Delphic Apollo, through the responses of the Pythia, declared Socrates the wisest of all men. And he is recorded to have said, wisely and most learnedly, that the breasts of men ought to have been glazed and open, so that they might hold their thoughts not hidden but exposed for inspection. Would that indeed the nature of things had followed his judgment and had so established them, plain and manifest. For if it had been so, then not only the praises or the vices of souls would be visible at hand, but also the knowledge of the disciplines, submitted to the inspection of the eyes, would not be proved by uncertain judgments, but to the learned and the knowing an extraordinary and lasting authority would be added. But since these things are not so, but have been constituted as the nature of things would have them, it does not come about that men, with minds obscured under their breasts, can judge knowledge of the arts which lie entirely hidden within, as it really is. And the craftsmen themselves, though they promise their own skill, unless they are abundant in money, or have a reputation from the age of their workshop, or have been provided with favor in the forum and eloquence, cannot have authority in proportion to their industry of studies, to make it believed that they know what they profess. §1
This we may especially observe from the ancient sculptors and painters, because of these, those who had the marks of dignity and the favor of commendation, endure to posterity in an eternal memory, such as Myron, Polyclitus, Phidias, Lysippus, and the rest who attained renown from their art. For as they made works for great cities or for kings or for noble citizens, they won that renown. But those who were of no less study, talent, and skill, and for citizens of low fortune made works no less excellently accomplished, obtained no memory, because these men were abandoned not by industry nor by the skill of art but by fortune: as Teleas the Athenian, Chion of Corinth, Myagrus of Phocaea, Pharax of Ephesus, Boedas of Byzantium, and many others. Likewise painters: Aristomenes of Thasos, Polycles and Andron of Ephesus, Theo of Magnesia, and the rest, whom neither industry nor zeal for their art nor dexterity failed, but either the slenderness of their estate, or the weakness of their fortune, or the triumph of opposites in the contest of ambition, stood in the way of their dignity. §2
Nor indeed is it to be wondered at if, on account of ignorance of art, virtues are obscured. But it is most to be lamented, when often the favor of dinner-parties coaxes from true judgments a false approbation. Therefore, as Socrates thought, if the senses and the sentences and the knowledges built up by learning had been open and clear, neither favor nor ambition would prevail; but those who, by true and certain labors of study, had come to the highest knowledge, would have works brought to them without their seeking. Since, however, these things are not manifest nor clear at sight as I think they ought to be, and since I observe that the unlearned, rather than the learned, prevail by favor, judging that I must not contend with the unlearned by ambition, I will rather, by setting forth these precepts, show the virtue of our knowledge. §3
Therefore, Imperator, in the first volume I set forth to you concerning the art, and what virtues it has, and with what disciplines the architect ought to be furnished; and I added the causes why he ought to be skilled in these, and I divided the reasonings of the highest architecture by partition and bounded them by definitions. Then, what was first and necessary, of walls I explained by reasonings how healthful sites are to be chosen, and I showed, by geometrical figures, which and from what regions the several winds blow; and I taught how the distributions of streets and lanes should be rightly made within the walls; and so I made an end in the first volume. In the second, likewise, I went through the properties which material has in works, and by what virtues it has been put together by the nature of things. Now in the third I shall speak of the sacred buildings of the immortal gods, and set them out as is fitting, in writing. §4
The composition of temples rests on symmetry, whose reasoning the architects must most diligently hold. It is brought forth by proportion, which in Greek is called ἀναλογία. Proportion is a determinate commensurability of the parts of the members in every work, and of the whole, from which the reasoning of symmetries is produced. For no temple can have a reasoning of composition without symmetry and proportion, save if it have been built to an exact calculation of its members like that of a well-figured man. §5
For the nature of things has so composed the body of a man that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part; likewise the palm of the hand, from the wrist to the tip of the middle finger, is the same; the head, from the chin to the top of the crown, is an eighth part; from the top of the breast with the bottom of the neck to the lowest roots of the hair, a sixth; from the middle of the breast to the top of the crown, a quarter. Of the face itself, from the bottom of the chin to the bottom of the nose is a third part; the nose from the bottom of the nostrils to the line between the eyebrows, likewise; from there to the lowest roots of the hair, the forehead, likewise a third part. The foot is a sixth part of the height of the body; the cubit a fourth; the breast also a fourth. The remaining members too have their own proportions of measurement, which the ancient painters and famous sculptors used, and thereby attained great and infinite praise. §6
In like manner too, the members of sacred temples ought to have most fitting correspondences of measure, of the several parts to the whole sum of their size. The natural center of the body is the navel. For if a man be placed on his back with hands and feet spread out, and the center of the compasses be placed on his navel, by drawing round it the line will touch the tips of the fingers of both hands and of the feet. No less, just as the figure of a circle is produced on the body, so also a square figure is found there. For if one measures from the soles of the feet to the top of the head, and that measure be brought back to the outstretched hands, the breadth will be found to be the same as the height, as of plots which are squared to the rule. §7
If therefore the nature of things has so composed the body of a man that by proportions the members answer to its whole shape, the ancients seem to have established with reason that in the perfection of works also there should be an exact calculation of the single members to the appearance of the whole figure. Therefore, while they handed down orders in all works, they did so especially in the buildings of the gods, whose works' praises and blames alike tend to endure forever. §8
No less did they derive from the members of the body the reasonings of measurement, which in all works seem necessary: finger, palm, foot, cubit; and these they distributed into a perfect number, which the Greeks call τέλειον. The ancients established as a perfect number that which is called ten. For from the hands, from the number of fingers, the foot was discovered by the palm. But if in both hands, from the joints, by nature ten are perfected, it pleased Plato also that the number was perfect on this ground, which is made up of individual things (which the Greeks call μονάδες) by the decad. As soon, however, as eleven or twelve are made, because they have gone beyond, they cannot be perfect, until they come to the second decad. For individual things are parts of that number. §9
The mathematicians, disputing on the contrary, have said that the number which is called six is perfect, because it has these divisions corresponding to the reason of number: the sextans one, the triens two, the semis three, the bes (which they call δίμοιρον) four, the quintarius (which they call πεντάμοιρον) five, the perfect six. When by addition it increases, one added to six is ἐφεκτόν; when made eight, because a third has been added, another third (ἐπίτριτος); a half added, when made nine, the sesquialter (ἡμιόλιος); two parts added and a decad made, another bes (ἐπιδίμοιρον); in eleven, because five have been added, the quintarius (ἐπίπεμπτον); twelve, because effected from two simple numbers, διπλάσιον. §10
No less also, because the foot has a sixth part of the man's height, that is, because from the number of feet six make up the height-termination of the body, they established it as the perfect; and they noticed that the cubit consists of six palms and twenty-four fingers. Thence also the cities of the Greeks seem to have done the same: as the cubit is of six palms, in the drachma which they used as coin they minted, as if asses, six bronze pieces by an equal rule, which they call oboli; and the quarter-obols (which some call dichalca and some trichalca), as their fingers, twenty-four in the drachma. §11
But our people first made the ancient number, and in the denarius established ten pieces of bronze; and for this reason the composition of the name denarius is retained to this day. And that the fourth part was effected from two asses and a third semis, they called it sestertius. But afterwards, when they saw that both numbers were perfect, six and ten, they combined both in one and made the most perfect number, sixteen (decussis sexis). They found the foot to be the author of this. For when from the cubit two palms are removed, there remains a foot of four palms; and a palm has four fingers. Thus it is effected that the foot has sixteen fingers, and as many asses of bronze is the denarius. §12
If therefore it agrees that the number has been found from the articulations of man, and that from the separate members to the whole appearance of the body a correspondence of commensurate parts is made, it remains for us to admire those who, in setting up also the temples of the immortal gods, so ordered the members of their works that by proportions and symmetries the distributions of them, separate and whole, should be made to correspond. §13
The principles of temples, of which the appearance of their figures consists, are these. First, in antis, which in Greek is called ναὸς ἐν παραστάσιν; then prostyle; amphiprostyle; peripteral; pseudodipteral; dipteral; hypaethral. Of these the formations are expressed by these methods. §14
In antis will be a temple when it shall have in front the antae of the walls which enclose the cella, and between the antae, in the middle, two columns; and above, a pediment laid with that symmetry which shall have been set down in this book. The exemplar of this will be at the temple of the Three Fortunes, of the three that is nearest to the Colline gate. §15
Prostyle has all that is in the antae-temple, but also two columns opposite the angular antae, and above architraves as in the antae-temple, and on the right and on the left in the returns one column each. The exemplar is on the Tiberine island, in the temple of Jupiter and Faunus. §16
Amphiprostyle has all that the prostyle has, and in addition has, at the back, in like manner, columns and a pediment. §17
The peripteral will be that which shall have in front and at the rear six columns, at the sides with the angular, eleven. These columns shall be so placed that the space of the intercolumniation be, from the walls round to the outermost rows of columns, of one intercolumniation; and let it have an ambulatory around the cella of the temple, as in the portico of Metellus for Jupiter Stator by Hermodorus, and in the Marian temple of Honour and Virtue built by Mucius without rear portico. §18
The pseudodipteral is so placed that in front and at the rear there are eight columns, and at the sides with the angular, fifteen. And let the walls of the cella be opposite the four middle columns in the front and at the rear. Thus the space of two intercolumniations and of the lowest diameter of a column will stand from the walls to the outermost ranks of columns. The exemplar of this is not at Rome, but at Magnesia is the temple of Diana by Hermogenes, and at Alabanda also that of Apollo by Menestheus. §19
The dipteral, moreover, is octastyle both in pronaos and in rear portico, but around the temple it has double rows of columns: such is the temple of Quirinus, Doric, and at Ephesus that of Diana, Ionic, built by Chersiphron. §20
The hypaethral, however, is decastyle in front and at the rear. In everything else it is like the dipteral, but in the interior it has columns of a double height, standing off from the walls for circulation, like the porticoes of peristyles. In the middle it lies open to the sky, without roof. The approach of the doors is on each side, in the pronaos and at the rear. An exemplar of this too is not at Rome; but at Athens it is octastyle, in the temple of Olympian Jupiter. §21
There are five species of temples; whose names are these: pycnostyle (that is, of close-set columns), systyle (with slightly wider spaces of intercolumniation), diastyle (still wider), araeostyle (columns more widely set than is fitting), eustyle (with just distribution of intervals). §22
The pycnostyle, then, is that in whose intercolumniation a column-thickness of one and a half can be inserted, as is that of the deified Julius, and in Caesar's forum that of Venus, and others composed in like manner. The systyle, likewise, is that in which the thickness of two columns can be placed in the intercolumniation, and the plinths of the bases are equal in size to the space that lies between two plinths: as is that of Fortuna Equestris, by the stone theater, and the others composed by the same reasonings. §23
Both these kinds have a faulty usage. For when the matrons go up by the steps for supplication, they cannot go in through the intercolumniations in their groups, unless they form into rows; likewise the view of the doors is blocked by the close-set columns, and the statues themselves are obscured; and around the temple, on account of the narrowness, the walking is impeded. §24
Of the diastyle the composition will be this: when we can place the thickness of three columns in the intercolumniation, as is the temple of Apollo and of Diana. This arrangement has this difficulty, that the architraves break on account of the greatness of the intervals. §25
In araeostyles, moreover, neither stone nor marble architraves can be used, but continuous timber beams must be laid on. And of these temples themselves, the appearance is heavy-headed, low, and broad, and their pediments are adorned with terra-cotta or gilt bronze figures in the Tuscan manner, as at the Circus Maximus the temple of Ceres, of Pompeian Hercules, and of the Capitoline Jupiter. §26
Now the reasoning of the eustyle must be rendered, which has reasonings most commendable, both for use, for appearance, and for firmness. For the spaces are to be made in the intervals of two columns and a fourth of a column's thickness; the middle intercolumniation, the one in front, and the other at the rear, of three columns' thickness. So it will have a graceful look of its figure, an approach without obstruction, and about the cella an ambulatory of authority. §27
The reasoning of this matter will be unfolded thus. The front of the place in which the temple is to be set, if it is to be tetrastyle, is to be divided into eleven and a half parts, aside from the stylobates and projections of the bases; if six-columned, into eighteen; if octastyle, into twenty-four and a half. Of these parts, whether tetrastyle, hexastyle, or octastyle, one part is to be taken, and that will be the module. Of this module one will be the thickness of the columns. The single intercolumniations, except the middle ones, will be of two modules and a fourth of a module; the middle one in front and at the rear, each of three modules. The height of the columns themselves, nine modules and a half of a module. By this division the intercolumniations and the heights of the columns will have a just proportion. §28
Of this we have no exemplar at Rome, but in Asia at Teos the hexastyle of Father Liber. These symmetries Hermogenes established, who also first invented the reasoning of the pseudodipteral octastyle. For from the symmetry of the dipteral temple he removed the thirty-eight interior columns, and by that reasoning made a saving of expense and labor. In the middle he made space excellently for walking about the cella, nor diminished anything from the look, but without need of superfluities preserved the authority of the whole work in the distribution. §29
For the device of the wing and the arrangement of columns around the temple were invented that the aspect might have authority from the frequency of intercolumniations; besides, that if the force of water from the rains should seize and shut in a multitude of men, they might have within the temple and around the cella, with ease, a free wait. These things are set forth in the pseudodipteral arrangements of temples. Wherefore Hermogenes seems to have wrought the effect of works with keen and great dexterity, and to have left the springs whence posterity could draw the reasonings of their disciplines. §30
In araeostyle temples the columns are to be so made that their thickness be an eighth part of their height. In diastyle, the height of the column is to be divided into eight and a half parts, and the thickness of the column set at one of those parts. In systyle, the height is to be divided into nine and a half parts, and of these one is given to the thickness of the column. Likewise in pycnostyle the height is to be divided into ten, and one part of it is to be made the thickness of the column. Of the eustyle temple, as of the systyle, the height is to be divided into nine parts and a half, and one part of it fixed for the thickness of the lower shaft. So one will have a proportioned reasoning of the intercolumniations. §31
For as the spaces between the columns increase, so by proportions must the thickness of the shafts be augmented. For if in an araeostyle the thickness is a ninth or a tenth part, it will appear thin and slender, because through the breadth of the intercolumniations the air consumes and diminishes the thickness of the shafts to the view. In a pycnostyle, on the contrary, if the thickness be an eighth part, on account of the close-set and narrow intercolumniations it will produce a swollen and graceless appearance. Therefore one must pursue the symmetries of the kind of work. Also the corner columns are to be made thicker than the rest by a fiftieth part of their diameter, because they are cut by the air and seem to the beholders slimmer. Therefore what the eye deceives must be made good by reasoning. §32
The tapering at the tops of the necks of the columns must be so made that, if the column be at the smallest of fifteen feet, let the lower thickness be divided into six parts, and of these parts five be made the top. Likewise that which shall be from fifteen to twenty feet, let the lower shaft be divided into six and a half parts, and of these five and a half let the upper thickness of the column be made. Likewise that which shall be from twenty to thirty feet, let the lower shaft be divided into seven parts, and of these six be the top's tapering. And that which shall be from thirty feet to forty, let the bottom be divided into seven and a half, and of these six and a half let it have at the top by the reasoning of the tapering. Those that shall be from forty feet to fifty, likewise, are to be divided into eight parts, and of these seven shall be tapered on the top shaft beneath the capital. Likewise, if any shall be higher, in proportion let the taperings be established in the same manner. §33
Now these compensations, on account of the interval of the height, are added to the thicknesses, as the eye's sight climbs. For sight pursues beauty; and if we do not humor its pleasure by proportions and additions of modules, so that what deceives may be increased by tempering, an ungraceful and rough aspect will be returned to the beholders. Of the addition (entasis in Greek, ἔντασις) which is added in the middle of the columns, at the end of this book will be the figure and the reasoning of it, how it may be made soft and proper, subscribed. §34
Let the foundations of these works be dug, if it can be found, down to and into solid ground, so much as, from the amplitude of the work, shall seem fit; and let a structure be built up through the whole area, the firmest possible. Above ground let walls be raised beneath the columns, thicker by half than the columns will be, that the lower may be firmer than the higher. These also are called stereobates, for they sustain the loads. The projections of the bases should not go forth beyond the solid. Likewise above, the thickness of the wall is to be preserved in the same fashion; the intervals between are to be either vaulted or consolidated by rammings, so that they may be held apart. §35
But if solid ground be not found, and the place be filled up at the bottom, or marshy, then let that place be dug out and hollowed, and let piles of alder or olive or charred oak be driven in, and let the piles be driven by engines as close as possible; and let the intervals between the piles be filled with charcoals, and then let the foundations be filled with the firmest structures. The foundations built, let the stylobates be laid to the level. §36
Above the stylobates let the columns be disposed as has been written above, whether in pycnostyle in the pycnostyle manner, or in systyle, diastyle, or eustyle as has been written and established. In araeostyles, indeed, there is liberty to establish as one pleases. But in peripteral temples the columns are to be placed so that as many intercolumniations as are in the front, twice as many shall be made in the sides. Thus the length of the work will be double its breadth. For those who have doubled the columns seem to have erred, because one intercolumniation projects in length more than is fitting. §37
The steps in the front are to be so set that they be always odd in number. For when the right foot ascends the first step, likewise on the temple's threshold it must be the first to be set. I judge the thicknesses of those steps to be so limited that they be set neither thicker than ten inches, nor thinner than nine. For thus the ascent will not be hard. The retractions of the steps are to be made neither less than a foot and a half, nor more than two feet. Likewise if about the temple there are to be steps, they should be made in the same fashion. §38
But if about the temple on three sides a podium is to be made, let it be so established that the square plinths of the bases, their dadoes, and the cornice and lysis (base-crowning) may correspond to the stylobate itself which shall be under the bases of the columns. The stylobate must be so leveled that it have in the middle a rising by unequal scamilli. For if it be directed to the level, to the eye it will seem hollow. Now how the scamilli suited to this purpose may be made, likewise at the end of the book will the figure and demonstration be drawn. §39
These things done, let the bases be set in their places, and be made symmetrically, so that the thickness with the plinth be a half of the column's thickness, and let them have an equal projection (which the Greeks call ἐκφορά). So it will be broad and long one and a half of the column's thickness. §40
If the base be in the Attic manner, let its height be so divided that the upper part be a third part of the column's thickness, and the rest be left to the plinth. With the plinth removed, let the rest be divided into four parts, and let the upper torus be made a fourth; the remaining three be divided equally, and let one be the lower torus, the other part, with its fillets, be the scotia (which the Greeks call τρόχιλον). §41
If, however, they are to be made Ionic, their symmetries shall be so constituted that the breadth of the base each way be the column-thickness with a quarter and an eighth added; the height as in the Attic, and its plinth likewise; the remaining portion beside the plinth, which will be a third part of the column-thickness, let be divided into seven parts. Of these, three parts be the upper torus; the remaining four are to be divided equally; one part with its astragals and the cyma-fillet be the upper trochilos, the other part be left to the lower trochilos. But the lower will look larger, because it will have its projection to the outer plinth. The astragals are to be made an eighth part of the trochilos. The projection of the base will be an eighth part plus a sixteenth of the column's thickness. §42
The bases set and placed, the middle columns in the pronaos and rear portico are to be set perpendicular to the middle center; the corner columns and those which shall stand in line with them, on the right and left sides of the temple, shall be set so that their inside parts, which look towards the walls of the cella, are placed perpendicular, while their outer parts follow the tapering as has been said before. Thus the shapes of the composition of temples will have been worked out, in the matter of tapering, by a just reasoning. §43
With the shafts of the columns set up, the reasoning of the capitals, if they are of the cushion sort, will be this: they shall be formed by these symmetries so that, to the thickness of the shaft at the foot, an eighteenth part being added, the abacus shall have that as its length and breadth, the thickness with the volutes being half of that. Step back from the extreme of the abacus, towards the inside, on the fronts of the volutes, by a nineteenth part and a half. Then divide the thickness into nine and a half parts; next, against the abacus, in the four parts of the volutes, from the square of the uttermost abacus, let lines be dropped which are called cathetoes. Then, of the nine and a half parts, let one part and a half be left for the thickness of the abacus; the remaining eight let be set aside for the volutes. §44
Then from the line dropped by the outermost part of the abacus, let another line recede into the interior by the breadth of one and a half parts. Then let those lines be so divided that four and a half parts be left under the abacus. Then in that place which divides the four and a half and the three and a half, let the center of the eye be placed, and from that center let a round circle be marked out as great in diameter as one part out of the eight. This will be the size of the eye, and in it let a diameter corresponding to the cathetus be drawn. Then, beginning at the top under the abacus, at each quadrant's turn, let the space of the eye be diminished by half, until one comes back to the same quadrant which is under the abacus. §45
The thickness of the capital must be so made that, of the nine and a half parts, three parts hang down beneath the astragal of the top of the shaft, with the cymatium, the abacus and channel removed, the rest being the part. The projection of the cymatium beyond the square of the abacus should be equal to the size of the eye. The belts of the cushion-volutes (pulvini) are to have this projection from the abacus: when one point of the compasses is placed in the quadrant of the capital and the other is opened to the extreme of the cymatium, let the sweep touch the extreme parts of the belts. The axes of the volutes are not to be thicker than the size of the eye; and the volutes themselves are to be undercut by a twelfth of their height. These will be the symmetries of capitals of columns which shall be, at the least, up to twenty-five feet. Those higher will have their symmetries in the same way, but the abacus will be longer and broader than the lower thickness of the column is, by a ninth part, so that by as much as the taller column has less in tapering, the capital may not have less of the projection of its own symmetry and of the addition of its own part in breadth. §46
Of the drawings of the volutes, how they are drawn so that they be rightly scrolled to the compasses, at the end of the book the figure and the reasoning of them will be subscribed. The capitals made, then, the columns being placed in proportion, not to the level but to an equal module, so that, what addition has been made in the stylobates, may respond in the members above, the reasoning of the architraves is to be taken thus: if the columns shall be, at the least, from twelve to fifteen feet, let the height of the architrave be half of the thickness of the lowest column; likewise if from fifteen to twenty feet, let the column's height be divided into thirteen parts and one of those parts be the height of the architrave; likewise if from twenty to twenty-five feet, let the height be divided into twelve and a half parts and one part of it be the height of the architrave; likewise if from twenty-five to thirty, let it be divided into twelve parts and one part be the height; likewise if taller, by a proportioned part in the same way, out of the heights of the columns, the heights of the architraves are to be worked out. §47
For the further up the look of the eye climbs, the less easily it cuts through the thickness of the air. So, having slipped by the space of height and drained of vigor, it gives back to the senses an uncertain quantity of the modules. Wherefore there must always be added a supplement of reasoning in the members of the symmetries, so that, when works shall be in higher places, or even be themselves colossal, they may have a reasoning of their magnitudes. The breadth of the architrave at the bottom, above the capital, shall be as much as the thickness of the top of the column below the capital; at the top, as much as the lower shaft. §48
The cymatium of the architrave is to be made a seventh part of its own height, and of equal projection. The rest, beside the cymatium, is to be divided into twelve parts, of which three are the lowest fascia, the second four, the highest five. Likewise, the frieze above the architrave is a fourth part less than the architrave; but if figures are to be designed there, it is to be a fourth part higher than the architrave, that the sculptures may have authority. The cymatium is a seventh part of its own height; the projection of the cymatium, as its thickness. §49
Above the frieze the dentil-band is to be made as high as the middle fascia of the architrave; its projection, as much as its height. The intersection (in Greek μετόπη) is to be so divided that the dentil have, in front, a half of its own height; the hollow of this intersection, in front, be two thirds of it; its cymatium a sixth part of its height. The corona with its cymatium, beside the sima, is as high as the middle fascia of the architrave; the projection of the corona, with the dentils, must be made equal to the height from the frieze to the top cymatium of the corona; and in general all projections have a more graceful look if, equal to their height, they have equal projection. §50
Of the tympanum which is in the pediment, the height is to be made thus: the front of the corona from the extreme cymatia is to be divided in its whole length into nine parts, and one of them be set at the middle peak of the tympanum, provided that it correspond perpendicularly to the architraves and the necks of the columns. The coronas above are to be set equal to those below, save for the simae. Above the coronas the simae (which the Greeks call ἐπαιετίδας) are to be made higher than the height of the coronas by an eighth part. The corner acroteria are to be as high as the middle of the tympanum; the middle ones higher than the angular by an eighth part. §51
All the members which shall be above the capitals of the columns, that is, architraves, friezes, coronas, tympana, pediments, and acroteria, are to be inclined forward, each by a twelfth part of its own height. For when we stand against the fronts, if from the eye two lines be extended, and one touches the lowest part of the work, the other the topmost, that which touches the top will be longer. So the further the line of sight proceeds upward, the more supine appears the look of the work. But when, as has been written above, these members have been inclined forward, then in aspect they will appear to be perpendicular and to the rule. §52
Of the columns, twenty-four flutes are to be made, so excavated that, when a square is applied in the cavity of the flute, being swung around, the angles of the flute on the right and left sides shall touch its angles, and the apex of the square be able to wander round the curvature. The thicknesses of the flutes are to be made so large as the addition that is found in the middle of the column by the drawing of the entasis. §53
In the simas that are above the corona at the sides of the temples, lion-heads are to be carved, disposed so that first, one is designated opposite each column, and the rest disposed evenly, so that each corresponds to each of the middle tiles. Those opposite the columns should be pierced through, down to the channel that receives the rain-water from the tiles; the middle ones solid, so that the force of the water which falls through the tiles into the channel may not be thrown down through the intercolumniations nor drench those passing by, while those opposite the columns may seem to send forth, vomiting up, the belchings of water out of their mouths. The dispositions of Ionic temples I have written, as plainly as I could, in this volume; but what are the proportions of the Doric and Corinthian I will unfold in the following book. §54