1. THIS finished, let the bases of the columns be set in place, and constructed in such proportions that their height, including the plinth, may be half the thickness of a column, and their projection (called in Greek e)kfora/) the same.[*](Reading aeque tantam as in new Rose. Codd. sextantem; Schn. quadrantem.) Thus in both length and breadth it will be one and one half thicknesses of a column.
2. If the base is to be in the Attic style, let its height be so divided that the upper part shall be one third part of the thickness of the column, and the rest left for the plinth. Then, excluding the plinth, let the rest be divided into four parts, and of these let one fourth constitute the upper torus, and let the other three be divided equally, one part composing the lower torus, and the other, with its fillets, the scotia, which the Greeks call troxi/los.
3. But if Ionic bases are to be built, their proportions shall be so determined that the base may be each way equal in breadth to the thickness of a column plus three eighths of the thickness; its height that of the Attic base, and so too its plinth; excluding the plinth, let the rest, which will be a third part of the thickness of a column, be divided into seven parts. Three of these parts constitute the torus at the top, and the other four are to be divided equally, one part constituting the upper trochilus with its astragals and overhang, the other left for the lower trochilus. But the lower will seem to be larger, because it will project to the edge of the plinth. The astragals must be one eighth of the trochilus. The projection of the base will be three sixteenths of the thickness of a column.
4. The bases being thus finished and put in place, the columns are to be put in place: the middle columns of the front and rear porticoes perpendicular to their own centre; the corner columns, and those which are to extend in a line from them along the sides
5. The shafts of the columns having been erected, the rule for the capitals will be as follows. If they are to be cushion-shaped, they should be so proportioned that the abacus is in length and breadth equivalent to the thickness of the shaft at its bottom plus one eighteenth thereof, and the height of the capital, including the volutes, one half of that amount. The faces of the volutes must recede from the edge of the abacus inwards by one and a half eighteenths of that same amount. Then, the height of the capital is to be divided into nine and a half parts, and down along the abacus on the four sides of the volutes, down along the fillet at the edge of the abacus, lines called “catheti” are to be let fall. Then, of the nine and a half parts let one and a half be reserved for the height of the abacus, and let the other eight be used for the volutes.
6. Then let another line be drawn, beginning at a point situated at a distance of one and a half parts toward the inside from the line previously let fall down along the edge of the abacus. Next, let these lines be divided in such a way as to leave four and a half parts under the abacus; then, at the point which forms the division between the four and a half parts and the remaining three and a half, fix the centre of the eye, and from that centre describe a circle with a diameter equal to one of the eight parts. This will be the size of the eye, and in it draw a diameter on the line of the “cathetus.” Then, in describing the quadrants, let the size of each be successively less, by half the diameter of the eye, than that which begins under the abacus, and proceed from the eye until that same quadrant under the abacus is reached.
7. The height of the capital is to be such that, of the nine and a half parts, three parts are below the level of the astragal at the top of the shaft, and the rest, omitting the abacus and the channel,
8. With regard to the method of describing volutes, at the end of the book a figure will be subjoined and a calculation showing how they may be described so that their spirals may be true to the compass.
The capitals having been finished and set up in due proportion to the columns (not exactly level on the columns, however, but with the same measured adjustment, so that in the upper members there may be an increase corresponding to that which was made in the stylobates), the rule for the architraves is to be as follows. If the columns are at least twelve feet and not more than fifteen feet high, let the height of the architrave be equal to half the thickness of a column at the bottom. If they are from fifteen feet to twenty, let the height of a column be measured off into thirteen parts, and let one of these be the height of the architrave. If they are from twenty to twenty-five feet, let this height be divided into twelve and one half parts, and let one of them form the height of the architrave. If they are from twenty-five feet to thirty, let it be divided into twelve parts, and let one of
9. For the higher that the eye has to climb, the less easily can it make its way through the thicker and thicker mass of air. So it fails when the height is great, its strength is sucked out of it, and it conveys to the mind only a confused estimate of the dimensions. Hence there must always be a corresponding increase in the symmetrical proportions of the members, so that whether the buildings are on unusually lofty sites or are themselves somewhat colossal, the size of the parts may seem in due proportion. The depth of the architrave on its under side just above the capital, is to be equivalent to the thickness of the top of the column just under the capital, and on its uppermost side equivalent to the foot of the shaft.
10. The cymatium of the architrave should be one seventh of the height of the whole architrave, and its projection the same. Omitting the cymatium, the rest of the architrave is to be divided into twelve parts, and three of these will form the lowest fascia, four, the next, and five, the highest fascia. The frieze, above the architrave, is one fourth less high than the architrave, but if there are to be reliefs upon it, it is one fourth higher than the architrave, so that the sculptures may be more imposing. Its cymatium is one seventh of the whole height of the frieze, and the projection of the cymatium is the same as its height.
11. Over the frieze comes the line of dentils, made of the same height as the middle fascia of the architrave and with a projection equal to their height. The intersection (or in Greek meto/ph) is apportioned so that the face of each dentil is half as wide as its height and the cavity of each intersection two thirds of this face in width. The cymatium here is one sixth of the whole height of this part. The corona with its cymatium, but not including the sima, has the height of the middle fascia of the architrave, and the total projection of the corona and dentils should be equal to the height from the frieze to the cymatium at the top of the corona.
12. The height of the tympanum, which is in the pediment, is to be obtained thus: let the front of the corona, from the two ends of its cymatium, be measured off into nine parts, and let one of these parts be set up in the middle at the peak of the tympanum, taking care that it is perpendicular to the entablature and the neckings of the columns. The coronae over the tympanum are to be made of equal size with the coronae under it, not including the simae. Above the coronae are the simae (in Greek e)paieti/des), which should be made one eighth higher than the height of the coronae. The acroteria at the corners have the height of the centre of the tympanum, and those in the middle are one eighth part higher than those at the corners.
13. All the members which are to be above the capitals of the columns, that is, architraves, friezes, coronae, tympana, gables, and acroteria, should be inclined to the front a twelfth part of their own height, for the reason that when we stand in front of them, if two lines are drawn from the eye, one reaching to the bottom of the building and the other to the top, that which reaches to the top will be the longer. Hence, as the line of sight to the upper part is the longer, it makes that part look as if it were leaning back. But when the members are inclined to the front, as described above, they will seem to the beholder to be plumb and perpendicular.
14. Each column should have twenty-four flutes, channelled out in such a way that if a carpenter's square be placed in the hollow of a flute and turned, the arm will touch the corners of the fillets on the right and left, and the tip of the square may keep touching some point in the concave surface as it moves through it. The breadth of the flutes is to be equivalent to the enlargement in the middle of a column, which will be found in the figure.
15. In the simae which are over the coronae on the sides of the temple, lion's heads are to be carved and arranged at intervals thus: First one head is marked out directly over the axis of each