w
light. Any extended elucidation would be out of place here: it is
sufficient to remind the reader that the circle is the symbol of the
universe; the equilateral triangle, of the higher trinity (_atma,
buddhi, manas_); and the square, of the lower quaternary of man's
sevenfold nature.

[Illustration 69]

[Illustration 70]

The square is principally used in preliminary plotting: it is the
determining figure in many of the palaces of the Italian Renaissance;
the Arc de Triomphe, in Paris is a modern example of its use
(Illustrations 59, 60). The circle is often employed in conjunction
with the square and the triangle. In Thomas Jefferson's Rotunda for
the University of Virginia, a single great circle was the determining
figure, as his original pen sketch of the building shows (Illustration
61). Some of the best Roman triumphal arches submit themselves to a
circular synopsis, and a system of double intersecting circles has
been applied, with interesting results, to facades as widely different
as those of the Parthenon and the Farnese Palace in Rome, though
it would be fatuous to claim that these figures determined the
proportions of the facades.

By far the most important figure in architectural proportion,
considered from the standpoint of geometry, is the equilateral
triangle. It would seem that the eye has an especial fondness for
this figure, just as the ear has for certain related sounds. Indeed it
might not be too fanciful to assert that the common chord of any key
(the tonic with its third and fifth) is the musical equivalent of
the equilateral triangle. It is scarcely necessary to dwell upon
the properties and unique perfection of this figure. Of all regular
polygons it is the simplest: its three equal sides subtend equal
angles, each of 60 degrees; it trisects the circumference of a circle;
it is the graphic symbol of the number three, and hence of every
threefold thing; doubled, its generating arcs form the _vesica
piscis_, of so frequent occurrence in early Christian art; two
symmetrically intersecting equilateral triangles yield the figure
known as "Solomon's Seal," or the "Shield of David," to which mystic
properties have always been ascribed.

It may be stated as a general rule that whenever three important
points in any architectural composition coincide (approximately or
exactly) with the three extremities of an equilateral triangle, it
makes for beauty of proportion. An ancient and notable example