Ten Books on Architecture

in our common [parlance]; concerning which I shall briefly collect the observations most to be considered.

Antae, or pilasters, ought not to be too tall or slender, lest they appear to be columns, nor too squat or thick, lest they imitate the piers of bridges. A rustic surface becomes them better than elegance; for they aspire more to firmness and strength than to elegance. In private buildings, it is not appropriate for them to be narrower than one-third, nor wider than two-thirds of the entire void between one anta and another. However, to those which stand at the corners, a slightly greater width may be given for the sake of strengthening the angles; in theaters, amphitheaters, and such heavy structures, Palladius observes that they may be as wide as one-half or, at times, the entire interval. He notes, moreover (and others agree), that their proper symmetry is an exact square; but for the sake of reducing expenses and enlarging the space, they are commonly narrower on the sides than in the front. Their grace consists in the half or whole columns which are applied to them: in which case it is well noted by authors that the columns may be slightly taller than usual, because they lean against such good supports. And let these suffice concerning antae, which are a type of structure of small expense, but firm and noble. Furthermore, because they are found vaulted more often than otherwise, as much for beauty as for majesty, I must treat of vaults, and under the same title of chambers; for a vault is in truth nothing other than a contracted chamber, and a chamber is a dilated vault; wherefore, that I may deal with this part concisely and fundamentally, I shall reduce the whole matter into a few theorems.

Theorem I. All solid materials, unless obstructed, descend perpendicularly downward, because weight has a natural inclination toward the center of the universe, and nature accomplishes its motions through the shortest lines.

Theorem II. If bricks, laid in their ordinary rectangular form, are joined in a level arrangement between supports sustaining both ends, all intermediate parts will necessarily subside by their natural gravity, and much more so if they are pressed by a weight from above; because, since their sides are parallel, they have space to descend perpendicularly without impediment, as in the previous theorem; wherefore, in order for them to persist, it is necessary that either their position, or their figure, or both, be changed.

Theorem III. If bricks or squared stones are placed in a level arrangement in a wedge-like manner (that is, wider above than below), with the ends supported as in the preceding theorem, and with the points concurring at a single center, none of the middle parts can subside until the supports give way, because they lack the space in that figure to descend perpendicularly. But this species of structure is still weak, because the supports are liable to much impulse, especially if the line is long; wherefore this form is rarely used, except in windows and narrower doors. Therefore, just as to strengthen the work in this third theorem we have supposed all materials to be different from those in the second, so now the position must also be changed, as will be clear in the following theorem.

Theorem IV. If materials shaped (as before) in a wedge-like manner are not placed levelly, but in the form of an arch or a portion of a circle, concurring at one center, neither can the parts of the chamber subside, because they lack space to descend perpendicularly, nor can the supports (as they are called) of the said chamber suffer such violence as in the preceding flat position; for roundness will make the incumbent weight rest upon the supports rather than impel them. From which an evident corollary can be deduced: that the most secure of all chambers is the semicircular, and of all vaults the hemispherical, though not absolutely free from all natural infirmity (which is the sole prerogative of the line of perpendiculars).