half of these at the
top. Columns of from forty feet to fifty should be divided into eight
parts, and diminish to seven of these at the top of the shaft under the
capital. In the case of higher columns, let the diminution be determined
proportionally, on the same principles.

13. These proportionate enlargements are made in the thickness of
columns on account of the different heights to which the eye has to
climb. For the eye is always in search of beauty, and if we do not
gratify its desire for pleasure by a proportionate enlargement in these
measures, and thus make compensation for ocular deception, a clumsy and
awkward appearance will be presented to the beholder. With regard to the
enlargement made at the middle of columns, which among the Greeks is
called [Greek: entasis], at the end of the book a figure and calculation
will be subjoined, showing how an agreeable and appropriate effect may
be produced by it.

CHAPTER IV

THE FOUNDATIONS AND SUBSTRUCTURES OF TEMPLES

1. The foundations of these works should be dug out of the solid ground,
if it can be found, and carried down into solid ground as far as the
magnitude of the work shall seem to require, and the whole substructure
should be as solid as it can possibly be laid. Above ground, let walls
be laid under the columns, thicker by one half than the columns are to
be, so that the lower may be stronger than the higher. Hence they are
called "stereobates"; for they take the load. And the projections of the
bases should not extend beyond this solid foundation. The wall-thickness
is similarly to be preserved above ground likewise, and the intervals
between these walls should be vaulted over, or filled with earth rammed
down hard, to keep the walls well apart.

[Illustration: THE ENTASIS OF COLUMNS

1. The entasis as given by Fra Giocondo in the edition of 1511.

2. The entasis from the temple of Mars Ultor in Rome compared with
Vignola's rule for entasis.]

2. If, however, solid ground cannot be found, but the place proves to be
nothing but a heap of loose earth to the very bottom, or a marsh, then
it must be dug up and cleared out and set with piles made of charred
alder or olive wood or oak, and these must be driven down by machinery,
very closely together like bridge-piles, and the intervals between them
filled in with charcoal, and finally the foundations are to be laid on
them in the most solid form of construction. The foundations having been
b