Those who have unfolded their meditations and precepts of talent in fuller volumes, Imperator, have added to their writings the greatest and most excellent authority. I should wish that our studies too would suffer this, so that authority might be increased in these precepts also by amplifications; but this is not so easy as is thought. For writing on architecture is not as writing on history or poetry. Histories hold their readers by themselves, for they have varied expectations of new matters. The meters of poems, too, the feet, the elegant disposition of words, and the pronouncement, toward the verse, of sentences distributed among persons, by alluring the feelings of readers lead them on without offense to the end of the writing. §1
But this cannot be done in the writings of architecture, because the words conceived from the proper necessity of the art, by unaccustomed speech, throw obscurity upon the senses. Since, therefore, these are not of themselves clear, nor do their names lie open in common usage, and further the wandering writings of precepts, if they are not contracted and unfolded in few and very clear sentences, will, by the frequency and multitude of words impeding the reader, make the reader's thoughts uncertain. So I shall set forth briefly, by proclaiming from the members of works their hidden namings and dimensions, that they may be handed down to memory. For so minds will be able more readily to receive them. §2
No less, when I noticed that the city was distended by occupations, public and private, I judged that I should write in few words, so that readers, in the narrow space of leisure, might briefly grasp them. It also pleased Pythagoras and those who had followed his school to write precepts in volumes by cubic reasonings; they established the cube as of two hundred and sixteen verses, and thought that there should be not more than three of them in one composition. §3
The cube is a body squared on all sides of equal breadth of its planes. When thrown, on whichever side it falls it has, while undisturbed, an unmoved stability, as the dice do which players throw in the box. They seem to have taken this likeness because so great a number of verses, like a cube, wherever it sits in the mind, makes there an unmoved stability of memory. The Greek comic poets also, inserting a song from the chorus, divided the spaces of their plays. Thus, making parts by cubic reasoning, they relieve the deliveries of the actors with interposed intervals. §4
Therefore since these things have been observed naturally by our forebears, and since I notice I have to write things unaccustomed and obscure to many, in order that they may more easily reach the feelings of readers, I have judged to write in brief volumes. So they will be ready for understanding. And I have so instituted their orderings that they are not to be gathered separately by the inquirer, but, out of one body, may have in the several volumes the unfoldings of their kinds. Therefore, Caesar, in the third and fourth volumes I have set forth the principles of sacred temples; in this book I shall set forth the dispositions of public places. And first I shall speak of how the forum ought to be established, because in it the principles of both public and private affairs are governed by the magistrates. §5
The Greeks establish their fora in a square, with most ample and double porticoes, and adorn them with close-set columns and stone or marble architraves, and above they make walks in the floors. But for the cities of Italy, the reasoning is not to be the same, because by our forebears the custom has been handed down to give gladiatorial games in the forum. §6
Therefore, round the shows, more spacious intercolumniations are to be distributed, and around, in the porticoes, the shops of the money-changers and galleries in the upper stories on joists are to be placed; which will be rightly disposed both for use and for the public revenues. The sizes, however, must be made proportionate to the crowd of people, lest the space be too small for use, or, on account of a scarcity of population, the forum seem vast. The breadth is to be so determined that, when the length is divided into three parts, two of these be given to the breadth. For thus its shape will be oblong, and its disposition useful for the scheme of the shows. §7
The upper columns are to be made a fourth part less than the lower, because for bearing a burden, what is below ought to be firmer than what is above; no less because it is fitting also to imitate the nature of what grows, as in round trees, in fir, cypress, pine, of which none is not thicker at the roots; then, as it goes up in growth, by natural contraction it is equalized as it grows toward the top. Therefore, if the nature of what grows so demands, it is rightly established that the upper parts, in both heights and thicknesses, be contracted beneath the lower. §8
The places of the basilicae, joined to the forum, should be established in the warmest quarters, so that in winter the merchants may gather there without the molestation of the weather; and the breadths of these are not to be established less than a third, nor more than half of the length, unless the nature of the place hinders and compels the symmetry to be altered otherwise. If, however, the place be wider in length, chalcidica are to be set at the ends, as in the Julian and Aquilian. §9
The columns of basilicae seem to need to be made as tall as the portico is broad. The portico, which shall be the middle space, is determined by a third. The upper columns, smaller than the lower, are to be established as written above. The breastwork which shall be between the upper and the lower columns, likewise, seems ought to be made a fourth part less than the upper columns, so that those walking on the upper floor of the basilica may not be seen by the merchants. Architraves, friezes, coronas, by the symmetries of the columns, as we said in the third book, are to be unfolded. §10
No less may comparisons of basilicae have supreme dignity and beauty of the kind which I have placed and provided to be built at the colony of Julia Fanestri, whose proportions and symmetries have been so established. The middle vaulted roof between the columns is a hundred and twenty feet long, sixty broad. Its portico around this vault, between the walls and the columns, is twenty feet wide. The columns are of perpetual heights with their capitals of fifty feet, of five feet thickness, having behind them pilasters twenty feet high, two feet and a half wide, one and a half thick, which sustain the beams on which are laid the floors of the porticoes. And above them, other pilasters eighteen feet high, two feet wide, a foot thick, which receive the beams sustaining the rafters, and the roofs of the porticoes set lower beneath the vault. §11
The remaining spaces between the beams of the pilasters and of the columns, through the intercolumniations, are left for lights. The columns are, in the breadth of the vault, with the corner columns on right and left, four each; in the length that is nearest the forum, with the same corner columns, eight; on the other side, with the corner, six; because the two middle ones on that side are not placed, lest they impede the view of the pronaos of the temple of Augustus, which is placed in the middle of the side wall of the basilica, looking upon the middle of the forum and the temple of Jupiter, and likewise the tribunal, which is in this temple, shaped with the curvature of a hemicycle of a lesser figure. §12
The frontal interval of this hemicycle is forty-six feet; inward, the curvature is fifteen feet, so that those standing before the magistrates in their business may not hinder those in the basilica. Above the columns, beams compacted of three two-foot timbers are placed around; and from the third columns, which are on the inner side, they return to the antae that run forth from the pronaos and touch the hemicycle on right and left. §13
Above the beams, opposite the capitals, piers are placed on supports, three feet high and four feet wide each way. Above them, beams of two pairs of two-foot timbers are laid around. Upon these, transoms with struts placed against the bodies of the columns, the antae, and the walls of the pronaos support one ridge of the basilica running its whole length, the other from the middle above the pronaos of the temple. §14
Thus the double disposition of the pediments, T-shaped, gives to the outside of the roof and to the interior of the lofty vault a graceful appearance. Likewise, with the architraves' ornaments and the distribution of the breastwork and of the upper columns removed, laborious annoyance is taken away, and a great part of the expense diminished. The columns themselves, however, carried up in continuous height beneath the beams of the vault, seem to add magnificence of expense and authority to the work. §15
The treasury, the prison, and the curia are to be joined to the forum; but so that the size and symmetry of these correspond to the forum. Above all, the curia is to be made chiefly to the dignity of the municipality or the state. And if it be square, let the height be established with half its breadth added; but if oblong, let its length and breadth be combined, and of the sum thus composed let half be given to the height beneath the coffered ceiling. §16
Moreover, the walls are to be girded in the middle with coronas of joinery or of stucco, up to the middle of their height. If these be not, the voice of the disputers, rising aloft, will not be able to be understood by the listeners. But when the walls are girded with coronas, the voice rising from below, restrained before it is dissipated in the air on high, will be understood by the ears. §17
When the forum has been established, a site is then to be chosen for the theater, as healthful as possible, for the viewing of the games on the festal days of the immortal gods, as written in the first book on the healthfulness of the placing of walls. For during the games, sitting with wives and children, enthralled by the delights, they have their bodies still with pleasure; and their open veins take the blasts of the breezes, and if these come from marshy regions or from other faulty quarters, they pour hurtful airs into the bodies. Therefore, if the site of the theater be chosen with care, these defects will be avoided. §18
Care must also be taken that the sun have no impact from the south. For when it fills the rounding, the air, shut in by the curve and without power to wander, by turning grows hot, and, burning, scorches and bakes and diminishes the moistures of bodies. Therefore above all these faulty regions are to be avoided, and healthful ones chosen. §19
The foundations, if they are on hills, will be an easier reasoning; but if necessity has compelled them to be set in a level or marshy place, the consolidations and substructures must be made as written about the foundations of sacred temples in the third book. Above the foundations, the steps from the substructure are to be made in supplies of stone and marble. §20
The precinctions (diazomata), proportional to the heights of the theaters, seem proper to be made, and not higher than the breadth of the precinction's walkway. For if they be too lofty, they will throw back and cast out the voice from the upper part, nor will they suffer, in the seats on top above the precinctions, the words' cases to reach the ears with certain significance. And, in general, it must be so governed that, when a line is extended from the lowest step to the topmost, it touches all the peaks and angles of the steps. §21
Thus the voice will not be hindered. Entrances must be set several and spacious, not joining the upper with the lower, but from all places continuous and straight without turnings, so that when the people shall be dismissed from the shows, they may not be pressed together, but may have exits separate from all places without hindrance. Care must also be taken diligently that the place be not deaf, but that in it the voice may range as clearly as possible. This can be done if a place is chosen where resonance is not impeded. §22
The voice is flowing breath of air, sensible by the sense of hearing at its touch. It is moved by the roundings of infinite circles, as if in standing water a stone be thrown in, innumerable circles of waves arise, growing from the center as widely as they can, until the narrowness of place interrupts them, or some obstacle that does not suffer the shapings of those waves to reach their exits. So when they are interrupted by obstructions, the first, flooding back, disturb the shapings of those following. §23
By the same reasoning the voice makes motions as in a circle; but in water the circles move in breadth on a plane; the voice both goes forth in breadth and climbs step by step upwards. Therefore, as with the shapings of waves in water, so also in the voice, when no obstruction has interrupted the first wave, it does not disturb the second, nor those following; but all, without resonance, reach the ears of those at the bottom and at the top. Therefore, the ancient architects, following the footprints of nature in their inquiries into the climbing voice, perfected the gradations of theaters, and sought, by the canonical reasoning of the mathematicians and of music, that whatever voice was on the stage might reach clearer and sweeter to the ears of the spectators. §24
For as instruments are perfected, for the clearness of the sounds of strings, with bronze or horn echea (sounding-plates), so in theaters, by harmonic reasoning, reasonings for amplifying the voice have been established by the ancients. §25
Harmonic theory, however, is a musical erudition obscure and difficult, especially to those who do not know the Greek letters. If we wish to unfold it, it is necessary to use Greek words too, because some of them have no Latin names. Therefore I will interpret, as openly as I can, from the writings of Aristoxenus, and will subscribe his diagram and designate the bounds of the notes, so that one who attends diligently may more easily grasp it. §26
For the voice, when it is bent by alterations, is made at one time sharp (high), at another heavy (low), and it is moved in two ways: of these one has effects continuous, the other discrete. The continuous voice neither halts at fixed bounds nor in any place, but produces terminations not apparent, while the intervals between are apparent, as in speech when we say sol, lux, flos, vox. For now it is neither understood whence it begins nor where it ceases; but that from sharp it has become heavy, and from heavy sharp, is apparent to the ears. Through discreteness, on the other hand, the reverse. For when the voice is bent by alteration, it stands itself at the bound of some sound, then at another's; and by doing this back and forth often, it appears to the senses as constant, as in songs when, bending the voice, we make variety of modulation. And so by intervals, when it is so treated, both whence it made its beginning and where it ceased appear in the open bounds of the sounds, but the middle spaces lie hidden in the intervals. §27
There are three kinds of modulation: first, that which the Greeks call ἁρμονίαν; second, χρῶμα; third, διάτονον. The modulation of the enharmonic (harmonia) is conceived by art, and for that reason its song has chiefly grave and extraordinary authority. The chroma, by subtle skill and frequency of modules, has a sweeter delight. The diatonic, because it is natural, has an easier distance of intervals. In these three kinds, the dispositions of the tetrachords are unlike, because the enharmonic tetrachord has two tones and two dieseis. A diesis is a fourth part of a tone, so in a semitone two dieseis are placed. In the chromatic, two semitones in sequence are placed together; the third is a trihemitone interval. In the diatonic, two tones are continuous; a third semitone ends the extent of the tetrachord. Thus in the three kinds the tetrachords are equalized as two tones and a semitone; but when considered separately in the bounds of each kind, they have unlike shaping of intervals. §28
Therefore nature divided in the voice the intervals of tones and semitones in the tetrachord, and bounded their terminations by the measures of the intervals' quantity, and by fixed modes standing apart established the qualities, which even the craftsmen who fabricate instruments, using what is set by nature, fit together so as to produce harmonies of their concords. §29
The notes (which in Greek are called φθόγγοι) in each kind are eighteen; of which eight in the three kinds are perpetual and standing; the remaining ten, since they are modulated not uniformly, are moving. The standing (fixed) are those placed between the movables, holding the conjunction of the tetrachord and, through the differences of kind, remaining at their own bounds. These are called: proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaion. The movables are those which, placed in the tetrachord between the fixed, change places by places in the kinds; and they have these names: parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, paranete synhemmenon, trite diezeugmenon, paranete diezeugmenon, trite hyperbolaion, paranete hyperbolaion. §30
Those which move, take on other virtues, for they have intervals and distances that grow. Thus the parhypate, which in the enharmonic is distant from hypate by half a semitone, in the chromatic, transposed, has a semitone. That which in the enharmonic is called lichanos, is distant from hypate by a semitone; in the chromatic, transposed, advances two semitones; in the diatonic, is distant from hypate by three semitones. Thus the ten sounds, through their transpositions in the kinds, make a triple variety of modulations. §31
There are five tetrachords: the first, the lowest, which is called in Greek ὕπατον; the second, the middle, called μέσον; the third, the conjunct, called συνημμένον; the fourth, the disjunct, called διεζευγμένον; the fifth, the highest, called in Greek ὑπερβολαῖον. The concords, which the nature of man can modulate (called in Greek συμφωνίαι), are six: the fourth, the fifth, the octave, the octave-plus-fourth, the octave-plus-fifth, and the double octave. §32
They have taken their names, too, from number, because when the voice has stood at one bound of sounds, and, bending itself from it, has changed and arrived at a fourth termination, it is called diatessaron (fourth); at a fifth, diapente; at a sixth, diapason; at the eighth and a half, diapason-plus-diatessaron; at the ninth and a half, diapason-plus-diapente; at the twelfth, disdiapason. §33
For between two intervals, when a sound of strings or a song of the voice has been made, nor between three or six or seven, can consonances come about; but, as has been written above, the fourth and fifth and in order up to the double octave have their bounds of agreement from the nature of congruent voice; and these concords are produced from the junction of sounds (which in Greek are called φθόγγοι). §34
So from these inquiries, let bronze vessels be made by mathematical reasonings in proportion to the size of the theater, and so fabricated that when struck they may make sounds among themselves of the fourth and the fifth, and in order up to the double octave. Then, with cells built between the seats of the theater, let them be placed there by musical reasoning so that they touch no wall, and around them have an empty place, and space from above; and let them be placed inverted, and have on the side that faces the stage wedges beneath them of not less than half a foot, and against these cells let openings be left in the bedding of the lower steps, two feet long, a half-foot high. §35
The designations of these, in what places they are to be set, let be so unfolded. If the theater be not of ample size, let a transverse region of the middle height be designated, and in it let thirteen cells at twelve equal intervals be vaulted, so that those echea above written, sounding the nete hyperbolaion, be placed in the cells that are at the extreme horns on either side, as the first; the second from the ends, the fourth, sounding the nete diezeugmenon; the third, a fourth, to paramese; the fourth, to nete synhemmenon; the fifth, a fourth, to mese; the sixth, a fourth, to hypate meson; in the middle, one, a fourth, to hypate hypaton. §36
Thus by this reasoning the voice from the stage, as if poured out from a center, turning itself about and by its touch striking the hollows of the single vessels, will produce an increased clarity and a consonance agreeing in concord with itself. If the size of the theater be greater, then the height is divided into four parts, so that three regions of cells be designated across: one for the enharmonic, another for the chromatic, a third for the diatonic. And from the bottom, the first, which is of the enharmonic, be placed as has been written above in the smaller theater. §37
In the middle row, let the first, at the extreme horns, be placed sounding the chromatic hyperbolaion; at the seconds from these, a fourth, sounding the chromatic diezeugmenon; at the thirds, the chromatic synhemmenon; at the fourths, a fourth, the chromatic meson; at the fifths, a fourth, the chromatic hypaton; at the sixths, paramese, because it has the community of consonance with both the chromatic hyperbolaion (a fifth) and the chromatic synhemmenon (a fourth). §38
In the middle (of the chromatic) nothing is to be placed, because no other quality of sound in the chromatic kind can have a consonance of symphony. In the highest division, in the region of the cells, at the first horns let vessels made to sound the diatonic hyperbolaion be placed; at the seconds, a fourth, the diatonic diezeugmenon; at the thirds, the diatonic synhemmenon; at the fourths, a fourth, the diatonic meson; at the fifths, a fourth, the diatonic hypaton; at the sixths, a fourth, proslambanomenos; in the middle, mese, because it has the communities of symphonies both with proslambanomenos (an octave) and with the diatonic hypaton (a fifth). §39
If any one wishes to bring this easily to perfection, let him look at the end of the book for the diagram set out by musical reasoning, which Aristoxenus, with great vigor and industry, left established by generically divided modulations. If anyone attends to these reasonings, he will more easily be able, from the nature of voice, to perfect theaters for the delight of listeners. §40
Someone will say, perhaps, that many theaters are made every year at Rome, and that none of the reasoning of these matters has been applied in them; but he will err in this, because all public wooden theaters have several planked stages, which must necessarily sound. This is to be observed even in lyric singers, who, when they wish to sing with a higher tone, turn toward the stage's doors, and thus receive the consonance of the voice from their help. But when theaters are made of solid materials, that is, of concrete rubble, stone, marble, which cannot sound, then the reasonings of the echea are to be unfolded. §41
But if it be asked in what theater they have been made, we cannot show them in Rome, but in the regions of Italy and in several cities of the Greeks; we have also L. Mummius as our authority, who, having destroyed the theater of the Corinthians, carried off those bronze vessels to Rome, and dedicated them from the spoils to the temple of Luna. Many skillful architects, too, who in small towns built theaters, used, on account of poverty, earthenware jars sounding thus, chosen and composed by this reasoning, and so achieved most useful effects. §42
The shaping of the theater itself is to be made thus: as great as the perimeter shall be at the bottom, with its middle center placed, a circular line be drawn; and in it let there be inscribed four triangles with equal sides and distances, which shall touch the outermost line of the circle, as also in the description of the twelve signs of heaven the astrologers reason from the musical agreement of the stars. Of these triangles, that one whose side is nearest the stage, in the region where it cuts off the curvature of the circle, shall be the finishing of the stage's front; and from that place, through the center, let a parallel line be drawn, which separates the proscaenium's platform and the region of the orchestra. §43
Thus the pulpit was made wider than that of the Greeks, because all the artists perform their work on the stage, while in the orchestra places are assigned for the seats of the senators. And the height of this pulpitum be not more than five feet, so that those who sit in the orchestra may be able to see the gestures of all the performers. The wedges (cunei) of the shows in the theater are to be so divided that the angles of the triangles which run round the curvature of the circle direct the ascents and stairs between the wedges up to the first precinction; and above, by alternate passages, let the middle upper wedges be directed. §44
The angles which are at the bottom and direct the stairways will be seven in number; the remaining five shall designate the composition of the scene: one in the middle ought to have opposite it the royal doors, and those on right and left shall designate the composition of the guest-chambers; the two outermost shall look toward the passages of the turnings. The steps where the benches are placed are not to be less than one foot and three inches high, nor more than one foot six inches; their breadths are to be established not more than two feet six inches, nor less than two feet. §45
The roof of the portico which is to be at the top of the gradation should be leveled with the height of the scene, because the voice, rising uniformly, will reach the highest steps and the roof. For if it be not equal, the less it be tall, the more the voice will be caught away, up to that height to which it reaches first. §46
Of the orchestra, at the bottom among the steps, let a sixth part of its diameter be taken; and in the horns on either side, opposite the approach, let the lower seats be cut off by the perpendicular of that measure; and where the cut-off shall be, there let the lintels of the passages be set. So their vaultings will have sufficient height. §47
The length of the scaena must be made double the diameter of the orchestra. The height of the podium from the level of the pulpit, with its corona and lysis, is a twelfth of the orchestra's diameter. Above the podium, columns with their capitals and bases be of a fourth part of the same diameter in height; the architraves and ornaments of these columns a fifth of their height. The breastwork above, with its wave-molding and corona, is half of the lower breastwork. Above that breastwork, columns be a fourth part less in height than the lower, and the architraves and ornaments of these columns a fifth. Likewise, if a third story is to be made, the top of the middle breastwork is half; the topmost columns less in height than the middle by a fourth; the architraves with their coronas of those columns likewise a fifth of their height. §48
Yet not in all theaters can the symmetries respond to all the reasonings and effects; but the architect must observe which proportions it is necessary to pursue the symmetry, and which must be tempered to the nature of the place or the size of the work. For there are things which it is necessary to be of the same size in both a small and a great theater for the use, as the steps, diazomata, breastworks, passages, ascents, pulpits, tribunals, and whatever else intervenes, from which necessity compels us to depart from symmetry, lest use be hindered. No less, if the supply of material (marble, timber, and the rest) is small in the work, to lessen or to add a little, provided it be not done too improperly but with sense, will not be alien. This will be, if the architect is practiced in use, and, besides, is not destitute of a mobile talent and dexterity. §49
The scenes themselves have their reasonings thus unfolded: the middle doors have the ornaments of the royal hall, on right and left the guest-quarters; next, the spaces arranged for ornaments, places which the Greeks call περιάκτους, because in these places are machines that turn about, triangular, each having three kinds of ornament, which, when either changes of plays are to come or the arrivals of gods with sudden thunders, turn and change the appearance of the ornament in front. Next to these places run forth the versurae, which make the approaches to the stage, one from the forum, the other from abroad. §50
There are three kinds of scene: one called tragic, another comic, the third satyric. Their ornaments, indeed, are of unlike and unequal reasoning among themselves; for tragic scenes are shaped with columns and pediments and figures and other royal things; comic have the look of private buildings, and their views are set out with windows in the manner, as in the principles of common buildings; satyric are adorned with trees, caves, mountains, and the other country things shaped in the likeness of a landscape. §51
In the theaters of the Greeks, all things are not to be done by the same reasonings. First, in the bottom of the circle, as in the Latin four triangles, so in theirs three squares, with their angles touching the line of the circle; and of the square whose side is nearest the stage and cuts off the curvature of the circle, in that region the finishing of the proscaenium is designated. And from that region to the farthest circumference, a parallel line is designated for the front of the scene; through the center of the orchestra a line parallel to the proscaenium region is drawn; and where it cuts the lines of the circle on right and left in the horns, the centers of the hemicycle are marked; and with the compass placed at the right, swept from the left interval around to the left of the proscaenium, likewise with the center placed at the left horn, swept from the right interval, round to the right of the proscaenium. §52
So by this description, from three centers, the Greeks have a more ample orchestra and a more receding scene, and a narrower pulpit, which they call λογεῖον, because upon it the tragic and comic actors perform on the stage, while the other artists show their performances through the orchestra; whence the Greeks separately name stage-players (σκηνικοί) and musicians (θυμελικοί). The height of this logeion ought to be not less than ten feet nor more than twelve. The gradations of stairs between the wedges and seats, opposite the angles of the squares, are to be directed to the first precinction; from the precinction, between these, other middle ones be directed; and to the top, as often as they are girded, the dividing increases by the same amount. §53
When all these have been unfolded with the highest care and skill, then must it be diligently attended to that the site be so chosen that the voice may softly attach itself, nor, rebounding back, report to the ears uncertain significations. For there are some sites naturally hindering the motions of the voice: dissonantes (which the Greeks call κατηχοῦντες), circumsonantes (among them περιηχοῦντες), likewise resonantes (ἀντηχοῦντες), and consonantes (συνηχοῦντας). Dissonantes are those in which the first voice, rising aloft, when it is struck on the hard bodies above and rebounds, settling at the bottom, overwhelms the rising of the next. Circumsonantes are those in which, by wandering around, the voice is driven in from the middle, without falling at the ends, and expires there with uncertain signification of words. Resonantes are those in which, struck at a solid touch and bouncing, it throws back images, producing the final cases as doubled in hearing. §54
Consonantes are those in which, helped from below, the voice, rising with increase, goes forth to the ears with a clear and distinct clarity of words. Thus, if, in choosing the site, there be a diligent attention, an effect of voice perfected by prudence for use in theaters will have been corrected. The designs of the plans will be distinguished from one another by these marks, that those which are drawn from squares will have the uses of the Greeks; the Latin from triangles with equal sides. Thus, whoever wishes to use these prescriptions will make perfect completions of theaters. §55
Behind the scene, porticoes are to be set up, so that when sudden rains interrupt the games, the people may have whither to retreat from the theater, and the stage-companies may have room for making ready. Such are the Pompeian porticoes; and at Athens, the Eumenic portico and the shrine of Father Liber; and on leaving the theater, on the left part, the Odeum, which Themistocles, with stone columns disposed, wove over with masts and yards of ships from the Persian spoils, and the same, when burnt in the Mithridatic war, King Ariobarzanes restored; at Smyrna the Stratonicum; at Tralles porticoes on each side of the stage above the stadium; and in the other cities which had more diligent architects, about the theaters there are porticoes and walks. §56
These seem ought to be placed so that they be double, and have outer Doric columns with architraves and ornaments perfect according to the reasoning of modulation. Their breadths seem ought to be made so, that whatever the height of the outer columns, such be the breadth from the lower part of the outermost columns to the middle, and from the middle to the walls enclosing the walks of the portico. The middle columns, however, be a fifth part taller than the outer; but be shaped either in the Ionic or Corinthian kind. §57
The proportions and symmetries of columns, however, shall not be by the same reasonings as I have written for sacred temples. For they should have one gravity in the temples of the gods, another subtlety in porticoes and other works. So if the columns be of the Doric kind, let their heights with the capital be measured into fifteen parts. One of these shall be set as the module, upon whose module's reasoning the whole work's unfolding shall depend. At the bottom of the column the thickness is two modules; the intercolumniation five and a half modules; the height of the column, apart from the capital, fourteen modules; the height of the capital one module; the breadth two modules and a sixth. The rest of the modulations of the work, as in the sacred temples it has been written in the fourth book, let be perfected. §58
If, however, the columns be Ionic, let the shaft, exclusive of base and capital, be divided into eight and a half parts, and one of these be given to the thickness of the column; the base, with the plinth, be established at half that thickness; the reasoning of the capital be as shown in the third book. If it be Corinthian, the shaft and base as in Ionic, but the capital as written in the fourth book; so let the reasoning be. And the rise in the stylobates by unequal scamilli be taken from the description above written in the third book. Architraves, coronas, and the rest, by the reasoning of columns, let be unfolded from the writings of the previous volumes. §59
The middle open spaces between the porticoes should be adorned with greenery, because walks in the open air have great healthfulness: first of the eyes, because from the greenery a subtle and thin air, flowing in by the motion of the body, smooths out the sight, and so, taking away the thick moisture from the eyes, leaves the sight thin and acute. Besides, since the body grows warm with the motions of the walk, the air, by drawing out moisture from the members, diminishes plenitudes and thins by dissipating what is more than the body can sustain. §60
That this is so may be noticed from this: that under roofs, though there be springs of water, or even a marsh abundant below the earth, no misty moisture rises from them; but in open places under the open sky, when the sun at rising touches the world with its vapor, it arouses moistures from moist and abounding places, and, having rolled them up, lifts them on high. Therefore if it appears so, that in open places moistures are drawn from bodies by the air more oppressively, as they are seen to be from the earth through mists, I do not think there is any doubt that the amplest and most adorned walks should be placed in the open air in cities. §61
That these may always be dry and not miry, so must it be made. Let them be dug and hollowed out as deep as possible. On the right and left let built drains be made, and in their walls, which look toward the walk, let little pipes be set, inclined at a slope into the drains. This done, let the places be filled with charcoal; then above, with sand, let the walks be strewed and leveled off. So, because of the natural rareness of the charcoal and the setting of the pipes into the drains, abundance of water shall be received; and thus the walks shall be dry and without moisture. §62
Moreover, in these works, storehouses are established by the forebears for cities in necessary things. For in sieges all other supplies are more easily gathered than timber. For salt is easily imported beforehand; grain, publicly and privately, is more readily collected; and if it fails, is supplied by herbs, meat, or legumes; water by digging wells and from sudden tempests from the tiles. But the supply of wood, which is most necessary for cooking food, is difficult and troublesome, because it is conveyed slowly and is consumed in great quantity. §63
In such times, then, these walks are opened, and measures are designated by tribes to each person. Thus the hypaethral walks furnish two extraordinary things, one of healthfulness in peace, the other of safety in war. So by these reasonings, the unfoldings of walks, not only behind the stage of theaters but also at the temples of all the gods, can furnish great uses to cities. Since these matters seem to us to have been sufficiently unfolded, now there shall follow demonstrations of the dispositions of baths. §64
First, a site is to be chosen as warm as possible, that is, facing away from north and northeast. The caldaria and tepidaria themselves should have their light from the winter west, or, if the nature of the place hinders, at least from the south, because the chief time of bathing is established from midday to evening. And this too must be observed, that the caldaria for women and men be joined, and placed in the same quarters. For so it will come about that in the boiler-room and in the hypocaust they shall be common to both. Three bronze coppers are to be set above the hypocaust: one hot, another tepid, a third cold; and they are to be so placed that however much hot water passes from the tepid to the hot, the same measure may flow from the cold into the tepid; and the vaults of the basins be heated from a common hypocaust. §65
The hypocausts of the caldaria are to be so made that the floor be first paved with tiles of a foot and a half, inclined toward the furnace, so that when a ball is thrown in it cannot stop within but returns of itself to the furnace. Thus the flame will more easily range beneath the suspended floor. Above, with bricks of a third of a foot (bessales), pillars are built, so arranged that tiles of two feet can be laid upon them. Let the pillars have a height of two feet, and let them be built with clay tempered with hair; and above, let two-foot tiles be placed, which sustain the pavement. §66
If the vaults are made of masonry, they will be more serviceable; but if floored, an earthenware work must be placed underneath, but it is to be done thus. Let iron rods, or arches, be made, and these by iron hooks be hung as thick as possible to the floor-joists; and let these rods or arches be so disposed that tiles without edges can sit upon two of them and be carried on; and thus entire vaults, resting on iron, may be perfected. The upper joints of these vaults, let be smeared with clay tempered with hair; and the lower part, which faces the pavement, first with pounded tile and lime trowelled over, and then polished with stucco or plasterwork. These vaults in the caldaria, if made double, will have a better use; for the vapor will not be able to corrupt the timbering of the floor-joists, but will wander between the two vaults. §67
The dimensions of the baths should be made proportionate to the number of people, provided they be so disposed. However long it be, let the breadth, with a third deducted, be, apart from the setting of the basin and the tub. The basin must be placed under the light, lest those standing round obscure the light with their shadows. The settings of the basins ought to be made so spacious that, when those first have occupied the places, the rest, looking on, may be able to stand well. The breadth of the tub between wall and breastwork be not less than six feet, so that the lower step and a cushion take off two feet. §68
The laconicum and the sweating-rooms are to be joined to the tepidarium; and let them have as great a height to the lowest curve of the hemisphere as their breadth. Let a central light be left in the hemisphere, and from it let a bronze disk hang by chains; by whose raisings and lowerings the temper of the sweat is effected. And it seems that the room itself must be made circular, so that the force of flame and vapor may range uniformly from the middle through the roundings of the curvature. §69
Now it seems well, although the buildings of palaestras are not of Italian custom, yet to unfold those which have been handed down, and to show how they are established by the Greeks. In palaestras let there be peristyles, square or oblong, so made that they have a circuit of walk of two stadia, which the Greeks call δίαυλον. Of these let three porticoes be made simple; the fourth, which faces the southern regions, double, so that when the storms are windy, the spray may not be able to reach the inner part. §70
Now in three porticoes let spacious exedrae be established, with seats, in which philosophers, rhetoricians, and the rest who delight in studies, sitting, may discourse. In the double portico let these members be placed: the ephebeum in the middle (this is the largest exedra with seats, which is a third longer than broad). Beneath the right the coryceum (ball-exerciser's room); then next the conisterium (dust-room); from the conisterium, at the corner of the portico, the cold wash (which the Greeks call λουτρόν). To the left of the ephebeum the elaeothesium (oil-room); next to it the tepidarium, and from it a passage to the propnigeum (heating-room) at the corner of the portico. Next, inward, opposite the frigidarium, let a vaulted sweating-room be placed, in length double the breadth, which shall have at its corners on one side a laconicum composed in the same fashion as written above; opposite the laconicum, a hot wash. In a palaestra with peristyle, as written above, so ought the distribution to be. §71
Outside let three porticoes be disposed, one for those going out from the peristyle, and two, on right and left, of a stadium in length; of which the one that looks to the north, let be made double of the widest breadth; the other single, so made that on the sides along the walls and by the columns it has margins, as paths no less than ten feet wide, and the middle sunken by a step of a foot and a half down from the margins to a level, which level is no less than twelve feet. Thus those who walk clothed on the margins will not be hindered by those who are oiled, at their exercises. §72
This portico, among the Greeks, is called ξυστός, because the athletes exercise in winter in roofed stadia. Next to the xystus and the double portico, let open walks be designated, which the Greeks call παραδρομίδας, and our people xysta, into which the athletes come out of the xystus in clear weather, in winter, to exercise. It seems that the xysta should be so made that between two porticoes there be groves or plane-trees, and in these, walks between the trees, and there, stations of hard concrete. Beyond the xysta, let the stadium be so figured that companies of men, with ease, may watch the athletes contending. I have now written the necessary things that seemed ought to be disposed aptly within the walls. §73
Concerning the opportunity of harbors, it must not be passed over, but it must be unfolded by what reasonings ships may be preserved in them from storms. These, if they are naturally well placed, and have acroteria or projecting promontories from which curves or returns of the site are shaped according to the place, seem to have the greatest utility. For round about, porticoes or shipyards are to be made, or, out of the porticoes, approaches to the marts; and towers are to be placed on either side, from which chains can be drawn across by engines. §74
But if we have no natural place fit for protecting ships from storms, it must be done thus: if no river hinders these places, but there is a station on one side, then on the other side let the approach be prepared by masonry or by moles. And so let the enclosures of the harbors be fashioned. The masonry that is to be in water seems so ought to be done: let the powder from the regions about Cumae, extending continuously to the promontory of Minerva, be brought; and let it be mixed, as in mortar, so that two parts answer to one. §75
Then, in that place which shall have been fixed, let cases (arcae) enclosed by oak stakes and chains be lowered into the water and firmly stayed; and, within, from crosspieces, let the lower part beneath the water be leveled and cleaned, and with rubble of mortar and material mixed (as above written) let it be heaped there, until the masonry fills the space between the cases. Now those places above described have this natural advantage. But if, because of the waves or the impulse of the open sea, the stays cannot hold the cases, then from the very land or from a quay let a pulvinus (bank) be built as firmly as possible, and let the pulvinus be built with an even plane for less than half its part, the rest, which is toward the shore, have an inclined side. §76
Then, next to the water, on the sides of the pulvinus, let margins of about a foot and a half be built, equal to the plane above written; then the inclination be filled with sand, and leveled with the margin and with the plane of the pulvinus. Then, above that leveling, let a pier as large as desired be built there, and when it is built up, let it remain for not less than two months, that it may dry. Then let the margin that holds the sand be cut away. So the sand, undermined by the waves, will cause the pier to fall precipitately into the sea. By this reasoning, whenever the work is required, there can be advance into the water. §77
But in places where this powder is not produced, by these reasonings it is to be done: that double cases tied together by charred stakes and chains be placed in that place which has been fixed, and between the stays let clay in baskets of marsh-rush be rammed down. When it has been thus well rammed and as densely as possible, then, with screws, wheels, and drums placed, the space which has been enclosed by that rampart is to be emptied and dried, and there, between the partitions, let foundations be dug. If they be earthy, let them be emptied and dried down to the solid, of a thickness greater than the wall that shall be above, and then let the masonry be completed of rubble, lime, and sand. §78
But if the place be soft, let charred piles of alder or olive be driven in, and let it be filled with charcoals, as was written about the foundations of theaters and walls. Then let the wall be drawn up of squared stone, with the longest joinings possible, so that the middle stones may be held chiefly by the joints. Then, within the space between, let it be filled with rubble-work or masonry. Thus there will come about that a tower may be built above. §79
These things being done, the reasoning of the ship-sheds will be that they be established facing chiefly the north. For the southern regions, because of the heats, breed rot, moth, shipworms, and the other kinds of noxious creatures, and, by feeding, preserve them; and those buildings are by no means to be made of timber, on account of fires. There ought to be no bound to their magnitudes, but they are to be made to the greatest model of ships, so that if greater ships have been hauled up, they may have, with room to spare, a place there. The things necessary for use in the public places of cities, how they should be established and perfected, I have written in this volume; but of the uses of private buildings and their symmetries, I shall reason in the following volume. §80