and
a half, not including the substructures and the projections of the
bases; if it is to be of six columns, into eighteen parts. If an
octastyle is to be constructed, let the front be divided into
twenty-four parts and a half. Then, whether the temple is to be
tetrastyle, hexastyle, or octastyle, let one of these parts be taken,
and it will be the module. The thickness of the columns will be equal to
one module. Each of the intercolumniations, except those in the middle,
will measure two modules and a quarter. The middle intercolumniations in
front and in the rear will each measure three modules. The columns
themselves will be nine modules and a half in height. As a result of
this division, the intercolumniations and the heights of the columns
will be in due proportion.

8. We have no example of this in Rome, but at Teos in Asia Minor there
is one which is hexastyle, dedicated to Father Bacchus.

These rules for symmetry were established by Hermogenes, who was also
the first to devise the principle of the pseudodipteral octastyle. He
did so by dispensing with the inner rows of thirty-eight columns which
belonged to the symmetry of the dipteral temple, and in this way he made
a saving in expense and labour. He thus provided a much wider space for
the walk round the cella between it and the columns, and without
detracting at all from the general effect, or making one feel the loss
of what had been really superfluous, he preserved the dignity of the
whole work by his new treatment of it.

9. For the idea of the pteroma and the arrangement of the columns round
a temple were devised in order that the intercolumniations might give
the imposing effect of high relief; and also, in case a multitude of
people should be caught in a heavy shower and detained, that they might
have in the temple and round the cella a wide free space in which to
wait. These ideas are developed, as I have described, in the
pseudodipteral arrangement of a temple. It appears, therefore, that
Hermogenes produced results which exhibit much acute ingenuity, and
that he left sources from which those who came after him could derive
instructive principles.

[Illustration: VITRUVIUS' RULES FOR THE DIAMETER AND HEIGHT OF COLUMNS
IN THE DIFFERENT CLASSES OF TEMPLE COMPARED WITH ACTUAL EXAMPLES]

10. In araeostyle temples, the columns should be constructed so that
their thickness is one eighth part of their height. In the diastyle, the
height of a column sh