my experience, to be "coaxed" a little in order to fit the theory; or it
is found that though the geometrical figure suggested corresponds
exactly with some points on the plan or section, these are really of no
more importance than other points which might just as well have been
taken. The theorist draws our attention to those points in the building
which correspond with his geometry, and leaves on one side those which
do not. Now it may certainly be assumed that any builders intending to
lay out a building on the basis of a geometrical figure would have done
so with precise exactitude, and that they would have selected the most
obviously important points of the plan or section for the geometrical
spacing. In illustration of this point, I have given (Fig. 25) a
skeleton diagram of a Roman arch, supposed to be set out on a
geometrical figure. The center of the circle is on the intersection of
lines connecting the outer projection of the main cornice with the
perpendiculars from those points on the ground line. This point at the
intersection is also the center of the circle of the archway itself. But
the upper part of the imaginary circle beyond cuts the middle of the
attic cornice. If the arch were to be regarded as set out in reference
to this circle, it should certainly have given the most important
line--the top line, of the upper cornice, not an inferior and less
important line; and that is pretty much the case with all these
proportion theories (except in regard to Greek Doric temples); they are
right as to one or two points of the building, but break down when you
attempt to apply them further. It is exceedingly probable that many of
these apparent geometric coincidences really arise, quite naturally,
from the employment of some fixed measure of division in setting out
buildings. Thus, if an apartment of somewhere about 30 feet by 25 feet
is to be set out, the builder employing a foot measure naturally sets
out exactly 30 feet one way and 25 feet the other way. It is easier and
simpler to do so than to take chance fractional measurements. Then comes