidium procurrit procedens ad septentrionalem partem. E tauro cum ingreditur in geminos exorientibus vergiliis, magis crescit supra terram et auget spatia dierum.

[1] For when it enters the sign of Aries and roams through the eighth part, it completes the vernal equinox. When it advances to the tail of the Bull and the constellation of the Vergiliae (Pleiades), of which the fore half of the Bull stands out, it runs forward into a greater expanse of the world than a half, proceeding toward the septentrional (northern) part. And from Taurus, when it enters into the Twins with the Vergiliae rising, it grows more above the earth and increases the spans of the days.

Deinde <e> geminis cum iniit ad cancrum, qui brevissimum tenet caeli spatium, cum pervenit in partem octavam, perficit solstitiale tempus, et peragens pervenit ad caput et pectus leonis, quod eae partes cancero sunt attributae.

Then, from Gemini, when it enters into Cancer, which holds the shortest span of the sky, when it reaches the eighth part, it completes the solstitial season; and, completing its course, it comes to the head and breast of the Lion, which parts are attributed to Cancer.

[2] E pectore autem leonis et finibus cancri solis exitus pecurrens reliquas partes leonis inminuit diei magnitudinem et circinationis reditque in geminorum aequalem cursum. Tunc vero a leone transiens in virginem progrediensque ad sinum vestis eius contrahit circinationem et aequat ad eam, quam taurus habet, cursus rationem. E virgine autem progrediens per sinum, qui sinus librae partes habet primas, in librae parte VIII perficit aequinoctium autumnale; qui cursus aequat eam circinationem, quae fuerat in arietis signo.

[2] But from the breast of the Lion and the boundaries of Cancer, the Sun’s egress, running through the remaining parts of the Lion, diminishes the magnitude of the day and of the circination, and returns to the equal course of Gemini. Then indeed, passing from Leo into Virgo and advancing to the fold of her garment, it contracts the circination and equalizes the proportion of the course to that which Taurus has. But from Virgo, proceeding through the fold—which fold has the first parts of Libra—in Libra’s part 8 it completes the autumnal equinox; which course equals that circination which had been in the sign of Aries.

[3] Scorpionem autem cum sol ingressus fuerit occidentibus vergiliis, minuit progrediens meridianas partes longitudines dierum. E scorpione cum percurrendo init in sagittarium ad eius, contractiorem diurnum pervolat cursum. Cum autem incipit a sagittarii, quae pars est attributa capricorno, ad partem octavam, brevissimum caeli percurrit spatium.

[3] However, when the sun has entered Scorpio, with the Vergiliae (Pleiades) setting, as it advances it diminishes the meridian portions, the lengths of the days. From Scorpio, when by running it enters into Sagittarius to its , it speeds through a more contracted diurnal course. But when it begins from the of Sagittarius, which part is attributed to Capricorn, up to the eighth part, it runs through the very shortest space of the sky.

Ex eo a brevitate diurna bruma ac dies brumales appellantur. E capricorno autem transiens in aquarium adauget et aequat sagittarii longitudine diei spatium. Ab aquario cum ingressus est in pisces favonio flante, scorpionis comparat aequalem cursum.

From this, on account of the diurnal brevity, the bruma and the brumal days are so called. But from Capricorn, as he passes into Aquarius, he increases and makes equal the span of the length of day to that of Sagittarius. From Aquarius, when he has entered Pisces with Favonius blowing, he matches an equal course with Scorpio.

Ita sol ea signa circum pervagando certis temporibus auget aut minuit dierum et horarum spatia.

Thus the sun, by roaming around those signs, at fixed times augments or diminishes the spans of days and hours.

Nunc de ceteris sideribus, quae sunt dextra ac sinistra zonam signorum meridiana septentrionalique parte mundi stellis disposita figurataque, dicam.

Now of the other constellations, which are on the right and on the left of the zone of the signs, on the meridional and septentrional part of the world, arranged and figured with stars, I will speak.

Caput Quartum

Chapter Four

[1] Namque septentrio, quem Graeci nominantarctum sive helicen, habet post se conlocatum custodem. Non longe conformata est virgo, cuius supra umerum dextrum lucidissima stella nititur, quam nostri provindemiatorem, Graeci protrugeten vocant; candens autem magis spica eius est colorata. Item alia contra est stella media genuorum custodis arcti: qui arcturus dicitur est ibi delicatus.

[1] For the Septentrion, which the Greeks namearctum or helicen, has a guardian set behind it. Not far off the Virgin is set, above whose right shoulder the brightest star shines, which our people call the Provindemiator, the Greeks protrugeten; but her Spica is more brightly colored. Likewise, opposite, there is another star in the middle of the knees of the guardian of the Arctus: he who is called Arcturus is there distinguished.

[2] E regione capitis septentrionis transversus ad pedes geminorum auriga stat in summo cornu tauri -- itemque in summo cornu laevo et auriga petis una tenet parte stellam -- et appelluntur aurigae manui haedi, capra laevo umero. Tauri quidem et arietis insuper Perseus -- dexterioribus subter currens basem vergiliis, at sinisterioris caput arietis -- et manu dextra innitens Cassipiae simulacro, laeva supra tauri tenet gorgoneum ad summum caput, subiciensque Andromedae pedibus.

[2] Opposite the head of the Septentrion, crosswise toward the feet of the Twins, the Charioteer stands at the top horn of the Bull -- and likewise at the top of the left horn the Charioteer with one part of his foot holds a star -- and at the Charioteer’s hand are called the Kids, the She-goat at the left shoulder. Above the Bull and the Ram is Perseus -- on his right running beneath the base of the Vergiliae, but on his left the head of the Ram -- and with his right hand leaning upon the image of Cassipeia, with his left above the Bull he holds the Gorgoneum at the very top of the head, and sets it under Andromeda’s feet.

[3] Item pisces supra Andromedam, et eius ventris et equi sunt supra spinam aequi, cuius ventris lucidissima stella finit ventrem equi et caput Andromedae. Manus Andromedae dextra supra Cassiopiae simulacrum est constituta, laeva aquilonalem piscem. Item aquarii supra equi capitis est.

[3] Likewise Pisces is above Andromeda, and its belly and the Horse are above the spine of the Horse, the brightest star of whose belly bounds the belly of the Horse and the head of Andromeda. The right hand of Andromeda is set above the simulacrum of Cassiopeia, the left above the northern Fish. Likewise Aquarius is above the head of the Horse.

Equi ungulae attingunt aquarii genua; Cassiopia media est dedicata. Capricorni supra in altitudinem aquila et delphinus. Secundum eos est sagitta.

The Horse’s hooves touch Aquarius’s knees; Cassiopeia is set in the middle. Above Capricorn in altitude are the Eagle and the Dolphin. Next to them is Sagitta (the Arrow).

Ab ea autem volucris, cuius pinna dextra Cephei manum adtingit et sceptrum, laeva supra Cassiopiae innititur. Sub avis cauda pedes equi sunt subtecti.

From that, however, the bird, whose right pinion touches the hand and scepter of Cepheus, leans with the left above Cassiopeia. Under the bird’s tail the horse’s feet are covered.

[4] Inde sagittarii, scorpionis, librae insuper serpens summo rostro coronam tangit. Ad eum medium ophiuchos in manibus tenet serpentem, laevo pede calcans mediam frontem scorpionis. A parte ophiuchi capitis non longe positum est caput eius, qui dicitur nisus in genibus.

[4] Thence, above Sagittarius, Scorpius, and Libra, the Serpent with its topmost snout touches the Crown. At its middle Ophiuchus holds the Serpent in his hands, trampling with his left foot the middle of the Scorpion’s brow. On the side of Ophiuchus’s head, not far off, is set the head of him who is called “striving on the knees.”

Autem eorum faciliores sunt capitum vertices ad cognoscendum, quod non obscuris stellis sunt conformati.

However, the vertices of their heads are easier to recognize, because they are configured not by obscure stars.

[5] Pes ingeniculati ad id fulcitur capitis tempus serpentis, cuius arctorum, qui septentriones dicuntur, inplicatus. Parve per eos flectitur delphinus; contra volucris rostrum proposita lyra. Inter umeros custodis et geniculati corona est ordinata.

[5] The foot of the Kneeler is braced against the temple of the Serpent’s head, which is entwined about the Bears, who are called the Septentriones. A little way near them the Dolphin is bent; opposite the bird’s beak the Lyre is set forth. Between the shoulders of the Guardian and the Kneeler a Crown is arrayed.

In septentrionali vero circulo duae positae sunt arctoe scapularum dorsis inter se compositae et pectoribus aversae. E quibus minor cynosura, maior helice a Graecis appellatur. Earumque capita inter se dispicientia sunt constituta, caudae capitibus earum adversae contra dispositae figurantur; utrarumque enim superando eminent.

In the northern circle, indeed, two Bears are placed, joined to each other by the backs of their shoulder-blades and turned away at the breasts. Of these the lesser is called Cynosura, the greater Helice by the Greeks. And their heads are set looking away from one another; their tails are depicted as arranged opposite to their heads; for by overpassing they stand out above both.

[6] In summo per caudas earum esse dicitur. Item serpens est porrecta, e qua stella quae dicitur polus elucet circum caput maioris septentrionis; namque quae est proxume draconem, circum caput eius involvitur. Una vero circum cynosurae caput iniecta est fluxu porrectaque proxime eius pedes.

[6] At the highest point the pole is said to be along their tails. Likewise a serpent is outstretched, from which the star that is called the pole shines, around the head of the Greater Septentrion; for the one which is nearest to the dragon is wound around its head. One, indeed, is cast around the head of the Cynosure, and, stretched out in its flow, close to its feet.

Haec autem intorta replicataque capite minoris ad maiorem, circa rostrum et capitis tempus dextrum. Item supra caudam minoris pedes sunt Cephei, ibique ad summum cacumen facientes stellae sunt trigonum paribus lateribus, insuper arietis signum. Septentrionis autem minoris et Cassiopiae simulacri complures sunt stellae confusae.

But these, twisted and folded back from the head of the Lesser toward the Greater, [go] around the snout and the right temple of the head. Likewise, above the tail of the Lesser are the feet of Cepheus, and there at the very summit the stars make a triangle with equal sides, and above [that] is the sign of the Ram (Aries). Moreover, of the Lesser Septentrion and the simulacrum of Cassiopeia there are several stars intermingled.

Quae sunt ad dextram orientis inter zonam signorum et septentrionum sidera in caelo disposita dixi esse; nunc explicabo, quae ad sinistram orientis meridianisque partibus ab natura sunt distributa.

I have said that those which are on the right of the east, between the zone of the Signs and the septentrional stars, are disposed in the sky; now I will explicate those which on the left of the east and in the meridional parts have been distributed by nature.

Caput Quintum

Chapter Five

[1] Primum sub capricorno subiectus piscis austrinus caudam prospiciens ceti. Ab eo ad sagittarium locus est inanis. Turibulum sub scorpionis aculeo.

[1] First beneath Capricorn lies the Southern Fish, looking toward the tail of Cetus. From it to Sagittarius the place is empty. The Thurible lies beneath the Scorpion’s sting.

Centauri priores partes proximae sunt librae et scorpioni. Tenet in manibus simulacrum, id quod bestiam astrorum periti nominaverunt. Ad virginem et leonem et cancrum anguis porrigens agmen stellarum intortus succingit, regione cancri erigens rostrum, ad leonem medioque corpore sustinens craterem ad manumque virginis caudam subiciens in qua inest corvos; quae sunt autem supra scapulas, peraeque sunt lucentia.

The foremost parts of the Centaur are nearest to Libra and to Scorpio. He holds in his hands a simulacrum, which the experts in the stars have named the Beast. The Serpent, extending toward the Virgin and the Lion and the Crab, intertwined, girds a band of stars, raising its snout in the region of the Crab, toward the Lion, and with its middle body supporting the Crater, and beneath the hand of the Virgin placing its tail, in which is Corvus; and those which are above the shoulders are equally luminous.

[2] Ad angulis inferius ventris, sub caudam subiectus est centaurus. Iuxta cratera et leonem navis est, quae nominatur Argo, cuius prora obscuratur, sed malus et quae sunt circa gubernacula eminentia videntur, ipsaque navicula et puppis per summam caudam cani iungitur. Geminos autem minusculus canis sequitur contra anguis caput.

[2] At the lower corners of the belly, beneath the tail, the Centaur is set. Next to the Crater and the Lion there is a ship, which is named Argo, whose prow is obscured, but the mast and the things around the steering-gear are seen as prominent, and the little ship itself and the stern are joined along the very top of the Dog’s tail. But the smaller Dog follows the Twins, opposite the head of the Serpent.

Maior item sequitur minorem. Orion vero transversus est subiectus, pressus ungula tauri, manu laeva tenens, clavam altera ad geminos tollens.

The greater likewise follows the lesser. Orion, however, is set crosswise beneath, pressed by the hoof of the Bull, holding with the left hand, raising the club with the other toward the Twins.

[3] Apud eius vero basim canis pano intervallo insequens leporem. Arieti et piscibus cetus est subiectus, a cuius crista ordinate utrisque piscibus disposita est tenuis fusio stellarum, quae graece vocitanturharpedonae. Magnoque intervallo introrsus pressus serpentium, attingit summam ceti cristam. Esse fuit per speciem stellarum flumen.

[3] At its base, indeed, a Dog, at a small interval, pursuing a Hare. To Aries and to the Fishes the Whale (Cetus) lies beneath; from whose crest there is, arranged in order for both Fishes, a slender strand of stars, which in Greek are calledharpedonae. And, at a great interval, pressed inward among the Serpents, it touches the top of the Whale’s crest. There is, in the appearance of the stars, a river.

Profluit initium fontis capiens a laevo pede Orionis. Quae vero ab aquario fundi memoratur aqua, profluit inter piscis austrini caput et caudam ceti.

The beginning of the spring flows forth, taking its rise from Orion’s left foot. But the water that is recounted to be poured out by the Water-bearer (Aquarius) flows between the head of the Southern Fish and the tail of the Whale (Cetus).

[4] Quae figurata conformataque sunt siderum in mundo simulacra, natura divinaque mente designata, ut Democrito physico placuit, exposui, sed tantum ea, quorum ortus et occasus possumus animadvertere et oculis contueri. Namque uti septentrionis circum axis cardinem versantur non occidunt neque sub terram subeunt, sic circa meridianum cardinem, qui est propter inclinationem mundi subiectus terrae, sidera versabunda latentiaque non habent egressus orientis supra terram. Itaque eorum figurationes propter obstantiam terrae non sunt notae.

[4] The images of the stars in the world, which have been figured and conformed, designated by nature and by divine mind, as it pleased Democritus the natural philosopher, I have set forth, but only those whose risings and settings we can observe and behold with our eyes. For just as those about the pivot of the axis of the North turn, they do not set nor go beneath the earth, so around the southern pivot, which, on account of the inclination of the world, is situated beneath the earth, the revolving and hidden stars have no emergence of rising above the earth. Therefore their configurations are not known on account of the obstruction of the earth.

Huius autem rei index est stella Canopi, quae his regionibus est ignota, renuntiant autem negotiatores, qui ad extremas Aegypti regiones proximasque ultimis finibus terrae terminationes fuerunt.

But an index of this matter is the star of Canopus, which is unknown in these regions; merchants, however, who have been to the farthest regions of Egypt and to the boundary-marks nearest to the utmost limits of the earth, report it.

Caput Sextum

Chapter Six

[1] De mundi circa terram pervolitantia duodecimque signorum ex septentrionali meridianaque parte siderum dispositione, ut sit perspectus docui. Namque ex ea mundi versatione et contrario solis per signa cursu gnomonumque aequinoctialibus umbris analemmatorum inveniuntur descriptiones.

[1] Concerning the world’s flying-around about the earth and the disposition of the stars of the twelve signs from the northern and the meridian (southern) side, I have instructed, so that the perspective may be seen. For from that revolution of the world and the contrary course of the sun through the signs, and from the equinoctial shadows of gnomons, the delineations of the analemmata are discovered.

[2] Cetera ex astrologia, quos effectus habeant signa XII, stellae V, sol, luna ad humanam vitae rationem, Chaldaeorum ratiocinationibus est concedendum, quod propria est eorum genethlialogiae ratio, uti possint ante facta et futura ex ratiocinationibus astrorum explicare. Eorum autem inventiones reliquerunt, in quae sollertia acuminibusque fuerunt magnis, qui ab ipsa natione Chaldaeorum profluxerunt. Primusque Berosus in insula et civitate Coo consedit ibique aperuit disciplinam, post ea studens Antipater iterumque Athenodorus, qui etiam non e nascentia sed ex conceptione genethlialogiae rationes explicatas reliquit.

[2] The rest from astrology—what effects the 12 signs, the 5 stars, the sun, and the moon have upon the ordering of human life—must be conceded to the ratiocinations of the Chaldeans, because their own method is that of genethlialogy, so that they can explicate past and future things from the ratiocinations of the stars. Their discoveries, moreover, were left by those who flowed forth from the Chaldean nation itself, who were of great skill and acumen. And first Berossus settled in the island and city of Cos and there opened the discipline; thereafter, cultivating it, Antipater, and again Athenodorus, who also left accounts of genethlialogy explained not from birth but from conception.

[3] De naturalibus autem rebus Thales Milesius, Anaxagoras Clazomenius, Pythagoras Samius, Zenophanes Colophonius, Democritus Abderites rationes, quibus e rebus natura rerum gubernaretur quemadmodum cumque effectus habeat, excogitatas reliquerunt. Quorum inventa secuti siderum et occasus tempestatumque significatus Eudoxus, Eudemus, Callippus, Meto, Philippus, Hipparchus, Aratus ceterique ex astrologia parapegmatorum disciplinis invenerunt et eas posteris explicatas reliquerunt. Quorum scientiae sunt hominibus suspiciendae, quod tanta cura fuerunt, ut etiam videantur divina mente tempestatium significatus post futuros ante pronuntiare.

[3] On natural matters, Thales the Milesian, Anaxagoras of Clazomenae, Pythagoras the Samian, Zenophanes of Colophon, and Democritus the Abderite left behind reasonings devised as to how, from things themselves, the nature of things is governed and whatever effects it may have. Following their inventions, Eudoxus, Eudemus, Callippus, Meto, Philippus, Hipparchus, Aratus, and the rest, from astrology, discovered by the disciplines of the parapegmata the indications of the stars and their settings and of the storms, and left these explained for posterity. Their sciences are to be looked up to by human beings, because they were pursued with such care that they even seem, with a divine mind, to announce beforehand the significations of storms that are yet to come.

Quas ob res haec eorum curis studiisque sunt concedenda.

For which reasons these things are to be conceded to their cares and studies.

Caput Septimum

Chapter Seven

[1] Nobis autem ab his separandae sunt rationes et explicandae menstruae dierum brevitates itemque depalationes. Namque sol aequinoctiali tempore ariete libraque versando, quas e gnomone partes habent novem, eas umbrae facit VIII in declinatione caeli, quae est Romae. Idemque Athenis quam magnae sunt gnomonis partes quattuor, umbrae sunt tres, ad VII Rhodo V, ad XI Tarenti IX, ad quinque ceterisque omnibus locis aliae alio modo umbrae gnomonum aequinoctiales a natura rerum inveniuntur disparatae.

[1] But our reckonings must be separated from these, and the monthly shortnesses of the days, as well as the depalations, must be explained. For the sun, at the equinoctial time, turning through Aries and Libra, in the declination of the sky which is at Rome, the shadows make 8 of those parts of which the gnomon has 9. And likewise at Athens, when the parts of the gnomon are 4, the shadows are 3; at Rhodes, for 7, 5; at Tarentum, for 11, 9; for five at ; and in all other places the equinoctial shadows of gnomons are found, by the nature of things, to be differently proportioned in other ways.

[2] Itaque in quibuscumque locis horologia erunt describenda, eo loci sumenda est aequinoctialis umbra et si erunt quemadmodum Romae gnomonis partes novem, umbrae octo, describatur in planitia et e mediapros orthas erigatur ut sit ad normam quae dicitur gnomon. Et a linea, quae erit planities in linea gnomonis circino novem spatia demetiantur; et quo loco nonae partis signum fuerit, centrum constituatur, ubi erit littera A; et deducto circino ab eo centro ad lineam planitiae, ubi erit littera B, circinatio circuli describatur, quae dicitur meridiana.

[2] Therefore, in whatever places horologes (sundials) are to be delineated, the equinoctial shadow must be taken for that locale; and if, as at Rome, the parts of the gnomon are nine and the shadows eight, let it be drawn on a level plane, and from the middle let the gnomon be raisedpros orthas, so that it stands to the square (ad normam), which is called the gnomon. And from the line, which will be the plane, along the line of the gnomon, with the compass let nine spaces be measured off; and at the place where the mark of the ninth part shall be, let a center be established, where the letter A will be; and, the compass drawn from that center to the line of the plane, where the letter B will be, let the circination of a circle be described, which is called the meridian.

[3] Deinde ex novem partibus quae sunt a planitia ad gnomonis centrum, VIII sumantur et signentur in linea, quae est in planitia, ubi erit littera C. Haec autem erit gnomonis aequinoctialis umbra. Et ab eo signo et littera C per centrum, ubi est littera A, linea perducatur, ubi erit solis aequinoctialis radius. Tunc a centro diducto circino ad lineam planitiae aequilatatio signetur, ubi erit littera E sinisteriore parte et I dexteriore in extremis lineis circinationis.

[3] Then, from the nine parts which are from the plane to the center of the gnomon, 8 shall be taken and marked on the line which is on the plane, where there will be the letter C. This, moreover, will be the gnomon’s equinoctial shadow. And from that mark and the letter C, through the center where the letter A is, let a line be drawn, where there will be the sun’s equinoctial radius. Then, with the compass spread from the center to the line of the plane, let equal spacing be marked, where there will be the letter E on the left-hand side and I on the right-hand side, at the extreme lines of the circination.

Et per centrum perducendum, ut aequa duo hemicyclia sint divisa. Haec autem linea a mathematicis dicitur horizon.

And it must be drawn through the center, so that the two hemicycles are divided equally. This line, moreover, is called the horizon by mathematicians.

[4] Deinde circinationis totius sumenda pars est XV; et circini centrum conlocandum in linea circinationis, quod loci secat eam lineam aequinoctialis radius, ubi erit littera F; et signandum dextra sinistra, ubi sunt litterae G H. Deinde ab his lineae usque ad lineam planitiae perducendae sunt, ubi erunt litterae T R. Ita erit solis radius unus hibernus, alter aestivus. Contra autem littera I erit, qua secat circinationem linea, quae est traiecta per centrum, ubi erunt litterae Y K L G, et contra K litterae erunt K H X L; et contra C et F et A erit littera N.

[4] Then a 15th part of the whole circination is to be taken; and the center of the compass is to be placed on the line of the circination, at the point where the equinoctial radius cuts that line, where there will be the letter F; and the right and left are to be marked, where the letters G H are. Then from these lines are to be drawn up to the line of the plane, where there will be the letters T R. Thus one solar radius will be winter, the other summer. Opposite, however, there will be the letter I, where the line which is drawn through the center cuts the circination, where there will be the letters Y K L G, and opposite K the letters will be K H X L; and opposite C and F and A there will be the letter N.

[5] Tunc perducendae suntdiametro ab G ad L et ab H <ad K>. Quae erit superior, partis erit aestivae, inferior hibernae. Eaeque diametro sunt aeque mediae dividendae, ubi erunt litterae O et M, ibique centra signanda. Et per ea signa et centrum A lineae ad extremas lineae circinationis sunt perducendae, ubi erunt litterae Q et P; haec erit linea pros orthas radio aequinoctiali.

[5] Then lines are to be drawnby a diameter from G to L and from H <to K>. The one which will be upper will belong to the summer part, the lower to the winter. And these are to be divided equally at the middle by a diameter, where the letters O and M will be, and there the centers are to be marked. And through those marks and the center A, lines are to be drawn to the extremities of the line of circination, where the letters Q and P will be; this will be the line pros orthas to the equinoctial ray.

Vocabitur autem haec linea mathematicis rationibus axon. Et ab eisdem centris deducto circino ad extremas diametros describantur hemicyclia, quorum unum erit aestivum, alterum hibernum.

Moreover, this line will be called, in mathematical terms, the axon. And from these same centers, with the compass set to the extreme diameters, let hemicycles be drawn, of which one will be summer, the other winter.

[6] Deinde in quibus locis secant lineae paralleloe lineam eam quae dicitur horizon, in dexteriore parte erit littera S, in sinisteriore V. Et ab littera S ducatur linea parallelos axoni ad extremum hemicyclium, ubi erit littera Y; et ab V ad sinistram hemicyclii item parallelos linea ducatur ad litteram X. Haec autem parallelos linea vocitaturlaeotomus. Et tum circini centrum conlocandum est eo loci, quo secat circinationem aequinoctialis radius, ubi erit littera D; et deducendum ad eum locum, quo secat circinationem aestivus radius, ubi est littera H. E centro aequinoctiali intervallo aestivo circinatio circuli menstrui agatur, qui manaeus dicitur. Ita habebitur analemmatos deformatio.

[6] Then, in the places where the parallel lines cut that line which is called the horizon, on the right-hand part there will be the letter S, on the left-hand V. And from the letter S let a line parallel to the axon be drawn to the extremity of the hemicycle, where there will be the letter Y; and from V to the left of the hemicycle likewise let a parallel line be drawn to the letter X. Moreover, this parallel line is called thelaeotomus. And then the center of the compass is to be placed at that spot where the equinoctial ray cuts the circination, where there will be the letter D; and it is to be drawn down to that place where the summer ray cuts the circination, where the letter H is. From the equinoctial center, with the summer interval, let the circination of the monthly circle be carried out, which is called the manaeus. Thus the deformation of the analemma will be obtained.

[7] Cum hoc ita sit descriptum et explicatum, sive per hibernas lineas sive per aestivas sive per aequinoctiales aut etiam per menstruas in subiectionibus rationes horarum erunt ex analemmatos describendae, subicianturque in eo multae varietates et genera horologiorum et describuntur rationibus his artificiosis. Omnium autem figurarum descriptionumque earum effectus unus, uti dies aequinoctialis brumalisque idemque solstitialis in duodecim partes aequaliter sit divisus. Quas ob res non pigritia deterritur praetermissis, sed ne multa scribendo offendam, a quibusque inventa sunt genera descriptionesque horologiorum, exponam.

[7] Since this has thus been drawn and explained, whether through the winter lines or through the summer or the equinoctial, or even through the monthly ones, in the projections the methods of the hours are to be delineated from the analemma, and upon it let many varieties and kinds of horologes be applied, and they are described by these artful methods. But the outcome of all the figures and their descriptions is one and the same: that the equinoctial day, the brumal, and likewise the solstitial be equally divided into twelve parts. For which reasons I am not deterred by laziness to pass things over, but lest I give offense by writing too much, I will set forth the kinds and descriptions of horologes, and by whom they were invented.

Neque enim nunc nova genera invenire possum nec aliena pro meis praedicanda videntur. Itaque quae nobis tradita sunt et a quibus sint inventa, dicam.

For I cannot now invent new genera, nor do things belonging to others seem fit to be proclaimed as mine. And so I shall say what has been handed down to us and by whom they were invented.

Caput Octavum

Chapter Eight

[1] Hemicyclium excavatum ex quadrato ad enclimaque succisum Berosus Chaldaeus dicitur invenisse; scaphen sive hemisphaerium dicitur Aristarchus Samius, idem etiam discum in planitia; arachnen Eudoxus astrologus, nonulli dicunt Apollonium; plinthium sive lacunar, quod etiam in circo Flaminio est positum, Scopinas Syracusius;pros ta historumena, Parmenion, pros pan clima, Theodosius et Andrias, Patrocles pelecinum, Dionysodorus conum, Apollonius pharetram, aliaque genera et qui supra scripti sunt et alii plures inventa reliquerunt, uti conarachnen, conicum plinthium, antiboreum. Item ex his generibus viatoria pensilia uti fierent, plures scripta reliquerunt. Ex quorum libris, si qui velit, subiectiones invenire poterit, dummodo sciat analemmatos descriptiones.

[1] The hemicyclium, hollowed out from a square and cut according to the inclinations (enclima), is said to have been invented by Berosus the Chaldaean; the scaphe or hemisphere by Aristarchus the Samian—he also the disc on a plane; the arachne by Eudoxus the astrologer, some say by Apollonius; the plinthium or lacunar, which is also set up in the Circus Flaminius, by Scopinas of Syracuse;pros ta historumena, by Parmenion; pros pan clima, by Theodosius and Andrias; the pelecinum by Patrocles; the cone by Dionysodorus; the quiver by Apollonius; and other kinds—both those written above and many others—left inventions behind, such as the conarachne, the conical plinthium, the antiboreum. Likewise, from these genera, many left writings on how hanging travel-dials (viatory) might be made. From whose books, if anyone should wish, he will be able to find the subjections, provided only that he knows the descriptions of the analemma.

[2] Item sunt ex aqua conquisitae ab eisdem scriptoribus horologiorum rationes, primumque a Ctesibio Alexandrino, qui etiam spiritus naturalis pneumaticasque res invenit. Sed uti fuerint ea exquisita, dignum studiosis agnoscere. Ctesibius enim fuerat Alexandriae natus patre tonsore.

[2] Likewise there are, fashioned from water by these same writers, the principles of horological devices, and first by Ctesibius of Alexandria, who also discovered matters of natural spirit and pneumatic things. But how these were contrived, it is worthy for the studious to recognize. For Ctesibius had been born at Alexandria, his father a barber.

Is ingenio et industria magna praeter reliquos excellens dictus est artificiosis rebus se delectare. Namque cum voluisset in taberna sui patris speculum ita pendere, ut, cum duceretur susumque reduceretur, linea latens pondus deduceret, ita conlocavit machinationem.

He is said, surpassing the rest, to have been excellent in genius and great industry, and to take delight in artificious things. For when he had wished a mirror in his father’s shop to hang in such a way that, when it was drawn up and brought back down, a hidden line would draw down a weight, he arranged the mechanism thus.

[3] Canalem ligneum sub tigno fixit ibique trocleas conlocavit; per canalem lineam in angulum deduxit ibique tubulos struxit; in eos pilam plumbeam per lineam dermittendam curavit. Ita pondus cum decurrendo in angustias tubulorum premeret caeli crebritatem vehementi decursu per fauces frequentiam caeli compressione solidatam extrudens in aerem patentem offensione tactus sonitus expresserat claritatem.

[3] He fixed a wooden canal beneath a beam and there placed trochleae; through the canal he led a line into a corner and there he constructed little tubes; into them he arranged that a leaden ball be let down along the line. Thus, as the weight, in running down, pressed within the narrowings of the tubules, driving out into the open air, by a vehement descent through the throats, the crowdedness of the air solidified by compression, by the shock of the contact it elicited the clarity of a sound.

[4] Ergo Ctesibius cum animadvertisset ex tractu caeli et expressionibus spiritus vocesque nasci, his principiis usus hydraulicas machinas primus instituit. Item aquarum expressiones automatopoetasque machinas multaque deliciarum genera, in his etiam horologiorum ex aqua conparationes explicuit. Primumque constituit cavum ex auro perfectum aut ex gemma terebrata; ea enim nec teruntur percussu aquae nec sordes recipiunt, ut obturentur.

[4] Therefore, when Ctesibius had observed that from the drawing of air and the expressions of breath voices arise, using these principles he was the first to institute hydraulic machines. Likewise he expounded the expressions of waters and automaton-making machines, and many kinds of delights, among these also the constructions of clocks from water. And first he established a cavity perfected of gold or of a bored gem; for these are neither worn by the striking of the water nor do they receive filth, so that they become stopped up.

[5] Namque aequaliter per id cavum influens aqua sublevat scaphium inversum, quod ab artificibus phellos sive tympanum dicitur. In quo conlocata est regula versatile tympanum. Denticulis aequalibus sunt perfecta, qui denticuli alius alium inpellentes versationes modicas faciunt et motiones.

[5] For the water, flowing evenly through that cavity, lifts an inverted scaphium, which by the artificers is called a phellos or a tympanum. In it there are set a regula and a rotatable tympanum. They are furnished with equal little teeth; and these little teeth, one driving another, produce modest revolutions and motions.

Item aliae regulae aliaque tympana ad eundem modum dentata una motione coacta versando faciunt effectus varietatesque motionum, in quibus moventur sigilla, vertuntur metae, calculi aut ova proiciuntur, bucinae canunt, reliquaque parerga.

Likewise other racks and other drums, toothed in the same manner, with one compelled motion by turning, produce effects and varieties of motions, in which little figures are moved, metae turning-posts are turned, pebbles or eggs are cast forth, the buccinae sound, and the remaining parerga.

[6] In his etiam aut in columna aut parastatica horae describuntur, quas sigillum egrediens ab imo virgula significat in diem totum. Quarum brevitates aut crescentias cuneorum adiectus aut exemptus in singulis diebus et mensibus perficere cogit. Praeclusiones aquarum ad temperandum ita sunt constitutae.

[6] In these as well, either on a column or on a parastatic, the hours are delineated, which a little figure, emerging from below, indicates with a small rod for the whole day. Their shortenings or increases the addition or subtraction of wedges compels to effect for individual days and months. The preclusions of the waters for regulating are constituted thus.

Metae fiunt duae, una solida, una cava, ex torno ita perfectae, ut alia in aliam inire convenireque possit et eadem regula laxatio earum aut coartatio efficiat aut vehementem aut lenem in ea vasa aquae influentem cursum. Ita his rationibus et machinatione ex aqua componuntur horologiorum ad hibernum usum conlocationes.

Two cones are made, one solid, one hollow, finished on the lathe in such a way that the one can enter into and fit the other, and by the same rule their loosening (laxation) or narrowing (coarctation) effects either a vehement or a gentle inflowing course of water into that vessel. Thus, by these reasonings and the machinery, the placements of clocks for winter use are constructed from water.

[7] Sin autem cuneorum adiectionibus et detractionibus correptiones dierum aut crescentiae ex cuneis non probabuntur fieri, quod cunei saepissime vitia faciunt, sic erit explicandum. In columella horae ex analemmatos transverse describantur, menstruaeque lineae columella signentur. Eaque columna versatilis perficiatur, uti ad sigillum virgulamque, qua virgula egrediens sigillum ostendit horas, columna versando continenter suis cuiusque mensibus brevitates et crescentias faceret horarum.

[7] But if corrections of the days by additions and subtractions of wedges, or the increases from wedges, are not approved to be effected—because wedges very often produce faults—thus it must be set out. On the little column (columella) let the hours from the analemma be drawn transversely, and let the monthly lines be marked on the little column. And let that column be made rotatable, so that, with respect to the little aperture (sigillum) and the little rod (virgula)—the rod, projecting through the aperture, shows the hours—by turning the column continuously it would produce, for each of the months, the shortenings and increases of the hours.

[8] Fiunt etiam alio genere horologia hiberna, quae anaphorica dicuntur perficiuntque rationibus his. Horae disponuntur ex virgulis aeneis ex analemmatos descriptione ab centro dispositae in fronte; in ea circuli sunt circumdati menstrua spatia finientes. Post has virgulas tympanum, in quo descriptus et depictus est mundus signiferque circulus descriptioque ex XII caelestium signorum fit figurata, cuius ex centro deformatio, unum maius, alterum minus.

[8] There are also made by another kind winter clocks, which are called anaphoric, and they are completed by these methods. The hours are laid out from little bronze rods, from the description of the analemma, arranged from the center on the face; on it circles are set around, defining the monthly spaces. After these rods comes a drum, on which the cosmos and the sign-bearing (zodiacal) circle are drawn and painted, and a figured description is made from the 12 celestial signs, whose projection from the center produces a deformation—one larger, the other smaller.

Posteriori autem parti tympano medio axis versatilis est inclusus inque eo axi aenea mollis catena est involuta, ex qua pendet ex una parte phellos (sive tympanum), qui ab aqua sublevatur, altera aequo pondere phelli sacoma saburrale.

But at the posterior part, in the middle of the tympanum, a rotatable axis is enclosed; and on that axis a pliant bronze chain is wound, from which there hangs on one side a phellos (or drum), which is lifted by the water, on the other a ballast sack equal in weight to the phellos.

[9] Ita quantum ab aqua phellos sublevatur, tantum saburrae pondus infra deducens versat axem, axis autem tympanum. Cuius tympani versatio alias effÏcit, uti maior pars circuli signiferi, alias minor in versationibus suis temporibus designet horarum proprietates. Namque in singulis signis sui cuiusque mensis dierum numeri cava sunt perfecta, cuius bulla, quae solis imaginem horologiis tenere videtur, significat horarun spatia.

[9] Thus, by as much as the cork is lifted by the water, by so much the weight of the ballast drawing it down beneath turns the axle, and the axle in turn the drum. The rotation of this drum at one time brings it about that a greater part of the zodiacal circle, at another a lesser, in its rotations, at their proper seasons, marks out the properties of the hours. For in each sign the hollows of the numbers of the days of each respective month are completed, whose boss, which seems on timepieces to hold the image of the sun, signifies the spans of the hours.

Ea translata ex terebratione in terebrationem mensis vertentis perficit cursum suum.

It, transferred from perforation to perforation of the revolving month, completes its course.

[10] Itaque quemadmodum sol per siderum spatia vadens dilatat contrahitque dies et horas, sic bulla in horologiis ingrediens per puncta contra centri tympani versationem, cotidie cum transfertur aliis temporibus per latiora, aliis per angustiora spatia, menstruis finitionibus imaginis efficit horarum et dierum.

[10] And thus, just as the sun, going through the spaces of the stars, dilates and contracts the days and the hours, so the bulla (boss) in the horologes, entering by the points against the rotation of the drum’s center, daily, as it is transferred—at some seasons through broader, at others through narrower spaces—by the monthly determinations of the image, brings about the measures of hours and days.

[11] De administratione autem aquae, quemadmodum se temperet ad rationem, sic erit faciendum. Post frotem horologii intra conloeetur castellum in idque per fistulam saliat aqua et in imo habeat cavum. Ad id autem adfixum sit ex aere tympanum habens foramen, per quod ex castello in id aqua influat.

[11] As for the administration of the water, how it should temper itself according to a rational rule, thus it is to be done. Behind the front of the horologe, on the inside, let a castellum (reservoir) be placed, and into it through a fistula (pipe) let the water flow, and at the bottom let it have a cavity. To it, moreover, let a tympanum of bronze be affixed, having an orifice (foramen), through which from the castellum the water may flow into it.

In eo autem minus tympanum includatur cardinibus ex torno masculo et femina inter se coartatis, ita uti minus tympanum quemadmodum epitonium in maiore circumagendo arte leniterque versetur.

Moreover, within it let the smaller tympanum be enclosed on pivots, turned on the lathe, with the male and female parts compressed together, so that the smaller tympanum, like an epitonium (stopcock), may be turned within the larger, by the technique of rotating, smoothly and gently.

[12] Maioris autem tympani labrum aequis intervallis CCCLXV puncta habeat signata, minor vero orbiculis in extrema circinatione fixam habeat ligulam, cuius cacumen dirigat ad punctorum regiones, inque eo orbiculo temperatum sit foramen, quia in tympanum aqua influit per id et servat administrationem. Cum autem inmaioris tympani labro fuerint signorum caelestium deformationes, id autem sit inmotum et in summo habeat deformatum cancri signum, ad perpendiculum eius in imo capricorni, ad dextram spectantis librae, ad sinistram arietis signum, ceteraque inter eorum spatia designata sint, uti in caelo videntur.

[12] Let the rim of the larger drum have 365 points marked at equal intervals, but let the smaller have a little tongue fixed on little circles at the outermost circumference, the tip of which it may direct toward the regions of the points; and in that little circle let a tuned/adjusted hole be set, because through it water flows into the drum and preserves the operation. Now when the figurations of the celestial signs have been on the rim of the larger drum, let that be motionless, and at the top let it have the sign of Cancer set forth; at its plumb-line beneath, Capricorn; to the right of the observer, Libra; to the left, the sign of Aries; and let the rest be designated in the spaces between them, as they are seen in the sky.

[13] Igitur cum sol fuerit in capricorni, orbiculi ligula in maioris tympani parte ex capricorni cotidie singula puncta tangens, ad perpendiculum habens aquae currentis vehemens pondus, celeriter per orbiculi foramen id extrudit ad vas. Tum excipiens eam, cum brevi spatio impletur, corripit et contrahit dierum minora spatia et horarum. Cum autem cotidiana versatione minoris tympani ligula ingrediatur in aquarii puncta, descendent foramina perpendiculo et aquae vehementi cursu cogitur tardius emittere salientem.

[13] Therefore, when the sun is in Capricorn, the little tongue of the orbicle, in the part of the larger tympanum from Capricorn, touching single points day by day, having at the perpendicular the vehement weight of the running water, swiftly extrudes it through the orbicle’s aperture into the vessel. Then, receiving it, since in a short span it is filled, it snatches and contracts the lesser spaces of the days and of the hours. But when, with the daily revolution, the little tongue of the smaller tympanum enters into the points of Aquarius, the apertures descend to the plumb, and by the vehement course of the water it is compelled to emit the leaping flow more slowly.

Ita quo minus celeri cursu vas excipit aquam, dilatat horarum spatia.

Thus, the less swiftly the vessel receives the water, it dilates the spaces of the hours.

[14] Aquarii vero pisciumque punctis uti gradibus scandens orbiculi foramen in ariete tangendo octavam partem aqua temperate salienti praestat aequinoctiales horas. Ab ariete per tauri et geminorum spatia ad summa cancri puncta partis octavae foramen se tympani versationibus peragens et in altitudinem eo rediens viribus extenuatur, et ita tardius fluendo dilatet morando spatia et efficit horas in cancri signo solstitiales. A cancro cum proclinat et peragit per leonem et virginem ad librae partis octavae puncta revertendo et gradatim corripiendo spatia contrahit horas, et ita perveniens ad puncta librae aequinoctialis rursus reddit horas.

[14] But using the points of Aquarius and of Pisces as steps, the little disk’s aperture, by touching the eighth part in Aries, with the water leaping moderately, furnishes equinoctial hours. From Aries, through the spaces of Taurus and Gemini, to the highest points of Cancer, the aperture of the eighth part, carrying itself along by the revolutions of the drum and returning thither into height, is weakened in its forces, and thus, by flowing more slowly, it dilates the intervals by delaying and makes the hours solstitial in the sign of Cancer. From Cancer, when it inclines and passes through Leo and Virgo to the points of the eighth part of Libra, by returning and by gradually shortening the intervals it contracts the hours, and thus, arriving at the points of equinoctial Libra, it renders the hours again.

[15] Per scorpionis vero spatia et sagittarii proclivius deprimens se foramen rediensque circumactione ad capricorni partem VIII, restituitur celeritate salientis ad brumales horarum brevitates.

[15] Through the spaces of Scorpio and of Sagittarius the aperture, lowering itself more steeply and, returning by revolution to Capricorn’s 8th part, is restored by the rapidity of the leaping flow to the brumal brevities of the hours.

Quae sunt in horologiorum descriptionibus rationes et adparatus, ut sint ad usum expeditiores, quam aptissime potui, perscripsi. Restat nunc de machinationibus et de earum principiis ratiocinari. Itaque de his, ut corpus emendatum architecturae perficiatur, insequenti volumine incipiam scribere.

The methods and apparatus in the descriptions of horologes, so that they may be more expeditious for use, I have written out as aptly as I could. It remains now to reason about machinations and their principles. And so concerning these, in order that the emended body of architecture may be perfected, in the following volume I shall begin to write.