#### CHAPTER III: PROPORTIONS OF THE PRINCIPAL ROOMS

1. THERE are five different styles of cavaedium, termed according to their construction as follows: Tuscan, Corinthian, tetrastyle, displuviate, and testudinate.

In the Tuscan, the girders that cross the breadth of the atrium have crossbeams on them, and valleys sloping in and running from the angles of the walls to the angles formed by the beams, and the rainwater falls down along the rafters to the roof-opening (compluvium) in the middle. In the Corinthian, the girders and roof-opening are constructed on these same principles, but the girders run in from the side walls, and are supported all round on columns. In the tetrastyle, the girders are supported at the angles by columns, an arrangement which relieves and strengthens the girders; for thus they have themselves no great span to support, and they are not loaded down by the crossbeams.

2. In the displuviate, there are beams which slope outwards, supporting the roof and throwing the rainwater off. This style is suitable chiefly in winter residences, for its roof-opening, being high up, is not an obstruction to the light of the dining rooms.

3. In width and length, atriums are designed according to three classes. The first is laid out by dividing the length into five parts and giving three parts to the width; the second, by dividing it into three parts and assigning two parts to the width; the third, by using the width to describe a square figure with equal sides, drawing a diagonal line in this square, and giving the atrium the length of this diagonal line.

4. Their height up to the girders should be one fourth less than their width, the rest being the proportion assigned to the ceiling and the roof above the girders. The alae, to the right and left, should have a width equal to one third of the length of the atrium, when that is from thirty to forty feet long. From forty to fifty feet, divide the length by three and one half, and give the alae the result. When it is from fifty to sixty feet in length, devote one fourth of the length to the alae. From sixty to eighty feet, divide the length by four and one half and let the result be the width of the alae. From eighty feet to one hundred feet, the length divided into five parts will produce the right width for the alae. Their lintel beams should be placed high enough to make the height of the alae equal to their width.

5. The tablinum should be given two thirds of the width of the atrium when the latter is twenty feet wide. If it is from thirty to forty feet, let half the width of the atrium be devoted to the tablinum. When it is from forty to sixty feet, divide the width into five parts and let two of these be set apart for the tablinum. In the case of smaller atriums, the symmetrical proportions cannot be the same as in larger. For if, in the case of the smaller, we employ the proportion that belong to the larger, both tablina

6. The height of the tablinum at the lintel should be one eighth more than its width. Its ceiling should exceed this height by one third of the width. The fauces in the case of smaller atriums should be two thirds, and in the case of half the width of the tablinum. Let the busts of ancestors with their ornaments be set up at a height corresponding to the width of the alae. The proportionate width and height of doors may be settled, if they are Doric, in the Doric manner, and if Ionic, in the Ionic manner, according to the rules of symmetry which have been given about portals in the fourth book. In the roof-opening let

7. Peristyles, lying athwart, should be one third longer than they are deep, and their columns as high as the colonnades are wide.

8. Dining rooms ought to be twice as long as they are wide. The height of all oblong rooms should be calculated by adding together their measured length and width, taking one half of this total, and using the result for the height. But in the case of exedrae or square oeci, let the height be brought up to one and one half times the width. Picture galleries, like exedrae, should be constructed of generous dimensions. Corinthian and tetrastyle oeci, as well as those termed Egyptian, should have the same symmetrical proportions in width and length as the dining rooms described above, but, since they have columns in them, their dimensions should be ampler.

9. The following will be the distinction between Corinthian and Egyptian oeci: the Corinthian have single tiers of columns, set either on a podium or on the ground, with architraves over them and coronae either of woodwork or of stucco, and carved vaulted ceilings above the coronae. In the Egyptian there are architraves over the columns, and joists laid thereon from the architraves to the surrounding walls, with a floor in the upper story to allow of walking round under the open sky. Then, above the architrave and perpendicularly over the lower tier of columns, columns one fourth smaller should be imposed. Above their architraves and ornaments are decorated ceilings, and the upper columns have windows set in between them. Thus the Egyptian are not like Corinthian dining rooms, but obviously resemble basilicas.

10. There are also, though not customary in Italy, the oeci which the Greeks call Cyzicene. These are built with a northern exposure and generally command a view of gardens, and have folding doors in the middle. They are also so long and so wide that two sets of dining couches, facing each other, with room to pass round them, can be placed therein. On the right and left they have windows which open like folding doors, so that views of the garden may be had from the dining couches through the opened windows. The height of such rooms is one and one half times their width.

11. All the above-mentioned symmetrical relations should be observed, in these kinds of buildings, that can be observed without embarrassment caused by the situation. The windows will be an easy matter to arrange if they are not darkened by high walls; but in cases of confined space, or when there are other unavoidable obstructions, it will be permissible to make diminutions or additions in the symmetrical relations,—with ingenuity and acuteness, however, so that the result may be not unlike the beauty which is due to true symmetry.