Vitruvius: DE ARCHITECTVRA

[1] Qui amplioribus voluminibus, imperator, ingenii cogitationes praeceptaque explicaverunt, maximas et egregias adiecerunt suis scriptis auctoritates. Quod etiam vel in nostris quoque studiis res pateretur, ut amplificationibus auctoritas et in his praeceptis augeretur; sed id non est, quemadmodum putatur, expeditum. Non enim de architectura sic scribitur uti historia aut poemata.

[1] Those who, in more ample volumes, Emperor, have explicated the cogitations of the intellect and the precepts, have appended to their writings the greatest and most distinguished authorities. Which also, were the matter to allow it, might be done even in our studies, so that by amplifications authority too in these precepts would be augmented; but that is not, as is supposed, expeditious. For one does not write about architecture thus as one writes history or poems.

Historiae per se tenent lectores; habent enim novarum rerum varias expectationes. Poematorum vero carminum metra et pedes, ac verborum elegans dispositio et sententiarum inter personas distinctas, versuum pronuntiatio prolectando sensus legentium perducit sine offensa ad summam scriptorum terminationem.

Histories in themselves hold readers; for they have various expectations of new things. But the meters and feet of poets’ songs, and the elegant disposition of words and the sentences divided among distinct personae, the pronunciation of the verses, by alluring the senses of the readers, conducts them without offense to the ultimate termination of the writings.

[2] Id autem in architecturae conscriptionibus non potest fieri, quod vocabula ex artis propria necessitate concepta inconsueto sermone obiciunt sensibus obscuritatem. Cum ergo ea per se non sint aperta nec pateant eorum in consuetudine nomina, tum etiam praeceptorum late evagantes scripturae, si non contrahentur, et paucis et perlucidis sententiis explicentur, frequentia multitudineque sermonis inpediente incertas legentium efficient cogitationes. Itaque occultas nominationes commensusque e membris operum pronuntians, ut memoriae tradantur, breviter exponam; sic enim experitius ea recipere poterunt mentes.

[2] But this cannot be done in the writings of architecture, because terms conceived from the art’s proper necessity, in unfamiliar speech, present obscurity to the senses. Since therefore these are not clear in themselves nor are their names evident in common usage, then also the widely-wandering writings of the precepts, if they are not contracted and explained in few and very pellucid sentences, with the frequency and multitude of discourse hindering, will render the readers’ thoughts uncertain. Therefore, declaring the occult designations and the commensurations from the members of works, so that they may be handed to memory, I will set them forth briefly; for thus minds will be able to receive them more expertly.

[3] Non minus cum animadvertissem distentam occupationibus civitatem publicis et privatis negotiis, paucis iudicavi scribendum, uti angusto spatio vacuitatis ea legentes breviter percipere possent.

[3] No less, when I had observed the city stretched with occupations, with public and private businesses, I judged it should be written in few words, so that, in the narrow space of leisure, those reading might briefly perceive them.

Etiamque Pythagorae quique eius haeresim fuerunt secuti, placuit cybicis rationibus praecepta in voluminibus scribere, constitueruntque cybum CCXVI versus eosque non plus tres in una conscriptione oportere esse putaverunt.

And likewise Pythagoras and those who followed his sect judged it good to write the precepts in volumes by cubic ratios, and they established the cube as 216 lines, and they thought that not more than three of these ought to be in a single composition.

[4] Cybus autem est corpus ex lateribus aequali latitudine planitiarum perquadratus. Is cum est iactus, quam in partem incubuit, dum est intactus, inmotam habet stabilitatem, uti sunt etiam tesserae quas in alveo ludentes iaciunt. Hanc autem similitudinem ex eo sumpsisse videntur, quod is numerus versuum, uti cybus, in quemcumque sensum insederit, inmotam efficiat ibi memoriae stabilitatem.

[4] A cube, moreover, is a body squared by planes, with sides of equal breadth. When it has been cast, into whatever part it has settled, so long as it is untouched, it has motionless stability, just as do also the dice which players throw in a tray. They seem to have taken this likeness from the fact that that number of verses, like a cube, into whatever sense it has settled, produces there an unmoved stability for memory.

Graeci quoque poetae comici interponentes e choro canticum diviserunt spatia fabularum. Ita partes cybica ratione facientes intercapedinibus levant auctorum pronuntiationis.

The Greek comic poets too, inserting a song from the chorus, divided the spaces of their plays. Thus, making the parts by a cybic rationale, they lighten the authors’ delivery by intervals.

[5] Cum ergo haec naturali modo sint a maioribus observata animoque advertam inusitatas et obscuras multis res esse mihi scribendas, quo facilius ad sensus legentium pervenire possint, brevibus voluminibus iudicavi scribere; ita enim expedita erunt ad intellegendum. Eorumque ordinationes institui, uti non sint quaerentibus separatim colligenda, sed e corpore uno et in singulis voluminibus generum haberent explicationes. Itaque, Caesar, tertio et quarto volumine aedium sacrarum rationes exposui, hoc libro publicorum locorum expediam dispositiones.

[5] Since therefore these things have been observed by our elders in a natural manner, and I advert that there are matters unusual and obscure to many which must be written by me, in order that they may more easily come to the senses of readers, I have judged to write in brief volumes; for thus they will be unimpeded for understanding. And I have instituted their arrangements, so that seekers need not gather them separately, but from one corpus, and in the individual volumes, they may have explications of the kinds. And so, Caesar, in the 3rd and 4th volume I have set forth the principles of sacred buildings; in this book I will expound the dispositions of public places.

Primumque forum uti oporteat constitui dicam, quod in eo et publicarum et privatarum rerum rationes per magistratus gubernantur.

And first I will say how the forum ought to be constituted, since in it the conduct of public and private affairs is governed through the magistrates.

Caput Primum

Chapter One

[1] Graeci in quadrato amplissimis et duplicibus porticibus fora constituunt crebrisque columnis et lapideis aut marmoreis epistyliis adornant et supra ambulationes in contignationibus faciunt. Italiae vero urbibus non eadem est ratione faciendum, ideo quod a maioribus consuetudo tradita est gladiatoria munera in foro dari.

[1] The Greeks establish the fora in a square with very ample and double porticoes, and they adorn them with frequent columns and epistyles of stone or marble, and above they make ambulations on the storeys. But in the cities of Italy it must not be done by the same method, because a custom has been handed down from the ancestors that gladiatorial munera are given in the forum.

[2] Igitur circum spectacula spatiosiora intercolumnia distribuantur circaque in porticibus argentariae tabernae maenianaque superioribus coaxationibus conlocentur; quae et ad usum et ad vectigalia publica recta erunt disposita.

[2] Therefore, around the spectator-stands let more spacious intercolumniations be distributed, and around, in the porticoes, let argentary shops be set, and maeniana be placed on upper-level bracings; which will be rightly arranged both for use and for the public revenues.

Magnitudines autem ad copiam hominum oportet fieri, ne parvum spatium sit ad usum aut ne propter inopiam populi vastum forum videatur. Latitudo autem ita finiatur uti, longitudo in tres partes cum divisa fuerit, ex his duae partes ei dentur; ita enim erit oblonga eius formatio et ad spectaculorum rationem utilis dispositio.

But the dimensions ought to be made according to the supply of people, lest the space be too small for use, or lest, on account of the people’s scarcity, the forum seem vast. The breadth, moreover, should be determined thus: when the length has been divided into three parts, let two of these parts be given to it; for thus its formation will be oblong and its disposition useful for spectacles.

[3] Columnae superiores quarta parte minores quam inferiores sunt constituendae, propterea quod oneri ferendo quae sunt inferiora firmiora debent esse quam superiora. Non minus quod etiam nascentium oportet imitari naturam, ut in arboribus teretibus, abiete, cupresso, pinu, e quibus nulla non crassior est ab radicibus, dein decrescendo proceditur in altitudinem naturali contractura peraequata nascens ad cacumen. Ergo si natura nascentium ita postulat, recte est constitutum et altitudinibus et crassitudinibus superiora inferiorum fieri contractiora.

[3] The upper columns are to be made a fourth part smaller than the lower, because for bearing the burden the things below ought to be stronger than the things above. No less, the nature of things that are born must also be imitated, as in round trees—fir, cypress, pine—of which not one is not thicker at the roots; then, by decreasing, it proceeds in height, a natural contraction, evened out, growing to the peak. Therefore, if the nature of things that are born thus demands, it is rightly established that both in altitudes and in thicknesses the upper parts be made more contracted than the lower.

[4] Basilicarum loca adiuncta foris quam calidissimis partibus oportet constitui, ut per hiemen sine molestia tempestatium se conferre in eas negotiatores possint. Earumque latitudines ne minus quam ex tertia, ne plus ex dimidia longitudinis constituantur, nisi si loci natura inpedierit et aliter coegerit symmetriam commutari. Sin autem locus erit amplior in longitudine, chalcidica in extremis constituantur, uti sunt in Iulia Aquiliana.

[4] The sites of basilicas, adjoining the forum, ought to be placed in the warmest parts, so that during winter merchants may betake themselves into them without the annoyance of the weather. And their widths should be established as not less than one third and not more than one half of the length, unless the nature of the site has impeded and has compelled the symmetry to be altered otherwise. But if the place is more ample in length, chalcidica should be set at the ends, as they are in the Julia Aquiliana.

[5] Columnae basilicarum tam altae, quam porticus latae fuerint, faciendae videntur; porticus, quam medium spatium futurum est, ex tertia finiatur. Columnae superiores minores quam inferiores, uti supra scriptum est, constituantur. Pluteum, quod fuerit inter superiores et inferiores columnas, item quarta parte minus, quam superiores columnae fuerint, oportere fieri videtur, uti supra basilicae contignationem ammulantes ab negotiatoribus ne conspiciantur.

[5] The columns of basilicas seem to be made as high as the porticoes are wide; the portico which will be the middle space should be finished at one third. The upper columns should be set smaller than the lower, as written above. The pluteum (parapet), which will be between the upper and lower columns, likewise seems proper to be made a fourth less than the upper columns are, so that those walking above the basilica’s flooring may not be seen by the merchants.

Epistylia zophora coronae ex symmetriis columnarum, uti in tertio libro diximus, explicentur.

Let the epistyles, zophora, and cornices be set out according to the symmetries of the columns, as we have said in the third book.

[6] Non minus summam dignitatem et venustatem possunt habere comparationes basilicarum, quo genere Coloniae Iuliae Fanestri conclavi curavique faciendam, cuius proportiones et symmetriae sic sunt constitutae. Mediana testudo inter columnas est longa pedes CXX, lata pedes LX. Porticus eius circa testudinem inter parietes et columnas lata pedes XX. Columnae altitudinibus perpetuis cum capitulis pedes L, crassitudinibus quinum, habentes post se parastaticas altas pedes XX, latas pedes II s, crassas I s, quae sustinent trabes, in quibus invehuntur porticuum contignationes. Supraque eas aliae parastaticae pedum XVIII, latae binum, crassae pedem, quae excipiunt item trabes sustinentes cantherium et porticum, quae sunt summissa infra testudinem, tecta.

[6] No less can the comparisons of basilicas have the highest dignity and charm; of this kind at Colonia Julia Fanestris I designed a basilica with a council‑chamber and took care to have it built, whose proportions and symmetries were thus established. The middle vault between the columns is 120 feet long, 60 feet wide. Its portico around the vault, between the walls and the columns, is 20 feet wide. The columns, in continuous heights with capitals, are 50 feet high, 5 in thickness, having behind them parastatics 20 feet high, 2 and a half feet wide, 1 and a half thick, which sustain the beams, on which the floorings of the porticoes are carried. And above them other parastatics of 18 feet, 2 in width, 1 foot in thickness, which likewise receive beams supporting the cantherium (purlin) and the portico, which are roofed, set down below the vault.

[7] Reliqua spatia inter parastaticarum et columnarum trabes per intercolumnia luminibus sunt relicta. Columnae sunt in latitudine testudinis cum angularibus dextra ac sinistra quaternae, in longitudine, quae est foro proxima, cum isdem angularibus octo, ex altera parte cum angularibus VI, ideo quod mediae duae in ea parte non sunt positae, ne inpediant aspectus pronai aedis Augusti, quae est in medio latere parietis basilicae conlocata spectans medium forum et aedem Iovis.

[7] The remaining spaces between the beams of the parastatics and of the columns were left as lights through the intercolumniations. The columns are, in the breadth of the vault, with the corner ones on the right and left, four apiece; in the length, which is nearest to the forum, with those same corner ones, eight; on the other side, with the corner ones, 6, for the reason that the two middle ones on that side are not set, lest they impede the view of the pronaos of the temple of Augustus, which is placed on the middle side of the wall of the basilica, facing the middle of the forum and the temple of Jupiter.

[8] Item tribunal quod est in ea aede, hemicycli schematis minoris curvatura formatum; eius autem hemicycli in fronte est intervallum pedes XLVI, introrsus curvatura pedes XV, uti, qui apud magistratus starent, negotiantes in basilica ne inpedirent. Supra columnas ex tribus tignis bipedalibus conpactis trabes sunt circa convocatae, eaeque ab tertiis columnis quae sunt in interiore parte, revertuntur ad antas quae a pronao procurrunt, dextraque et sinistra hemicyclium tangunt.

[8] Likewise, the tribunal which is in that aedes is formed by the curvature of a smaller-hemicycle schema; and the front interval of that hemicycle is 46 feet, the inward curvature 15 feet, so that those who would stand before the magistrates might not impede those negotiating business in the basilica. Above the columns, beams are assembled around, made from three bipedal timbers compacted together; and from the third columns which are on the interior side they turn back to the antae which run out from the pronaos, and on the right and left they touch the hemicycle.

[9] Supra trabes contra capitula ex fulmentis dispositae pilae sunt conlocatae, altae pedes III, latae quoqueversus quaternos. Supra eas ex duobus tignis bipedalibus trabes everganeae circa sunt conlocatae. Quibus insuper transtra cum capreolis columnarum contra corpora et antas et parietes pronai conlocata sustinente unum culmen perpetuae basilicae, alterum a medio supra pronaum aedis.

[9] Above the beams, opposite the capitals, piers set upon supports are placed, 3 feet high, and 4 feet wide each way. Above them, from two-foot timbers, overhanging beams are set around. Upon these moreover, crossbeams with the capreoli of the columns, set opposite the shafts and the antae and the walls of the pronaos, sustain one ridge of the continuous basilica, the other from the middle above the pronaos of the temple.

[10] Ita fastigiorum duplex tecti nata dispositio extrinsecus tecti et interioris altae testudinis praestat speciem venustam. Item sublata epistliorum ornamenta et pluteorum columnarumque superiorum distributio operosam detrahit molestiam sumptusque inminuit ex magna parte summam. Ipsae vero columnae in altitudine perpetua sub trabe testitudinis perductae et magnificentiam inpensae et auctoritatem operi adaugere videntur.

[10] Thus the double disposition of the gables of the roof, naturally arisen, affords a graceful aspect of both the exterior roof and the lofty interior vault. Likewise, the removal of the ornaments of the epistyles (architraves) and the distribution of the parapets and of the upper columns takes away laborious trouble and, for the most part, diminishes the total sum of expense. But the columns themselves, carried up in continuous height beneath the beam of the vault, seem to augment both the magnificence of the outlay and the authority of the work.

Caput Secundum

Chapter 2

[1] Aerarium, carcer, curia foro sunt coniungenda, sed ita uti magnitudo symmetriae eorum foro respondeant. Maxime quidem curia in primis est facienda ad dignitatem municipii sive civitatis. Et si quadrata erit, quantum habuerit latitudinis dimidia addita constituatur altitudo; sin autem oblonga fuerit, longitudo et latitudo componatur, et summae compositae eius dimidia pars sub lacunaris altitudini detur.

[1] The aerarium (treasury), the prison, and the curia are to be joined to the forum, but in such a way that the magnitude of their symmetry corresponds to the forum. Above all, the curia is to be made foremost to suit the dignity of the municipality or city. And if it is square, let the height be established as much as it has in width with a half added; but if it is oblong, let the length and the width be combined, and let half of that composed sum be given to the height up to the lacunar (coffered ceiling).

[2] Praeterea praecingendi sunt parietes medii coronis ex intestino opere aut albario ad dimidiam partem altitudinis. Quae si non erunt, vox ibi disputantium elata in altitudinem intellectui non poterit esse audientibus. Cum autem coronis praecincti parietes erunt, vox ab imis morata priusquam in area elata dissipabitur, auribus erit intellecta.

[2] Moreover, the middle walls must be girded with cornices of roughcast work or stucco, up to half their height. If these are not present, the voice of the disputants, carried aloft into the height, will not be able to be intelligible to the hearers. But when the walls are girded with cornices, the voice, checked from below, before it is lifted into the open area and dissipated, will be understood by the ears.

Caput Tertium

Chapter Three

[1] Cum forum constitutum fuerit, tum deorum inmortalium diebus festis ludorum expectationibus eligendus est locus theatro quam saluberrimus, uti in primo libro de salubritatibus in moenium conlocationibus est scriptum. Per ludos enim cum coniugibus et liberis persedentes delectationibus detinentur et corpora propter voluptatem inmota patentes habent venas, in quas insiduntur aurarum flatus, qui, si a regionibus palustribus aut aliis regionibus vitiosis advenient, nocentes spiritus corporibus infundent. Itaque si curiosius eligetur locus theatro, vitabuntur vitia.

[1] When the forum has been established, then, on the festal days of the immortal gods, amid the expectations of the games, a site must be chosen for the theater as healthful as possible, as is written in the first book about salubrity in the collocations of city walls. For during the games, sitting through with their spouses and children, they are held fast by delectations, and their bodies, motionless because of pleasure, have open veins, into which the breaths of the airs settle; which, if they come from marshy regions or other noxious regions, will pour harmful spirits into the bodies. Therefore, if the site for the theater is selected more carefully, the faults will be avoided.

[2] Etiamque providendum est, nene impetus habeat a meridie. Sol enim cum implet eius rutunditatem, aer conclusus curvatura neque habens potestatem vagandi versando confervescit et candens adurit excoquitque et inminuit e corporibus umores. Ideo maxime vitandae sunt his rebus vitiosae regiones et eligendae salubres.

[2] And provision must also be made that it have no impulse from the meridian. For when the sun fills its rotundity, the air enclosed by the curvature, not having the power of wandering, by turning grows hot, and, glowing, it adures, excocts, and diminishes the humors from bodies. Therefore regions faulty in these matters are most to be avoided, and healthful ones to be chosen.

[3] Fundamentorum autem, si in montibus fuerit, facilior erit ratio; sed si necessitas coegerit in plano aut palustri loco ea constitui, solidationes substructionesque ita erunt faciendae, quemadmodum de fundationibus aedium sacrarum in tertio libro est scriptum. Insuper fundamenta lapideis et marmoreis copiis gradationes ab substructione fieri debent.

[3] As for the foundations, if it is in the mountains, the method will be easier; but if necessity has compelled that they be established on level or marshy ground, the solidations and substructions must be made as is written concerning the foundations of sacred edifices in the third book. Moreover, above the foundations, stepped gradations are to be made from the substructure with supplies of stone and marble.

[4] Praecinctiones ad altitudines theatrorum pro rata parte faciendae videntur neque altiores quam quanta praecinctionis itineris sit latitudo. Si enim excelsiores fuerint, repellent et eicient in superiorem partem vocem nec patientur in sedibus suis, quae supra praecinctiones, verborum casus certa significatione ad aures pervenire. Et ad summam ita est gubernandum, uti, linea cum ad imum gradum et ad summum extenta fuerit, omnia cacumina graduum angulosque tangat; ita vox non inpedietur.

[4] The praecinctions seem to have to be made in proportion to the heights of the theaters, and not higher than the breadth of the praecinction’s passage. For if they are loftier, they will repel and cast the voice into the upper part, nor will they allow, in the seats which are above the praecinctions, the inflections of the words, with definite signification, to reach the ears. And in sum it must be so governed, that, when a line has been stretched to the lowest step and to the highest, it touches all the summits of the steps and the angles; thus the voice will not be impeded.

[5] Aditus complures et spatiosos oportet disponere, nec coniunctos superiores inferioribus, sed ex omnibus locis perpetuos et directos sine inversuris faciendos, uti, cum populus dimittatur de spectaculis, ne comprimatur, sed habeat ex omnibus locis exitus separatos sine inpeditione.

[5] It is necessary to arrange numerous and spacious approaches, and not to have the upper joined to the lower, but from all places they must be made continuous and straight without turn-backs, so that, when the people is dismissed from the spectacles, it may not be compressed, but may have from every place separate exits without impediment.

Etiam diligenter est animadvertendum, ne sit locus surdus, sed ut in eo vox quam clarissime vagari possit. Hoc vero fieri ita poterit, si locus electus fuerit, ubi non inpendiantur resonantia.

It must also be carefully observed, that the place not be deaf, but that in it the voice can wander as clearly as possible. This indeed can be done thus, if a place is chosen where the resonances are not impeded.

[6] Vox autem ut spiritus fluens aeris, et actu sensibilis auditu. Ea movetur circulorum rutundationibus infinitis, uti si in stantem aquam lapide inmisso nascantur innumerabiles undarum circuli crescentes a centro, quam latissime possint, et vagantes, nisi angustia loci interpellaverit aut aliqua offensio, quae non patitur designationes earum undarum ad exitus pervenire. Itaque cum interpellentur offensionibus, primae redundantes insequentium disturbant designationes.

[6] The voice, moreover, is like a spirit flowing of air, and in its act perceptible to hearing. It is moved by infinite roundings of circles, as if, when a stone has been cast into standing water, innumerable circles of waves are born, growing from the center as widely as they can and wandering, unless the narrowness of the place should have interposed, or some obstruction, which does not allow the delineations of those waves to reach the outlets. And so, when they are interrupted by obstructions, the first, overflowing, disturb the delineations of those that follow.

[7] Eadem ratione vox ita ad circinum efficit motiones; sed in aqua circuli planitiae in latitudine moventur, vox et in latitudine progreditur et altitudinem gradatim scandit. Igitur ut in aqua undarum designationibus, item in voce cum offensio nulla primam undam interpellaverit, non disturbat secundam nec insequentes, sed omnes sine resonantia perveniunt ad imorum et ad summorum aures.

[7] By the same reasoning the voice thus effects motions by the compass; but in water the planes of the circles move in breadth, while the voice both advances in breadth and climbs in altitude by degrees. Therefore, as in water by the designations of the waves, so also in the voice, when no offense has interrupted the first wave, it does not disturb the second nor those following, but all without resonance reach the ears of those below and of those above.

[8] Ergo veteres architecti naturae vestigia persecuti indagationibus vocis scandentis theatrorum perfecerunt gradationes, et quaesierunt per canonicam mathematicorum et musicam rationem, ut, quaecumque vox esset in scaena, clarior et suavior ad spectatorum perveniret aures. Uti enim organa in aeneis lamminis aut corneisecheis ad cordarum sonitum claritatem perficiuntur, sic theatrorum per harmonicen ad augendam vocem ratiocinationes ab antiquis sunt constitutae.

[8] Therefore the ancient architects, pursuing the vestiges of nature by investigations of the ascending voice, perfected the gradations of theaters, and sought, through the canonical rule of the mathematicians and the reasoning of music, that whatever voice was on the stage might come to the ears of the spectators more clear and more sweet. For just as instruments, by bronze plates or hornecheis, are perfected for the clarity of the sound of the strings, so the reasonings of theaters, through harmonics, for augmenting the voice, were established by the ancients.

Caput Quartum

Chapter Four

[1] Harmonia autem est musica litteratura obscura et difficilis, maxime quidem quibus graecae litterae non sunt notae. Quam si volumus explicare, necesse est etiam graecis verbis uti, quod nonnullae eorum latinas non habent appellationes. Itaque ut potuero quam apertissime ex Aristoxeni scripturis interpretabor et eius diagramma subscribam finitionesque sonituum designabo, uti, qui diligentius attenderit, facilius percipere possit.

[1] Harmony, moreover, is a musical literature that is obscure and difficult, especially indeed for those to whom the Greek letters are not known. Which, if we wish to explicate, it is necessary to use Greek words as well, because some of them do not have Latin appellations. Therefore, as I shall be able, as openly as possible I will interpret from the writings of Aristoxenus and will subjoin his diagram, and I will designate the definitions of the sounds, so that he who has paid more diligent attention may be able to perceive more easily.

[2] Vox enim mutationibus cum flectitur, alias fiat acuta, alias gravis; duobusque modis movetur, e quibus unus effectus habet continuatos, alter distantis. Continuata vox neque in finitionibus consistit neque in loco ullo, effiicitque terminationes non apparentes, intervalla autem media parentia, uti sermone cum dicamus: sol lux flos vox. Nunc enim nec unde incipit nec ubi desinit, intellegitur; sed quod ex acuta facta est gravis et ex gravi acuta, apparet auribus.

[2] For when the voice is flexed by mutations, at one time it becomes acute, at another grave; and it is moved in two modes, of which one outcome has the continuous, the other the separated. The continuous voice neither consists in finitions nor in any place, and it produces terminations not apparent, while the intermediate intervals appear, as in speech when we say: sol lux flos vox. For then neither whence it begins nor where it ends is understood; but that from acute it has become grave, and from grave acute, appears to the ears.

Per distantiam autem e contrario. Namque cum flectitur inmutatione vox statuit se in alicuius sonitus finitionem, deinde in alterius, et id ultro citro crebre faciendo constans apparet sensibus, uti in cantionibus cum flectentes vocem varietatem facimus. Modulationis itaque intervallis ea cum versatur, et unde initium fecit et ubi desiit, apparet in sonorum patentibus finitionibus, mediana autem patentia intervallis obscurantur.

But by distance, on the contrary. For when the voice is bent with a change, it sets itself in the termination of some sound, then in that of another; and by doing this to and fro frequently, it appears constant to the senses, as in songs when, bending the voice, we make variety. Therefore, when it moves within the intervals of modulation, both whence it made a beginning and where it ended appears in the manifest terminations of the sounds, but the intermediate apparent things are obscured by the intervals.

[3] Genera vero sunt modulationum tria: primum quod Graeci nominantharmoniam, secundum chroma, tertium diatonon. Est autem harmoniae modulatio ad artem concepta, et ea re cantio eius maxime gravem et egregiam habet auctoritatem. Chroma subtili sollertia ac crebritate modulorum suaviorem habet delectationem. Diatoni vero, quod naturalis est, facilior est intervallorum distantia.

[3] The kinds of modulations are three: the first, which the Greeks callharmony, the second chroma, the third diatone. Now the modulation of harmony is conceived according to art, and for that reason its chant has a most grave and distinguished authority. Chroma, by the subtle skill and the frequency of modulations, has a sweeter delectation. But in the diatone, because it is natural, the distance of the intervals is easier.

In his tribus generibus dissimiles sunt tetrachordorum dispositiones, quod harmonia tetrachordorum et tonos et dihesis habet binas (dihesis autem est toni pars quarta; ita in hemitonio duae diheses sunt conlocatae); chromati duo hemitonia in ordine sunt composita, tertium trium hemitoniorum est intervallum; diatono toni duo sunt continuati, tertium hemitonium finit tetrachordi magnitudinem. Ita in tribus generibus tetrachorda ex duobus tonis et hemitonio sunt peraequata, sed ipsa cum seperatim uniuscuiusque generis finibus considerantur, dissimilem habent intervallorum designationem.

In these three genera the dispositions of tetrachords are dissimilar, because in the harmonic genus the tetrachord has two tones and two dieses (moreover, a diesis is the fourth part of a tone; thus in a semitone two dieses are placed); in the chromatic, two semitones are composed in sequence, the third interval is of three semitones; in the diatonic, two tones are continuous, a third semitone bounds the magnitude of the tetrachord. Thus in the three genera the tetrachords are equalized out of two tones and a semitone; but when these themselves are considered separately within the limits of each genus, they have a dissimilar designation of intervals.

[4] Igitur intervallo tonorum et hemitoniorum et tetrachordorum in voce divisit natura finitque terminationes eorum mensuris intervallorum quantitate, modisque certis distantibus constituit qualitates, quibus etiam artifices qui organa fabricant, ex natura constitutis utendo comparant ad concentus convenientes eorum perfectiones.

[4] Therefore by the interval of tones, semitones, and tetrachords nature divided the voice, and it fixes their terminations by measures, by the quantity of the intervals, and with certain distinct modes it established the qualities, by which even the craftsmen who fashion instruments, by using what has been established by nature, match their perfections to fitting concords.

[5] Sonitus, qui graecephthongi dicuntur, in unoquoque genere sunt X et VIII, e quibus VIII sunt in tribus generibus perpetui et stantes, reliqui X, cum communiter modulantur, sunt vagantes. Stantes autem sunt, qui inter mobiles sunt interpositi. Continent tetrachordi coniunctionem et e generum discriminibus suis finibus sunt permanentes; appellantur autem sic: proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon.

[5] Sounds, which in Greek are calledphthongi, in each genus are 18, of which 8, in the three genera, are perpetual and standing, the remaining 10, when they are modulated in common, are wandering. The standing ones, moreover, are those which are interposed among the movable notes. They contain the conjunction of the tetrachord and, from the discriminations of the genera, remain within their own boundaries; they are called thus: proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon.

Mobiles autem sunt, qui in tetrachordo inter inmotos dispositi in generibus ex locis loca mutant; vocabula autem habent haec: parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, <paranete synhemmenon>, trite diezugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

Mobile, moreover, are those who, in the tetrachord, being set among the motionless, in the genera change places from their positions; moreover they have these names: parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, <paranete synhemmenon>, trite diezugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

[6] Ei autem qua moventur, recipiunt virtutes alias; intervalla enim et distantias habent crescentes. Itaque parhypate, quae in harmonia distat ab hypate hemitonium, in chroma tramutata habet hemitonium. Qui lichanos in harmonia dicitur, ab hypate distat hemitonium, in chroma translata progreditur duo hemitonia, in diatono distat ab hypate tria hemitonia.

[6] But these, by which movement is effected, receive other virtues; for they have increasing intervals and distances. Thus the parhypate, which in the harmonia is distant from the hypate by a semitone, when transmuted into the chroma has a semitone. The one which in the harmonia is called lichanos is distant from the hypate by a semitone; when transferred into the chroma it advances two semitones; in the diatonic it is distant from the hypate three semitones.

Ita X sonitus propter translationes in generibus efficiunt triplicem modulationum varietatem. Tetrachorda autem sunt quinque:

Thus 10 sounds, on account of transpositions in the genera, effect a threefold variety of modulations. But the tetrachords are five:

[7] primum gravissimum, quod graece diciturhypaton, secundum medianum, quod appellatur meson, tertium coniunctum, quod synhemmenon dicitur, quartum disiunctum, quod diezeugmenon nominatur, quintum, quod est acutissimum, graece hyperbolaeon dicitur. Concentos quos natura hominis modulari potest, graece quae synphoniae dicuntur, sunt sex: diatessaron, diapente, diapason, et disdiatessaron, et disdiapente, et disdiapason.

[7] first the gravest, which in Greek is calledhypaton; second the median, which is called meson; third the conjunct, which is called synhemmenon; fourth the disjunct, which is named diezeugmenon; fifth, which is the most acute, is in Greek called hyperbolaeon. The consonances which the nature of man can modulate, which in Greek are called synphoniae, are six: diatessaron, diapente, diapason, and disdiatessaron, and disdiapente, and disdiapason.

[8] Ideoque et a numero nomina ceperunt, quod, cum vox constiterit in una sonorum finitione ab eaque se flectens mutaverit et pervenerit in quartam terminationem, appellatur diatessaron, in quintam diapente [in sextam diapason in octavam et dimidiam diapason et diatessaron, in nonam et dimidiam diapason diapente, in XII disdiapason].

[8] And therefore also they took names from number, because, when the voice has stood fast in one finition of sounds and, bending itself away from it, has changed and has come through to the fourth termination, it is called the diatessaron; to the fifth, the diapente [to the sixth, the diapason; to the eighth and a half, the diapason and the diatessaron; to the ninth and a half, the diapason-diapente; to the 12, the disdiapason].

[9] Non enim inter duo intervalla, cum chordarum sonitus aut vocis cantus factus fuerit, nec in tertia aut sexta aut VII possunt consonantiae fieri, sed, uti supra scriptum est. diatessaron et diapente et ex ordine disdiapason convenientiae ex natura vocis congruentis habent finitiones. Et ei coventus procreantur ex coniunctione sonituum, qui graecephthongi dicuntur.

[9] For neither in the second interval, when the sounding of the strings or the chanting of the voice has been made, nor in the third or sixth or 7th can consonances be formed, but, as has been written above. the diatessaron and the diapente and, in order, the disdiapason have definitions of congruences from the nature of a congruent voice. And these gatherings are produced from the conjunction of sounds, which in Greek are calledphthongi.

Caput Quintum

Chapter Five

[1] Ita ex his indagationibus mathematicis rationibus fiant vasa aerea pro ratione magnitudinis, theatri, eaque ita fabricentur, ut cum tangantur sonitum facere possint inter se diatessaron diapente ex ordine ad disdiapason. Postea inter sedes theatri constitutis cellis ratione musica ibi conlocentur ita, uti nullum parietem tangant circaque habeant locum vacuum et ab summo capite spatium, ponanturque inversa et habeant in parte, quae spectat ad scaenam, suppositos cuneos ne minus altos semipede; contraque eas cellas relinquantur aperturae inferiorum graduum cubilibus longae pedes duo, altae semipede.

[1] Thus, from these investigations by mathematical ratios, bronze vessels are to be made in proportion to the magnitude of the theatre, and fashioned in such a way that, when they are touched, they can produce sound among themselves of a diatessaron, a diapente, in sequence up to the disdiapason. Afterwards, with cells established among the seats of the theatre by musical principle, let them be placed there so that they touch no wall, have empty space around them and a clearance at the top end; and let them be set upside down and have on the side that faces the stage wedges placed beneath, not less than half a foot high; and opposite those cells let openings be left from the benches of the lower tiers, two feet long and half a foot high.

[2] Designationes autem eorum, quibus in locis constituantur, sic explicentur. Si non erit ampla magnitudine theatrum, media altitudinis transversa regio designetur et in ea tredecim cellae duodecim aequalibus intervallis distantes confornicentur, uti ea echea quae supra scripta sunt, ad neten hyperbolaeon sonantia in cellis quae sunt in cornibus extremis, utraque parte prima conlocentur, secunda ab extremis diatessaron ad neten diezeugmenon, tertia diatessaron ad paramesen, quarta ad neten synhemmenon, quinta diatessaron ad mesen, sexta diatessaron ad hypaten meson, in medio unum diatessaron ad hypaten hypaton.

[2] The designations, moreover, of these—namely, in what places they should be established—are to be explained thus. If the theatre will not be of ample magnitude, a transverse region at the middle of the height should be marked out, and in it thirteen cells, spaced at twelve equal intervals, should be vaulted, so that those echea which have been written above, sounding to the neten hyperbolaeon, may be placed first, on either side, in the cells that are in the outermost corners; the second from the extremes, a diatessaron to the neten diezeugmenon; the third, a diatessaron to the paramesen; the fourth, to the neten synhemmenon; the fifth, a diatessaron to the mesen; the sixth, a diatessaron to the hypaten meson; and in the middle one, a diatessaron to the hypaten hypaton.

[3] Ita hac ratiocinatione vox a scaena uti ab centro profusa se circumagens tactuque feriens singulorum vasorum cava excitaverit auctam claritatem et concentu convenientem sibi consonantiam. Sin autem amplior erit magnitudo theatri, tunc altitudo dividatur in partes IIII, uti tres efficiantur regiones cellarum transverse designatae, una harmoniae, altera chromatos, tertia diatoni. Et ab imo quae erit prima, ea ex harmonia conlocetur ita uti in minore theatro supra scriptum est.

[3] Thus by this ratiocination the voice, poured forth from the stage as from a center, wheeling itself around and by its touch striking the hollows of each vessel, will have produced increased clarity and a consonance agreeing with it in concert. But if the magnitude of the theater is larger, then let the height be divided into 4 parts, so that three regions of cells be made, designated transversely: one of harmony, a second of chromatic, a third of diatonic. And from the lowest, the one which will be first, let it be arranged from the harmony, just as in the smaller theater written above.

[4] In mediana autem prima in extremis cornibus ad chromaticen hyperbolaeon habentia sonitum ponantur, in secundis ab his diatessaron ad chromaticen diezeugmenon, in tertiis ad chromaticen synhemmenon, quartis diatessaron ad chromaticen meson, quintis diatessaron ad chromaticen hypaton, sextis ad paramesen, quod et in chromaticen hyperbolaeon diapente et ad chromaticen meson diatessaron habeant consonantiae communitatem.

[4] Moreover, in the middle region, first, at the extreme horns let those be placed which have a sound to the chromatic hyperbolaeon; in the second from these, a diatessaron to the chromatic diezeugmenon; in the third, to the chromatic synhemmenon; in the fourth, a diatessaron to the chromatic meson; in the fifth, a diatessaron to the chromatic hypaton; in the sixth, to the paramesen, since they have a community of consonance both a diapente to the chromatic hyperbolaeon and a diatessaron to the chromatic meson.

[5] In medio nihil est conlocandum, ideo quod sonitum nulla alia qualitas in chromatico genere symphoniae consonantiam potest habere. In summa vero divisione et regione cellarum in cornibus primis ad diatonon hyperbolaeon fabricata vasa sonitu ponantur, in secundis diatessaron ad diatonon , tertiis ad diatonon synhemmenon, quartis diatessaron ad diatonon meson, quintis diatessaron ad diatonon hypaton, sextis diatessaron ad proslambanomenon, in medio ad mesen, quod ea et ad proslambanomenon diapason et ad diatonon hypaton diapente habet symphoniarum communitates.

[5] In the middle nothing is to be placed, because no other quality of sound in the chromatic genus can have consonance of symphony. But in the topmost division and region of the cells, at the first corners let vessels, fashioned for sound, to the Diatonic Hyperbolaeon be placed; at the second, a diatessaron to the Diatonic ; at the third, to the Diatonic synhemmenon; at the fourth, a diatessaron to the Diatonic meson; at the fifth, a diatessaron to the Diatonic hypaton; at the sixth, a diatessaron to the proslambanomenon; in the middle, to the mesen, because it has communities of symphonies both with the proslambanomenon at the diapason and with the Diatonic hypaton at the diapente.

[6] Haec autem si qui voluerit ad perfectum facile perducere, animadvertat in extremo libro diagramma musica ratione designatum, quod Aristoxenus magno vigore et industria generatim divisis modulationibus constitutum reliquit, de quo, si qui ratiocinationibus his attenderit, ad naturas vocis et audientiun delectationes facilius valuerit theatrorum efficere perfectiones.

[6] These things, however, if anyone should wish to bring to perfection easily, let him note at the end of the book a musical diagram designed by reason, which Aristoxenus, with great vigor and industry, left constituted with the modulations divided by genera; concerning which, if anyone shall have attended to these ratiocinations, he will be able more easily to effect the perfections of theaters according to the natures of the voice and the delights of the audiences.

[7] Dicet aliquis forte multa theatra quotannis Romae facta esse neque ullam rationem harum rerum in his fuisse; sed errabit in eo, quod omnia publica lignea theatra tabulationes habent complures, quas necesse est sonare. Hoc vero licet animadvertere etiam ab citharoedis qui, superiore tono cum volunt canere, avertunt se ad scaenae valvas et ita recipiunt ab earum auxilio consonantiam vocis . Cum autem ex solidis rebus thera constituuntur, id est ex structura caementorum, lapide, marmore, quae sonare non possunt, tunc echeis hae rationes sunt explicandae.

[7] Someone will perhaps say that many theatres are made at Rome every year and that in them there has been no method or consideration of these matters; but he will err in this: that all public wooden theatres have several tiers, which of necessity must resound. This indeed one may observe even from the cithara-players who, when they wish to sing in a higher tone, turn themselves toward the doors of the scaena and thus by their aid receive a consonance of the voice . But when theatres are constituted from solid materials, that is, from a structure of cement-work, stone, marble, which cannot sound, then these arrangements with echo-vessels (echea) must be set forth.

[8] Sin autem quaeritur, in quo theatro ea sint facta, Romae non possumus ostendere, sed in Italiae regionibus et in pluribus Graecorum civitatibus. Etiamque auctorem habemus Lucium Mummium qui diruto theatro Corinthiorum ea aenea Romam deportavit et de manubiis ad aedem Lunae dedicavit. Multi etiam sollertes architecti, qui in oppidis non magnis theatra constituerunt, propter inopiam fictilibus doleis ita sonantibus electis hac ratiocinatione compositis perfecerunt utilissimos effectus.

[8] But if it is asked in what theater these were made, we cannot point them out at Rome, but in the regions of Italy and in many cities of the Greeks. And we even have as an authority Lucius Mummius, who, with the theater of the Corinthians torn down, carried those bronzes to Rome and dedicated them, from the spoils, to the temple of Luna. Many also skillful architects, who established theaters in not-great towns, because of want, with earthenware casks chosen as sounding in such a way and arranged by this ratiocination, achieved most useful effects.

Caput Sextum

Chapter Six

[1] Ipsius autem theatri conformatio sic est facienda, uti, quam magna futura est perimetros imi, centro medio conlocato circumagatur linea rutundationis, in eaque quattuor scribantur trigona paribus lateribus; intervallis extremam lineam circinationis, tangant, quibus etiam in duodecim signorum caelestium astrologia ex musica convenientia astrorum ratiocinantur. Ex his trigonis cuius latus fuerit proximum scaenae, ea regione, qua praecidit curvaturam circinationis, ibi finiatur scaenae frons, et ab eo loco per centrum parallelos linea ducatur, quae disiungat proscaenii pulpitum et orchestrae regionem.

[1] But the very configuration of the theater is to be made thus: whatever the perimeter of the lowest part is going to be, with a center placed in the middle, let a line of rotundation be swung around it, and on it let four triangles with equal sides be inscribed; let their intervals touch the outermost line of the circination, by which also, in the twelve signs of the heavens, the astrologers compute from music the consonances of the stars. From these triangles, the one whose side is nearest to the scaena, in the region where it cuts off the curvature of the circination, there let the front of the scaena be bounded; and from that place, through the center, let a parallel line be drawn, which separates the pulpitum of the proscenium and the region of the orchestra.

[2] Ita latius factum fuerit pulpitum quam Graecorum, quod omnes artifices in scaena dant operam, in orchestra autem senatorum sunt sedibus loca designata. Et eius pulpiti altitudo sit ne plus pedum quinque, uti, qui in orchestra sederint, spectare possint omnium agentium gestus. Cunei spectaculorum in theatro ita dividantur, uti anguli trigonorum, qui currunt circum curvaturam circinationis, dirigant ascensus scalasque inter cuneos ad primam praecinctionem; supra autem alternis itineribus superiores cunei medii dirigantur.

[2] Thus the pulpit will have been made broader than that of the Greeks, because all the performers give their work on the stage, whereas in the orchestra there are places marked out with seats for the senators. And let the height of this pulpit be no more than five feet, so that those who shall have sat in the orchestra may be able to behold the gestures of all who are acting. Let the cunei of the spectacles in the theater be divided in such a way that the angles of the triangles, which run around the curvature of the circination, guide the ascents and stairs between the cunei to the first praecinction; but above, by alternating pathways, let the upper middle cunei be aligned.

[3] Hi autem, qui sunt in imo et dirigiunt scalaria, erunt numero VII; reliqui quinque scaenae designabunt compositionem: et unus medius contra se valvas regias habere debet, et qui erunt dextra sinistra, hospitaliorum designabunt compositionem, extremi duo spectabunt itinera versurarum. Gradus spectaculorum, ubi subsellia componantur, gradus ne minus alti sint palmopede, et digito sex; latitudines eorum ne plus pedes duo ~~semis, ne minus pedes duo ~~constituantur.~~~~

[3] Those, however, who are at the lowest and direct the stairways will be in number 7; the remaining five will designate the composition of the scaena: and the one in the middle ought to have opposite itself the royal doors, and those which will be on the right and left will designate the composition of the hospitalia, the two at the extremes will face the routes of the turnings. The steps of the spectator-places, where the benches are set, let the risers be not less high than a palm, and six digits; let their widths be established not more than 2 and a half feet, not less than 2 feet.

[4] Tectum porticus, quod futurum est in summa gradatione cum scaenae altitudine libratum perspiciatur, ideo quod vox crescens aequaliter ad summas gradationes et tectum perveniet. Namque si non erit aequale, quo minus fuerit altum, vox praeripietur ad eam altitudinem, quam perveniet primo.

[4] The roof of the portico, which is to be seen as balanced with the height of the stage at the topmost gradation, is for this reason: a voice, as it grows, will reach equally to the highest gradations and the roof. For if it is not equal, the lower it is, the voice will be preempted at that height which it first reaches.

[5] Orchestra inter grados imos quod diametron habuerit, eius sexta pars sumatur, et in cornibus, utrumque aeditus eius mensurae perpendiculum interiores sedes praecidantur, et quae praecisio fuerit, ibi constituantur itinerum supercilia; ita enim satis altitudinem habebunt eorum confornicationes.

[5] The orchestra, whatever diameter it shall have between the lowest tiers, let its sixth part be taken; and at the horns, let each aditus, by a perpendicular of that measure, cut off the interior seats, and where the excision shall be, there let the brows of the passages be established; for thus their confornications will have sufficient height.

[6] Scaenae longitudo ad orchestrae diametron duplex fieri debet. Podii altitudo ab libramento pulpiti cum corona et lysi duodecumam orchestrae diametri. Supra podium columnae cum capitulis et spiris altae quarta parte eiusdem diametri; epistylia et ornamenta earum columnarum altitudinis quinta parte.

[6] The length of the stage ought to be made double the diameter of the orchestra. The height of the podium from the level of the pulpitum, with the corona and the lysis, is the twelfth part of the orchestra’s diameter. Above the podium, columns with capitals and spirae are in height a fourth part of the same diameter; the epistyles and the ornaments are a fifth part of the height of those columns.

Pluteum insuper cum unda et corona inferioris plutei dimidia parte. Supra id pluteum columnae quarta parte minore altitudine sint quam inferiores; epistylium et ornamenta earum columnarum quinta parte. Item si tertia episcenos futura erit, mediani plutei summum sit dimidia parte; columnae summae medianarum minus altae sint quarta parte; epistylia cum coronis earum columnarum item habeant altitudinis quintam partem.

The pluteum above, with wave-molding and corona, should be one half of the lower pluteum. Above that pluteum, let the columns be less in height by a fourth part than the lower ones; let the epistyle and the ornaments of those columns be a fifth part. Likewise, if a third episkenion is to be made, let the top of the middle pluteum be by one half; let the topmost columns be less high than the middle ones by a fourth part; let the epistyles with the coronas of those columns likewise have a fifth part of the height.

[7] Nec tamen in omnibus theatris symmetriae ad omnis rationes et effectus possunt respondere, sed oportet architectum animadvertere, quibus proportionibus necesse sit sequi symmetriam et quibus ad loci naturam aut magnitudinem operis temperari. Sunt enim res quas et in pusillo et in magno theatro necesse est eadem magnitudine fieri propter usum, uti gradus, diazumata, pluteos, itinera, ascensus, pulpita, tribunalia et si qua alia intercurrunt, ex quibus necessitas cogit discedere ab symmetria, ne inpediatur usus. Non minus si qua exiguitas copiarum, id est marmoris, materiae reliquarumque rerum, quae parantur, in opere defuerint, paulum demere aut adicere, dum id ne nimium inprobe fiat sed cum sensu, non erit alienum.

[7] Nor, however, in all theaters can the symmetries answer to every rationale and effect, but the architect ought to observe with what proportions it is necessary to follow symmetry, and with what proportions it must be tempered to the nature of the place or the magnitude of the work. For there are things which, both in a small and in a great theater, must be made of the same size on account of use, such as steps, diazomata, plutei, passages, ascents, stages, tribunals, and whatever other things occur, from which necessity compels a departure from symmetry, lest use be impeded. No less, if any scantiness of supplies—that is, of marble, of material, and of the remaining things that are prepared—should be lacking in the work, to take away or to add a little, provided that this not be done too excessively but with discernment, will not be out of place.

Hoc autem erit, si architectus erit usu peritus, praeterea ingenio mobili sollertiaque non fuerit viduatus.

This, however, will be the case, if the architect is experienced in use, and, moreover, has not been bereft of nimble ingenuity and skill.

[8] Ipsae autem scaenae suas habent rationes explicitas ita, uti mediae valvae ornatus habeant aulae regiae, dextra ac sinistra hospitalia, secundum autem spatia ad ornatus comparata, quae loca Graeciperiactus dicunt ab eo, quod machinae sunt in his locis versatiles trigonos habentes in singula tres species ornationis, quae, cum aut fabularum mutationes sunt futura seu deorum adventus, cum tonitribus repentinis ea versentur mutentque speciem ornationis in frontes. Secundum ea loca versurae sunt procurrentes, quae efficiunt una a foro, altera a peregre aditus in scaenam.

[8] But the scenes themselves have their own detailed arrangements thus: that the middle valves bear the adornment of a royal hall, on the right and left guest-quarters; and next, spaces prepared for adornments, which places the Greeks callperiactus, from the fact that in these places there are machines, revolving, having trigonal forms, each with three kinds of ornamentation; and whenever either changes of the plays are to occur or advents of gods, with sudden thunders, they are turned and change the aspect of the ornamentation on the fronts. Next to these places are projecting turnings, which produce entrances into the scene—one from the forum, the other from abroad.

[9] Genera autem sunt scaenarum tria: unum quod dicitur tragicum, alterum comicum, tertium satyricum. Horum autem ornatus sunt inter se dissimili disparique ratione, quod tragicae deformantur columnis et fastigiis et signis reliquisque regalibus rebus; comicae autem aedificiorum privatorum et maenianorum habent speciem profectusque fenestris dispositos imitatione communium aedificiorum rationibus; satyricae vero ornantur arboribus, speluncis, montibus reliquisque agrestibus rebus in topeodi speciem deformati.

[9] The genera of scenes, moreover, are three: one which is called tragic, the second comic, the third satyric. The ornaments of these are among themselves of a dissimilar and unequal rationale, in that tragic [scenes] are formed with columns and pediments and statues and the remaining royal things; but comic [scenes] have the aspect of private buildings and of balconies, and projections arranged with windows, in imitation according to the principles of common buildings; but satyric [scenes] are adorned with trees, caves, mountains, and the remaining rustic things, fashioned into a topiary appearance.

Caput Septimum

Chapter Seven

[1] In Graecorum theatris non omnia isdem rationibus sunt facienda, quod primum in ima circinatione, ut in latino trigonorum IIII, in eo quadratorum trium anguli circinationis lineam tangunt, et cuius quadrati latus est proximum scaenae praeciditque curvaturam circinationis, ea regione designatur finitio proscaenii. Et ab ea regione ad extremam circinationem curvaturae parallelos linea designatur, in qua constituitur frons scaenae, per centrumque orchestrae proscaenii regione parallelos linea describitur, et qua secat circinationis lineas dextra ac sinistra in cornibus hemicycli centra signantur. Et circino collocato in dextra ab intervallo sinistro circumagatur circinatio ad proscaenii sinistram partem; item centro conlocato in sinistro cornu ab intervallo dextro circumagitur ad proscaenii dextram partem.

[1] In the theatres of the Greeks not all things must be done by the same methods, because first, in the lowest circination, as in the Latin one of 4 triangles, in it three angles of the squares touch the line of circination, and the side of that square which is nearest to the stage and cuts off the curvature of the circination, in that region the boundary of the proscaenium is designated. And from that region to the outermost circination of the curvature a parallel line is marked, on which the front of the stage is set; and through the center of the orchestra, from the region of the proscaenium, a parallel line is drawn, and where it cuts the lines of circination on the right and left, at the horns of the hemicycle the centers are marked. And with the compass placed at the right, at an interval from the left, let the circination be swung round to the left part of the proscaenium; likewise, with the center placed in the left horn, at an interval from the right, it is swung round to the right part of the proscaenium.

[2] Ita tribus centris hac descriptione ampliorem habent orchestram Graeci et scaenam recessiorem minoreque latitudine pulpitum, quodlogeion appellant, ideo quod <apud> eos tragici et comici actores in scaena peragunt, reliqui autem artifices suas per orchestram praestant actiones; itaque ex eo scaenici et thymelici graece separatim nominantur. Eius loci altitudo non minus debet esse pedum X, non plus duodecim. Gradationes scalarum inter cuneos et sedes contra quadratorum angulos dirigantur ad primam praecinctionem, a praecinctione inter eas iterum mediae dirigantur, et ad summam quotiens praecinguntur, altero tanto semper amplificantur.

[2] Thus, with this delineation, the Greeks have a more ample orchestra and a more recessed scaena, and a platform of smaller breadth, which they call thelogeion, because <apud> them the tragic and comic actors perform upon the scaena, while the remaining artists present their actions through the orchestra; and so from this the scenic and thymelic are in Greek named separately. The height of that place ought to be not less than 10 feet, not more than twelve. The gradations of the stairs between the wedges and the seats, opposite the angles of the squares, are to be directed to the first praecinction; from the praecinction, between them, again the middle ones are to be directed; and to the top, as often as they are girdled with praecinctions, they are always enlarged by as much again.

Caput Octavum

Chapter Eight

[1] Cum haec omnia summa cura sollertiaque explicata sunt, tunc etiam diligentius. Est enim advertendum, uti sit electus locus, in quo leniter adplicet se vox neque repulsa resiliens incertas auribus referat significationes. Sunt enim nonnulli loci naturaliter inpedientes vocis motus, uti dissonantes, qui graece dicunturcatechountes circumsonantes, qui apud eos nominantur periechountes item resonantes, qui dicuntur antechountes consonantesque, quos appellant synechountas. Dissonantes sunt, in quibus vox prima, cum est elata in altitudinem, offensa superioribus solidis corporibus repulsaque residens in imo opprimit insequentis vocis elationem;

[1] When all these things have been unfolded with the greatest care and skill, then even more carefully. For it must be observed that a site be chosen where the voice gently applies itself, and, not repelled and rebounding, does not carry back to the ears uncertain significations. For there are some places that naturally impede the motions of the voice, such as dissonant ones, which in Greek are calledcatechountes; surrounding-sounding ones, which among them are named periechountes; likewise resonating ones, which are called antechountes; and consonant ones, which they call synechountas. Dissonant are those in which the first voice, when it is lifted to altitude, meeting the upper solid bodies and, repelled, settling down in the depth, oppresses the elevation of the following voice;

[2] circumsonantes autem, in quibus circumvagando coacta exsolvens in medio sine extremis casibus sonans ibi extinguatur incerta verborum significatione; resonantes vero, in quibus, cum in solido tactu percussa resiliant, imagines exprimendo novissimos casus duplices faciant auditu; item consonantes sunt, in quibus ab imis auxiliata cum incremento scandens egrediatur ad aures disserta verborum claritate. Ita si in locorum electione fuerit diligens animadversio, emendatus erit prudentia ad utilitatem in theatris vocis effectus. Formarum autem descriptiones inter se discriminibus his erunt notatae, uti, quae ex quadratis designentur, Graecorum habeant usus, latine paribus lateribus trigonorum.

[2] circum-sonant, however, are those in which, by wandering around, the voice, being compelled and loosening itself, sounding in the middle without terminal cadences, is there extinguished, with an uncertain signification of the words; resonant, by contrast, are those in which, when, having been struck upon a solid contact, they rebound, and by expressing images make the newest cadences double to the hearing; likewise they are consonant, in which, aided from the depths, with an increment as it ascends, it goes forth to the ears with an articulate clarity of words. Thus, if there is diligent observation in the choice of places, the effect of the voice in theaters will be corrected by prudence for utility. But the descriptions of the forms will be marked among themselves by these discriminations, such that those which are delineated from squares may have the uses of the Greeks, in Latin of triangles with equal sides.

Ita his praescriptionibus qui voluerit uti, emendatas efficiet theatrorum perfectiones.

Thus, by these prescriptions, whoever shall wish to use them will effect corrected perfections of theaters.

Caput Nonum

Chapter Nine

[1] Post scaenam porticus sunt constituendae, uti, cum imbres repentini ludos interpellaverint, habeat populus, quo se recipiat ex theatro, choragiaque laxamentum habeant ad comparandum. Uti sunt porticus Pompeianae, itemque Athenis porticus Eumeniae Patrisque Liberi fanum et exeuntibus e theatro sinistra parte odeum, quod Themistocles columnis lapideis dispositus navium malis et antemnis e spoliis Persicis pertexit (idem autem etiam incensum Mithridatico bello rex Ariobarzanes restituit); Smyrnae Stratoniceum; Trallibus porticus ex utraque parte, ut scaenae, supra stadium; ceterisque civitatibus, quae diligentiores habuerunt architectos, circa theatra sunt porticus et ambulationes.

[1] Behind the scene, porticoes are to be set up, so that, when sudden showers interrupt the shows, the people may have a place to which to withdraw from the theater, and the choragia may have leeway for preparation. Such are the Pompeian porticoes, and likewise at Athens the Eumenian portico and the shrine of Father Liber, and, for those going out of the theater on the left side, the Odeum, which Themistocles, stone columns having been set in order, roofed over with the masts and yards of ships from the Persian spoils (the same, moreover, after it was burned in the Mithridatic war, King Ariobarzanes restored); at Smyrna the Stratoniceum; at Tralles porticoes on either side, like the scaenae, above the stadium; and in the other cities which have had more diligent architects, around the theaters there are porticoes and ambulations.

[2] Quae videntur ita oportere conlocari, uti duplices sint habeantque exteriores columnas doricas cum epistyliis et ornamentis ex ratione modulationis perfectas. Latitudines autem earum ita oportere fieri videntur, uti, quanta altitudo columnae fuerit exteriores, tantam latitudinem habeant ab inferiore parte columnarum extremarum ad medias et a medianis ad parietes qui circumcludunt porticus ambulationes. Medianae autem columnae quinta parte altiores sint quam exteriores, sed aut ionico aut corinthio genere deformentur.

[2] These seem to have to be arranged in such a way, that they be double and have exterior Doric columns with epistyles and ornaments perfected according to the rationale of modulation. The widths of them seem to have to be made thus: that, whatever the height of the outer columns shall have been, they have just so much width from the lower part of the outermost columns to the middle ones, and from the middle ones to the walls which enclose the ambulations of the porticoes. The middle columns, moreover, should be higher by a fifth than the outer ones, but be formed either in the Ionic or the Corinthian kind.

[3] Columnarum autem proportiones et symmetriae non erunt isdem rationibus quibus in aedibus sacris scripsi; aliam enim in deorum templis debent habere gravitatem, aliam in porticibus et ceteris operibus subtilitatem. Itaque si dorici generis erunt columnae, dimetiantur earum altitudines cum capitulis in partes XV. Ex eis partibus una constituatur et fiat modulus, ad cuius moduli rationem omnis operis erit explicatio. Et in imo columnae crassitudo fiat duorum modulorum; intercolumnium quinque et moduli dimidia parte; altitudo columnae praeter capitulum XIIII modulorum; capituli altitudo moduli unius, latitudo modulorum duorum et moduli sextae partis.

[3] But the proportions and symmetries of the columns will not be by the same ratios as I have written for sacred buildings; for in the temples of the gods they ought to have one gravity, in porticoes and the other works another subtlety. Therefore, if the columns are of the Doric kind, let their heights together with the capitals be measured off into 15 parts. Of these parts let one be established and made the modulus, according to whose modulus the entire work will be set out. And at the bottom of the column let the thickness be 2 moduli; the intercolumniation 5 and a half moduli; the height of the column, apart from the capital, 14 moduli; the height of the capital 1 modulus, the breadth 2 and one-sixth moduli.

Ceteri operis modulationes, uti in aedibus sacris in libro IIII scriptum est, ita perficiantur.

The other modulations of the work, as has been written in the sacred edifices in book 4, are to be completed thus.

[4] Sin autem ionicae columnae fient, scapus praeter spiram et capitulum in octo et dimidiam partem dividatur, et ex his una crassitudini columnae detur; cum plintho dimidia crassitudine constituatur; capituli ratio ita fiat, uti in libro tertio est demonstratum. Si corinthia erit, scapus et spira uti in ionica; capitulum autem, quemadmodum in quarto libro est scriptum, ita habeant rationem. Stylobatisque adiectio quae fit per scabillos inpares, ex descriptione, quae supra scripta est in libro tertio, sumatur.

[4] But if Ionic columns are to be made, let the shaft, apart from the spira and the capital, be divided into eight and a half parts, and of these let one be given to the thickness of the column; let the with the plinth be set at half the thickness; let the proportion of the capital be made as is demonstrated in book 3. If it is Corinthian, let the shaft and the spira be as in the Ionic; but let the capital have its proportion just as is written in book 4. And the addition to the stylobates which is made by means of odd scabelli is to be taken from the description which is written above in book 3.

Epistylia, coronae ceteraque omnia ad columnarum rationem ex scriptis voluminum superiorum explicentur.

Let the epistyles, the coronae, and all the other things be explained, according to the proportion of the columns, from the writings of the preceding volumes.

[5] Media vero spatia quae erunt subdiu inter porticus, adornanda viridibus videntur, quod hypaethroe ambulationes habent magnam salubritatem. Et primum oculorum, quod ex viridibus subtilis et extenuatus aer propter motionem corporis influens perlimat speciem et ita auferens ex oculis umorem crassum, aciem tenuem et acutam speciem relinquit; praeterea, cum corpus motionibus in ambulatione calescat, umores ex membris aer exsugendo inminuit plenitates extenuatque dissipando quod plus inest quam corpus potest sustinere.

[5] But the middle spaces which will be in the open air between the porticoes seem to be adorned with greenery, because hypaethral ambulations have great salubrity. And first, for the eyes: from the greenery the subtle and attenuated air, flowing in on account of the movement of the body, polishes the sight and thus, removing the thick humor from the eyes, leaves a fine edge and a sharp sight; moreover, when the body grows warm through movements in ambulation, the air, by sucking out the humors from the limbs, diminishes the plenitudes and attenuates them by dissipating what is present in excess beyond what the body can sustain.

[6] Hoc autem ita esse ex eo licet animadvertere, quod, sub tectis cum sint aquarum fontes aut etiam sub terra palustris abundantia, ex his nullus surgit umor nebulosus, sed in apertis hypaethrisque locis, cum sol oriens vapore tangat mundum, ex umidis et abundantius excitat umores et exconglobatos in altitudinem tollit. Ergo si ita videtur, uti in hypaethris locis ab aere umores ex corporibus exsugantur molestiores, quemadmodum ex terra per nebulas videntur, non puto dubium esse, quin amplissimas et ornatissimas subdiu hypaethrisque conlocari oporteat in civitatibus ambulationes.

[6] This, moreover, may be observed from the fact that, when under roofs there are springs of water, or even a marshy abundance beneath the ground, from these no nebulous moisture rises; but in open and hypaethral places, when the rising sun touches the world with warmth, from the wet things it more abundantly excites the humors and, conglobated, lifts them on high. Therefore, if it seems good that in hypaethral places the air should suck out from bodies the more troublesome humors, just as from the earth they are seen [to be drawn] through mists, I do not think there is any doubt that in cities the most ample and most adorned ambulations ought to be set under the open sky and hypaethral.

[7] Eae autem uti sint semper siccae et non lutosae, sic erit faciendum. Fodiantur et exinaniantur quam altissime. Dextra atque sinistra structiles cloacae fiant, inque eatum parietibus qui ad ambulationem spectaverint, tubuli instruantur inclinati fastigio.

[7] But in order that these may be always dry and not muddy, this will be done as follows. Let them be dug and emptied out as deep as possible. On the right and on the left, constructed sewers are to be made, and into these, in the walls which will look toward the ambulation, little pipes are to be installed, inclined with a pitch.

In cloacis his perfectis compleantur ea loca carbonibus, deinde insuper sabulone eae ambulationes sternantur et exaequentur. Ita propter carbonum raritatem naturalem et tubulorum in cloacas instructionem excipientur aquarum abundantiae, et ita siccae et sine umore perfectae fuerint ambulationes.

With these sewers completed, let those places be filled with charcoal; then, above, let those promenades be paved with sand and leveled. Thus, by reason of the natural rarity (porosity) of the charcoal and the installation of tubules into the sewers, the abundances of waters will be taken up, and so the promenades will be finished dry and without moisture.

[8] Praeterea in his operibus thensauri sunt civitatibus in necessariis rebus a moribus constituti. In conclusionibus enim reliqui omnes faciliores sunt apparatus quam lignorum. Sal enim facile ante inportatur, frumenta publice privatimque expeditius congeruntur, et si defit, holeribus, carne seu leguminibus defenditur, aquae fossuris puteorum et de caelo repentinis tempestatibus ex tegulis excipiuntur.

[8] Moreover, in these works there are treasuries for the cities in necessary matters, instituted by custom. For during blockades all the other supplies are easier preparations than those of wood. Salt, indeed, is easily imported beforehand; grains, both publicly and privately, are more expeditiously amassed; and if that is lacking, it is made up for by vegetables, meat, or legumes; water is obtained by digging wells and is caught from the sky, in sudden storms, from roof-tiles.

De lignatione quae maxime necessaria est ad cibum quoquendum, difficilis et molesta est apparatio, quod et tarde conportatur et plus consumitur.

On lignation, which is most necessary for cooking food, the preparation is difficult and troublesome, because it is both brought in slowly and consumed in greater quantity.

[9] In eiusmodi temporibus tunc eae ambulationes aperiuntur et mensurae tributim singulis capitibus designantur. Ita duas res egregias hypaethra ambulationem praestant, unam in pace salubritatis, alteram in bello salutis. Ergo his rationibus ambulationum explicationes non solum post scaenam theatri, sed etiam omnium deorum templis effectae magnas civitatibus praestare poterunt utilitates.

[9] In times of this sort, then, those ambulations are opened, and measures are designated by tribes for each head. Thus the hypaethral ambulation affords two outstanding things: one, in peace, of healthfulness; the other, in war, of safety. Therefore, on these principles, the unfoldings of ambulations, effected not only behind the scene of the theatre but also at the temples of all the gods, will be able to furnish great utilities to the cities.

Quoniam haec nobis satis videntur esse exposita, nunc insequentur balinearum dispositionum demonstrationes.

Since these things seem to us to have been set forth sufficiently, now demonstrations of the dispositions of baths will follow.

Caput Decimum

Chapter Ten

[1] Primum eligendus locus est quam calidissimus, id est aversus ab septentrione et aquilone. Ipsa autem caldaria tepidariaque lumen habeant ab occidente hiberno, si autem natura loci inpedierit, utique a meridie, quod maxime tempus lavandi a meridiano ad vesperum est constitutum. Et item est animadvertendum, uti caldaria muliebria et virilia coniuncta et in isdem regionibus sint conlocata; sic enim efficietur, ut in vasaria et hypocausis communis sit eorum utrisque.

[1] First, the site must be chosen as warm as possible, that is, turned away from the North and the North-wind. The caldaria and tepidaria themselves should have light from the winter West; but if the nature of the place shall impede it, then certainly from the South, since the chief time of bathing is fixed from midday to evening. And likewise it must be noted that the women’s and the men’s hot rooms be adjoining and placed in the same regions; thus it will be brought about that in the vessel-rooms (boiler rooms) and in the hypocausts the service is common to them both.

Aenea supra hypocausim tria sunt componenda, unum caldarium, alterum tepidarium, tertium frigidarium, et ita conlocanda, uti, ex tepidario in caldarium quantum aquae caldae exierit, influat de frigidario in tepidarium ad eundem modum, testudinesque alveolorum ex communi hypocausi calfaciantur.

Above the hypocaust three bronze vessels are to be set up: one a caldarium, another a tepidarium, the third a frigidarium; and they are to be arranged in such a way that, from the tepidarium into the caldarium, as much hot water as has gone out flows in, and from the frigidarium into the tepidarium in the same manner, and that the vaults (testudines) of the basins be heated from a common hypocaust.

[2] Suspensurae caldariorum ita sunt faciendae, ut primum sesquipedalibus tegulis solum sternatur inclinatum ad hypocausim, uti pila cum mittatur, non possit intro resistere, sed rursus redeat ad praefurnium ipsa per se; ita flamma facilius pervagabitur sub suspensione. Supraque laterculis besalibus pilae struantur ita dispositae, uti bipedales tegulae possint supra esse conlocatae; altitudinem autem pilae habeant pedes duo. Eaeque struantur argilla cum capillo subacta, supraque conlocentur tegulae bipedales quae sustineant pavimentum.

[2] The suspensions of the caldaria are to be made thus: first the floor is to be laid with sesquipedalian tiles, sloped toward the hypocaust, so that, when a ball is sent, it cannot come to rest inside, but will of itself roll back to the praefurnium; thus the flame will range more easily beneath the suspension. And above, little piers (pilae) are to be built of bessal bricks, arranged in such a way that bipedal tiles can be set upon them above; the piers, moreover, should have a height of two feet. And let them be built with clay worked with hair, and on top let bipedal tiles be placed which may support the pavement.

[3] Concamarationes vero si ex structura factae fuerint, erunt utiliores; sin autem contignationes fuerint, figlinum opus subiciatur. Sed hoc ita erit faciendum. Regulae ferreae aut arcus fiant, eaeque uncinis ferreis ad contignationem suspendantur quam creberrimis; eaeque regulae sive arcus ita disponantur, uti tegulae sine marginibus sedere in duabus invehique possint, et ita totae concamerationes in ferro nintentes sint perfectae.

[3] The vaultings, indeed, if they shall have been made of masonry, will be more serviceable; but if they shall be floor-structures, let ceramic (tiling) work be put beneath. But this is to be done thus. Let iron bars or arches be made, and let them be suspended from the flooring by iron hooks as very thickly set as possible; and let these bars or arches be so arranged that tiles without rims may be able to sit upon two and be slid in, and thus let the whole concamerations, resting on iron, be completed.

Earumque camararum superiora coagmenta ex argilla cum capillo subacta liniantur; inferior autem pars, quae ad pavimentum spectat, primum testa cum calce trullizetur, deinde opere albario sive tectorio poliatur. Eaeque camarae in caldariis si duplices factae fuerint, meliorem habebunt usum; non enim a vapore umor corrumpere poterit materiem contignationis, sed inter duas camaras vagabitur.

And the upper joints of those vaults should be coated with clay kneaded with hair; but the lower part, which looks toward the pavement, should first be troweled with potsherd mixed with lime, then polished with whitework or plastering. And those vaults in the caldaria, if made double, will have better use; for the moisture from the vapor will not be able to corrupt the material of the flooring, but will wander between the two vaults.

[4] Magnitudines autem balneorum videntur fieri pro copia hominum; sint ita conpositae. Quanta longitudo fuerit tertia dempta, latitudo sit, praeter scholam labri et alvei. Labrum utique sub lumine faciundum videtur, ne stantes circum suis umbris obscurent lucem.

[4] The magnitudes of the baths seem to be made according to the abundance of people; let them be composed thus. Let the width be as much as the length will be with a third deducted, besides the schola of the labrum and of the alveus. The labrum, assuredly, seems to be made beneath a light, lest those standing around obscure the light with their own shadows.

Scholas autem labrorum ita fuerit oportet spatiosas, uti, cum priores occupaverint loca circum, spectantes reliqui recte stare possint. Alvei autem latitudo inter parietem et pluteum ne minus sit pedes senos, ut gradus inferior inde auferat et pulvinus duos pedes.

But the scholae of the labra ought to be made so spacious that, when the first-comers have occupied the places around, the remaining onlookers can stand properly. And the width of the trough (alveus) between the wall and the parapet (pluteus) should be not less than six feet, so that the lower step and the cushion (pulvinus) may take up two feet from it.

[5] Laconicum sudationesque sunt coniungendae tepidario; eaeque quam latae fuerint, tantam altitudinem habeant ad imam curvaturam hemisphaerii. Mediumque lumen in hemisphaerio relinquatur, ex eoque clypeom aeneum catenis pendeat, per cuius reductiones et dimissiones perficietur sudationis temperatura. Ipsumque ad circinum fieri oportere videtur, ut aequaliter a medio flammae vaporisque vis per curvaturae rutundationes pervagetur.

[5] The Laconicum and the sudatories are to be joined to the tepidarium; and they should have, as wide as they are, so much height up to the lowest curvature of the hemisphere. And a central opening (lumen) should be left in the hemisphere, and from it a bronze shield should hang by chains, by the raising and lowering of which the temperature of the sweating will be effected. And it seems proper that it be made to the compass, so that equally from the center the force of flame and vapor may range through the rotundations of the curvature.

Caput Undecimum

Chapter Eleven

[1] Nunc mihi videtur, tametsi non sint italicae consuetudinis palaestrarum aedificationes, traditae tamen, explicare et quemadmodum apud Graecos constituantur, monstrare. In palaestris peristylia quadrata sive oblonga ita sint facienda, uti duorum stadiorum habeant ambulationis circuitionem, quod Graeci vocantdiaulon, ex quibus tres porticus simplices disponantur, quarta quae ad meridianas regiones est conversa, duplex, uti cum tempestates ventosae sint, non possit aspergo in interiorem partem pervenire.

[1] Now it seems to me, although the constructions of palaestrae are not of Italian custom, nevertheless to set forth those handed down, and to show how they are established among the Greeks. In the palaestrae, the peristyles, square or oblong, should be made in such a way as to have a walking circuit of two stadia, which the Greeks call adiaulon; of these, three porticoes should be arranged single, the fourth, which is turned toward the southern regions, double, so that when the weather is windy, the spray cannot reach the inner part.

[2] Constituantur autem in tribus porticibus exhedrae spatiosae, habentes sedes, in quibus philosophi, rhetores reliquique, qui studiis delectantur, sedentes disputare possint. In duplici autem porticu conlocentur haec membra: ephebeum in medio (hoc autem est exhedra amplissima cum sedibus) tertia parte longior sit quam lata; sub dextro coryceum, deinde proxime conisterium, a conisterio in versura porticus frigida lavatio, quam Graeciloutron vocitant; ad sinistram ephebei elaeothesium, proxime autem elaeothesium frigidarium, ab eoque iter in propnigeum in versura porticus. Proxime autem introrsus e regione frigidarii conlocetur concamerata sudatio longitudine duplex quam latitudo, quae habeat in versuris ex una parte laconicum ad eundem modum, uti quam supra scriptum est, compositum, ex adverso laconici caldam lavationem.

[2] But in the three porticoes let spacious exedrae be established, having seats, in which philosophers, rhetors, and the rest who delight in studies may be able, sitting, to dispute. And in the double portico let these members be set: the ephebeum in the middle (this, moreover, is the most ample exedra with seats) should be longer by a third than it is wide; on the right, the coryceum, then next the conisterium; from the conisterium, at the turn of the portico, a cold washing-room, which the Greeks call the loutron; to the left of the ephebeum, the elaeothesium, and next to the elaeothesium the frigidarium, and from it a passage into the propnigeum at the turn of the portico. Next, inwardly, opposite the frigidarium, let there be placed a vaulted sudatory, of length double the width, which shall have in the bends on one side a laconicum arranged in the same manner as has been written above, and opposite the laconicum a hot washing-room.

In palaestra peristylia, quemadmodum supra scriptum est, ita debent esse perfecta distributa.

In the palestra the peristyles, as has been written above, thus ought to be perfectly distributed.

[3] Extra autem disponantur porticus tres, una ex peristylo exeuntibus, duae dextra atque sinistra stadiatae, ex quibus una quae spectaverit ad septentrionem, perficiatur duplex amplissima latitudine, altera simplex, ita facta, uti in partibus, quae fuerint circa parietes et quae erit ad columnas, margines habeant uti semitas non minus pedum denum mediumque excavatum, uti gradus sint in descensu marginibus sesquipedem ad planitiem, quae planities sit non minus pedes XII, ita qui vestiti ambulaverint circum in marginibus, non inpedientur ab unctis se exercentibus.

[3] Outside, moreover, let three porticoes be arranged: one leading out from the peristyle, and two, right and left, stadiate; of which the one that shall face the north is to be completed double, with a most ample breadth, the other single, made in such a way that in the parts which shall be around the walls and that which shall be by the columns they have margins like footpaths not less than 10 feet, and the middle hollowed out, so that there are steps in the descent from the margins 1.5 feet to the level area, which level area should be not less than 12 feet, so that those clothed who walk around on the margins are not impeded by the oiled men exercising themselves.

[4] Haec autem porticusxystos apud Graecos vocitatur, quod athletae per hiberna tempora in tectis stadiis exercentur. Proxime autem xystum et duplicem porticum designentur hypaethroe ambulationes, quas Graeci paradromidas, nostri xysta appellant, in quas per hiemem ex xysto sereno caelo athletae prodeuntes exercentur. Faciunda autem xysta sic videntur, ut sint inter duas porticus silvae aut platanones, et in his perficiantur inter arbores ambulationes ibique ex opere signino stationes.

[4] This portico, however, is calledxystos among the Greeks, because athletes during the winter times are exercised in roofed stadia. Next to the xystus and the double portico let hypaethral promenades be laid out, which the Greeks call paradromides, our people call xysta; into these, in winter, coming forth from the xystus with the sky clear, the athletes are exercised. The xysta, moreover, seem to be made thus: that between two porticoes there be groves or plane-tree plantations, and in these, between the trees, promenades be completed, and there stations of signine work.

Post xystum autem stadium ita figuratum, ut possint hominum copiae cum laxamento athletas certantes spectare. Quae in moenibus necessaria videbantur esse, ut apte disponantur, perscripsi.

After the xystus, moreover, a stadium shaped so that multitudes of people can, with leeway, watch the athletes competing. The things that seemed necessary within the walls, in order that they may be suitably arranged, I have written out in full.

Caput Duodecimum

Chapter Twelve

[1] De opportunitate autem portuum non est praetermittendum sed, quibus rationibus tueantur naves in his ab tempestatibus, explicandum. Hi autem naturaliter si sint bene positi habeantque acroteria sive pronunturia procurrentia, ex quibus introrsus curvaturae sive versurae ex loci natura fuerint conformatae, maximas utilitates videntur habere. Circum enim portictus sive navalia sunt facienda sive ex porticibus aditus emporia, turresque ex utraque parte conlocandae, ex quibus catenae traduci per machinas possint.

[1] On the opportuneness of ports, moreover, it is not to be passed over, but it must be explained by what methods ships are protected in them from tempests. These, however, naturally, if they are well positioned and have acroteria or promontories projecting, from which inward curvatures or turnings have been shaped according to the nature of the place, seem to have the greatest advantages. For all around either porticoes or dockyards are to be made, or approaches from the porticoes emporia, and towers are to be set on either side, from which chains can be drawn across by machines.

[2] Sin autem non naturalem locum neque idoneum ad tuendas ab tempestatibus naves habuerimus, ita videtur esse faciendum, uti, si nullum flumen in his locis inpedierit sed erit ex una parte statio, tunc ex altera parte structuris sive aggeribus expediantur progressus, et ita conformandae portuum conclusiones. Eae autem structurae, quae in aqua sunt futurae, videntur sic esse faciendae, uti portetur pulvis a regionibus, quae sunt a Cumis continuatae ad promunturium Minervae, isque misceatur, uti in mortario duo ad unum respondeant.

[2] But if we shall not have a natural place nor one suitable for guarding ships from storms, it seems it must be done thus: if no river will hinder in these places but there will be an anchorage on one side, then on the other side let advances be executed by structures or embankments, and thus let the closures of the harbors be shaped. And those structures which are going to be in the water seem to be made thus: let powder be brought from the regions which are continuous from Cumae to the Promontory of Minerva, and let it be mixed so that in the mortar two correspond to one.

[3] Deinde tunc in eo loco, qui definitus erit, arcae stipitibus robusteis et catenis inclusae in aquam demittendae destinandaeque firmiter; deinde inter ea ex trastilis inferior pars sub aqua exaequanda et purganda, et caementis ex mortario materia mixta, quemadmodum supra scriptum est, ibi congerendum, donique conpleatur structurae spatium, quod fuerit inter arcas. Hoc autem munus naturale habent ea loca, quae supra scripta sunt.

[3] Then, in that place which shall have been designated, caissons enclosed with robust stakes and with chains are to be let down into the water and fastened firmly; then, between them, the lower part made of trellis-work is to be leveled and cleansed under water, and rubble-stone set in mortar, the material mixed as written above, is to be heaped up there, until the space of the structure which is between the caissons is filled. Moreover, those places which have been written above have this natural endowment.

Sin autem propter fluctus aut impetus aperti pelagi destinae arcas non potuerint continere, tunc ab ipsa terra sive crepidine pulvinus quam firmissime struatur, isque pulvinus exaequata struatur planitia minus quam dimidiae partis, reliquum quod est proxime litus, proclinatum latus habeat.

But if, on account of the waves or the onsets of the open sea, the appointed caissons cannot be made to hold, then from the very land or from the quay-edge a pulvinus (berm) should be constructed as firmly as possible; and this pulvinus should be built with a leveled flat for less than one half, while the remainder, which is nearest the shore, should have a sloping side.

[4] Deinde ad ipsam aquam et latera pulvino circiter sesquipedales margines struantur aequilibres ex planitia, quae est supra scripta; tunc proclinatio ea impleatur harena et exaequetur cum margine et planitia pulvini. Deinde insuper eam exaequationem pila quam magna constituta fuerit, ibi struatur; eaque, cum erit extructa relinquatur ne minus duos mensis, ut siccescat. Tunc autem, succidatur margo quae sustinet harenam; ita harena fluctibus subruta efficiet in mare pilae praecipitationem.

[4] Then along the water itself and the sides, margins about a foot and a half wide should be built level with the flat surface of the embankment (as written above); then that proclination should be filled with sand and made level with the margin and the flat surface of the embankment. Then on top of that leveling, let the pile, of whatever magnitude shall have been determined, be built there; and when it has been constructed, let it be left not less than two months, so that it may dry. Then, however, let the margin which supports the sand be cut away; thus the sand, undermined by the waves, will effect the precipitation of the pile into the sea.

Hac ratione, quotienscumque opus fuerit, in acquam poterit esse progressus.

By this method, whenever there is need, it will be possible to make progress into the water.

[5] In quibus autem locis pulvis non nascitur, his rationibus erit faciendum, uti arcae duplices relatis tabulis et catenis conligatae in eo loco, qui finitus erit, constituantur, et inter destinas creta in eronibus ex ulva palustri factis calcetur. Cum ita bene calcatum et quam densissime fuerit, tunc cocleis rotis tympanis conlocatis locus qui ea septione finitus fuerit, exinaniatur sicceturque, et ibi inter septiones fundamenta fodiantur. Si terrena erunt, usque ad solidum, crassiora quam qui murus supra futurus erit, exinaniatur sicceturque et tunc structura ex caementis calce et harena compleatur.

[5] But in those places where the powder does not occur, the work must be done by these methods: namely, that double coffers, with the planks laid together and bound with chains, be set up in the place which will have been marked out, and between the staked lines (destinae) the clay be trodden down in baskets (erones) made from marsh-reed. When it has thus been well trodden and as densely as possible, then, with screw-scoops, wheels, and drums installed, the place which has been bounded by that enclosure is emptied and dried, and there, between the partitions, the foundations are to be dug. If they are earthy, then down to solid ground, thicker than the wall which is going to be above, let it be excavated and dried, and then let the masonry be filled up with caementa, lime, and sand.

[6] Sin autem mollis locus erit, palis ustilatis alneis aut oleagineis configantur et carbonibus compleantur, quemadmodum in theatrorum et muri fundationibus est scriptum. Deinde tunc quadrato saxo murus ducatur iuncturis quam longissimis, uti maxime medii lapides coagmentis contineantur. Tunc, qui locus erit inter murum, ruderatione sive structura compleatur.

[6] However, if the place will be soft, let piles of scorched alder or olive-wood be driven in and let them be filled with charcoals, just as has been written concerning the foundations of theaters and of walls. Then let a wall be carried up in squared stone with joints as long as possible, so that especially the middle stones may be held fast by the bondings. Then the space which will be between the wall shall be filled with rubble-work or with masonry.

Ita erit uti possit turris insuper aedificari.

Thus it will be so that a tower can be built above.

[7] His perfectis navaliorum ea erit ratio, ut constuantur spectantia maxime ad septentrionem; nam meridianae regiones propter aestus cariem, tineam, teredines reliquaque bestiarum nocentium genera procreant alendoque conservant. Eaque aedificia minime sunt materianda propter incendia. De magnitudinibus autem finitio nulla debet esse, sed faciunda ad maximum navium modum, uti, etsi maiores naves subductae fuerint, habeant cum laxamento ibi conlocationem.

[7] With these things completed, the plan for the dockyards will be this: that they be constructed facing chiefly toward the north; for meridian regions, on account of the heat, produce caries, tinea, teredines, and the remaining genera of harmful beasts, and by nourishing them preserve them. And such buildings are by no means to be timbered because of fires. As to magnitudes, moreover, there ought to be no limitation, but they must be made to the maximum measure of ships, so that, even if larger ships have been hauled up, they may have their collocation there with clearance.

Quae necessaria ad utilitatem in civitatibus publicorum locorum succurrere mihi potuerunt, quemadmodum constituantur et perficiantur, in hoc volumine scripsi; privatorum autem aedificiorum utilitates et eorum symmetrias insequenti volumine ratiocinabor.

The things which could come to my aid as necessary for the utility in cities of public places—how they are to be constituted and perfected—I have written in this volume; but the utilities of private buildings and their symmetries I will ratiocinate in the following volume.