Archimedes Texts

156
they are not designed to support the Weight
of a vaulted Roof, but only a flat one of Sum
mers and Rafters. Let their Thickness there
fore be only one twentieth Part of their Height,
and let their Height be only once the Breadth
of the Front and an Half, and never more. At
the Angles of the Isles come out Pilasters from
the Naked of the Wall, running parallel with,
and on a Line with, the Columns, not less than
twice, nor more than three Times the Thick
ness of the Wall. Others, still more to strength
en the Building, make such a Pilaster in the
Middle of the Row of Columns, in Breadth
three of the Diameters of one the Columns, or
at most four. The Columns themselves too
must never have the same Solidity as those
used in Temples; and therefore, if we make
our Colonades with an Architrave over it, we
may observe the following Rules. If the Co
lumns are to be Corinthian, substract a twelfth
Part from their Diameter; if Ionic, a tenth;
if Doric, a ninth. As for the Composition of
the other Members, the Capitals, Architrave,
Freze, Cornice, and the like, you may proceed
in the same Manner as in Temples.

Of Colonades both with Architraves and with Arches; what Sort of Columns
are to be used in Basiliques, and what Cornices, and where they are to be
placed; of the Height and Wedth of Windows and their Gratings; of the
Roofs and Doors of Basiliques, and their Ornaments.

Columns that are to have Arches over
them, ought by rights to be square; for
if they were round, the Work would not be
true, because the Heads of the Arches would
not lie plum upon the Solid of the Column
underneath; but as much as their Squares ex
ceeded a Circle, so much of them would hang
over the Void. To remedy this Defect, the
best ancient Masters placed over the Capitals
of their Columns another Abacus or Plinth, in
Thickness sometimes one fourth and sometimes
one fisth Part of the Diameter of the Column;
the upper Part of this Plinth, which went off
with a Cima-recta, was equal to the greatest
Breadth of the Top of the Capital, and its Pro
jecture was equal to its Height, so that by this
means the Heads and Angles of the Arches had
a suller and firmer Seat. Colonades with
Arches, as well as those with Architraves, are
various, some being thinner set, others closer,
and so on. In the closer Sort the Height of
the Void must be three Times and an half the
Breadth of the Aperture; in the thin Set, the
Height must be once the Breadth and two
thirds; in the less thin, the Height must be
twice the Breadth; in the closest of all, the
Breadth must be one third of the Height. We
have formerly observed, that an Arch is no
thing else but a Beam bent. We may there
fore give the same Ornaments to Arches as to
Architraves, according to the different Sorts of
Columns over which they are turned; besides
which, if we would have our Structure very
rich, over the Heads of our Arches we may
run an Architrave, Freze, and Cornice in a
straight Line, with the same Proportions as we
should make them over Columns that should
reach to that Height. But as the Basilique is
sometimes encompassed only with one single
Isle, and at other Times with two, the Place of
the Cornice over the Columns and Arches must
vary accordingly. In those which are encom
passed only with one single Portico, having di
vided the Height of your Wall into nine Parts,
the Cornice must go only to five; or if you
divide it into seven, to four. But in those
which are to have double Isles, the Cornice
must be placed at one third of the Height of
the Wall at least, and at never more than three
eighths. We may also over the first Cornice,
as well for the greater Ornament as for real
Use, place other Columns, and especially Pi
lasters, directly plum over the Centers of the
Columns which are below them. And this
indeed is of great Service, as it maintains the
Strength and Firmness of the Ribs of the Work,
and adds Majesty to it, and at the same Time
takes off much from the Weight and Expence
of the Wall; and over this upper Colonade
too we make a regular Entablature, according
to the Order of the Columns. In Basiliques
with double Side Isles, we may raise three Rows
of Columns in this Manner one above another;
but in others we should make but two. Where