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Symmetry , and Modification in it to Suite the SiteChapter IIStandard of SymmetryFirst thing to settle is the standard of symmetry, from which we need not hesitate to vary, then lay out the ground lines of the length and breath of the work proposed and when once we have determined the size, let the construction follow this width with due regard to beauty of proportion, so that the beholder may feel no doubt of the eurhythmy of its effect. Proportions of the Principal RoomsChapter IIIStyles of CavaediumTuscan CorinthianTetrastyleDispluviateTestudinateTuscanThe 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.CorinthianThe girders and roof opening are constructed on these same principles, but the girders run in from the side walls, and are supported by all around on columns TetrastyleThe girders are supported at the angles by columns, an arrangement which relieves and strengthens the girders; for thus have themselves no great span to support, and they are not loaded down by the cross beams.DispluviateBeams slope upwards, supporting the roof and throwing the rainwater off. This sty7le is suitable chiefly in winter residences, for its roof opening, being high up, is not an obstruction to the light of the dining rooms.It is however, very troublesome to keep in repair, because the pipes, which are intended to hold the water that comes dripping down the halls all around, cannot take it quickly enough as it runs down from the channels, but get too full and run over, thus spoiling the wood work and the walls of houses of this style.

TestudinateEmployed where the span is not great and where large rooms are provided in upper storiesThree Classes of Atrium according to Width and Length 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 lineHeightTheir height should be one fourth less than their width, the rest being the proportion assigned to the ceiling and the roof above the girdersAlaeThe alae, to the right and left, should have a width equal to one third of the length of the atrium, when that is from 30 to 40 ft long. AlaeAlaeFrom 40- 50 ft, divide the length by three and one half, and give the alae the resultAlaeFrom 50 60 ft in length, devote one fourth of the length to the alae.AlaeFrom 60 80 ft, divide the length by four and one half and let the result be the width of the alae.AlaeFrom 80 100 ft, divide the length 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.TablinumTablinumIt should be given two thirds of the width of the atrium when the latter is twenty feet wide. 30-40 ft, let half of the width of the atrium be devoted to the tablinumTablinum40 60 ftDivide 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 and alae must be unserviceable, while if, in the case of the larger, we employ the proportions of the smaller, the rooms mentioned will be huge monstrosities. The height of the Tablinum at the lintel should be one eight 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 larger one half the width of the tablinum.OrnamentsLet the bust of ancestors with their ornaments be set up at a height corresponding to the width of the alae.DoorsThe 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 an aperture be left with a breadth of not less than one fourth nor more than one third the width of the atrium, and with a length proportionate to that of the atrium.PeristylesPeristylesLying athwart, should be one third longer than they are deep and their columns as high as the colonnades are wide. Intercolumniations of peristyles should be not less than three nor more than four times the thickness of the columnsIf the columns of the peristyle arc to be made in the Doric style, take the modules given in the fourth book, on the Doric Order, and arrange the columns with reference to these modules and to the scheme of the triglyphs

Dining RoomDining room 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 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 GalleryPicture Galleries, like exedrae, should be constructed 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.Distinction between Corinthian and Egyptian oeciCorinthian Have single tier of columns, set either on a podium or on the ground, with architraves over them and coronae either of wood work or of stucco, and carved vaulted ceilings above the coronae.Egyptian There are architraves over the columns, and joist laid thereon from the architraves to the surrounding walls, with a floor in the upper story to allow walking round under the open sky. Then, above the architrave and perpendicularly over the lower tier of column, columns one fourth smaller should be imposed. Above their architraves and ornamentsare decorated celings, and the upper columns have windows set in between them. Thus the Egyptian are not like Corinthian dining rooms, but obviously resemble basilicasCyziceneOeci in GreeksBuilt with a northern exposure and generally command a view of gardens, and have a 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 place 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 widthAll the above-mentioned symmetrical relations should be observed, in these kinds of buildings, that can be observed without embarrassments caused by the situations. 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 obstruction, it will be permissible to make diminutions or additions in the symmetrical relations, - with ingenuity and acuteness, however, so that the result may not be not unlike the beauty which is due to true symmetry