Architecture depends on Order, Arrangement, Eurythmy, Symmetry , Propriety , and Economy.

Noting all these things with the great delight which learning gives, we cannot but be stirred by these discoveries when we reflect upon the influence of them one by one.

Remembering that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.

The stone in quarries is found to be of different and unlike qualities. In some it is soft, in others it is medium, in still others it is hard as in lava quarries. There are also numerous other kinds: for instance, in Campania, red and black tufas; in Umbria, Picenum, and Venetia, white tufa which can be cut with a toothed saw like wood.

In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.

Consistency is found in that work whose whole and detail are suitable to the occasion. It arises from circumstance, custom, and nature.

Leave a cavity behind the [wall] facings, and on the inside build walls two feet thick, made of red dimension stone or burnt brick or lava in courses, and then bind them to the fronts by means of iron clamps and lead. The beds and builds, all settling equally and bonded at the joints, will not let the work bulge out, nor allow the fall of the face walls which have been tightly fastened together.