On Architecture

3. Now whether this appearance is due to the impact of the images, or to the effusion of the rays from the eye, as the physicists hold, in either case it is obvious that the vision may lead us to false impressions.

4. Since, therefore, the reality may have a false appearance, and since things are sometimes represented by the eyes as other than they are, I think it certain that diminutions or additions should be made to suit the nature or needs of the site, but in such fashion that the buildings lose nothing thereby. These results, however, are also attainable by flashes of genius, and not only by mere science.

5. Hence, the first 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 breadth of the work proposed, and when once we have determined its size, let the construction follow this with due regard to beauty of proportion, so that the beholder may feel no doubt of the eurythmy of its effect. I must now tell how this may be brought about, and first I will speak of the proper construction of a cavaedium.

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. It is, however, very troublesome to keep in repair, because the pipes, which are intended to hold the water that comes dripping down the walls all round, cannot take it quickly enough as it runs down from the channels, but get too full and run over, thus spoiling the walls of style. The testudinate is employed where the span is not great, and where large rooms are provided in stories.

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