Archimedes Texts

191
then, where the Roof is to be flat, the Height
must be equal to the Breadth; where the Roof
is to be vaulted, a third Part of that Breadth
more must be added. This may serve for mid
dling Buildings: In very large ones, if they are
to have a vaulted Roof, the whole Height must
be one whole Breadth, with the Addition of
one fourth Part; but if the Roof is to be flat
it must be one whole Breadth and two fifths.
If the Length of the Platform be three Times its
Breadth, and the Roof is to be flat, let the
Height be one whole Breath and three quarters,
if the Roof is to be vaulted, let the Height be
one whole Breadth and an half. If the Length
of the Platform be four Times its Breadth, and
the Roof is to be vaulted, let the Height be
half its Length; and if the Roof is to be flat,
divide the Breadth into four Parts, and give
one and three quarters of those Parts to the
Height. If the Length be five Times the
Breadth, make the Height the same as where
it is four Times, only with the Addition of
one sixth Part of that Height; and if it is six
Times the Breadth, make it as before, adding
not a sixth as in the former, but a fifth. If
the Platform be an exact Square with equal
Sides, and the Roof is to be vaulted, let the
Height exceed the Breadth as in the Platform
of three Breadths; but if the Roof is to be flat,
it must not exceed so much, and in the larger
Platforms, it must not exceed this Breadth
above one fourth Part. In those Platforms
where the Length exceeds the Breadth only
one ninth Part, let the Height be exceeded by
the Breadth one ninth Part too; but this must
be only in a flat Roof. When the Length is
to be one whole Breadth and a third, let the
Height be one whole Breadth and a sixth in flat
Roofs; but in vaulted ones, let the Height be
one whole Breadth and a sixth of the Length.
When the Length is one Breadth and an Half,
let the Height be one Breadth and a seventh of
that Breadth, in a flat Roof; but in a vaulted
one, let the Height be one Breadth, and a
seventh of the Length of the Platform. If the
Platform consist of Lines whereof one is as
seven, and the other as five, or the Length be
as five and the Breadth as three, or the like,
according as the Necessity of the Place, or Va
riety of Invention, or the Nature of the Orna
ments requires; add those two Lines together,
and allow one half of the Amount to the
Height. I must not here omit one Precaution,
namely, that the Vestibule ought never to be
above twice as long as broad, and the Apart
ments never less broad than two thirds of their
Length. The Platforms which are in Length
three or four Times their Breadth or more, be
long only to Porticoes, and even they ought
never to be above six Times their Breadth. In
the Wall Apertures are to be left both for
Windows and Doors. If the Window is broke
in the Wall of the Breadth-line of the Plat
form, which in its very Nature is shorter than
that of the Length, then there must be only a
single one; and this Window itself must either
be higher than it is broad, or else on the con
trary broader than it is high, which last Sort is
called a reclining Window. If the Breadth is
to be like that of the Door, somewhat less than
the Length; then let the Breadth of the clear
Opening be not more than a third, nor less than
a fourth Part of the Inside of the Wall in which
it is made; and let the Rest or Bottom of the
Window be in Height from the Floor not more
than four ninths of the whole Height, nor less
than two. The Height of the clear Open of
the Window must be one third more than its
Breadth; and this is the Proportion, if the Win
dow is to be higher than broad; but if the
Window is to be broader then high, than of
the whole inside Length of the Wall in which
it is made, you must not allow the Open of the
Window less than one half, nor more than two
thirds. In the same Manner its Height too
must be made either half its Breadth, or two
thirds, only it must have two little Columns to
support the Transom. If you are to make
Windows in the longer Side, there must be
more of them, and they should be in an odd
Number. I find the Ancients were best pleased
with three, which were made in the following
Manner: The whole longest Side of the Wall
must be divided into never more than seven, nor
less than five Parts, of which taking three, in
each of them make a Window, making the
Height of the Open one whole Breadth and
three quarters, or one Breadth and four fifths.
If you would make your Windows more nu
merous; as they will then partake of the Na
ture of a Portico, you may borrow the Dimen
sions of your Openings from the Rules of the
Portico itself, and especially from that of the
Theatre, as we laid them down in their proper
Place. The Doors must be made after the
Manner of those which we described for the
Court and Council-chamber. Let the Dress of
the Windows be Corinthian; of the principal
Door, Ionic; of the Doors of the Halls and
Chambers, Doric. And thus much of the Lines,
as far as they relate to this present Purpose.