ividually
interesting and dramatic figures. Michael Angelo, Andrea del Sarto,
and the great Venetians, in whose work the art of painting may be said
to have culminated, recognized and obeyed those mathematical laws of
composition known to their immediate predecessors, and the decadence
of the art in the ensuing period may be traced not alone to the false
sentiment and affectation of the times, but also in the abandonment by
the artists of those obscurely geometrical arrangements and groupings
which in the works of the greatest masters so satisfy the eye and
haunt the memory of the beholder (Illustrations 55, 56).

[Illustration 55: THE EMPLOYMENT OF THE EQUILATERAL TRIANGLE IN
RENAISSANCE PAINTING]

[Illustration 56: GEOMETRICAL BASIS OF THE SISTINE CEILING PAINTINGS]

[Illustration 57: ASSYRIAN; GREEK]

[Illustration 58: THE GEOMETRICAL BASIS OF THE PLAN IN ARCHITECTURAL
DESIGN]

[Illustration 59]

Sculpture, even more than painting, is based on geometry. The colossi
of Egypt, the bas-reliefs of Assyria, the figured pediments and
metopes of the temples of Greece, the carved tombs of Revenna,
the Della Robbia lunettes, the sculptured tympani of Gothic church
portals, all alike lend themselves in greater or less degree to a
geometrical synopsis (Illustration 57). Whenever sculpture suffered
divorce from architecture the geometrical element became less
prominent, doubtless because of all the arts architecture is the most
clearly and closely related to geometry. Indeed, it may be said that
architecture is geometry made visible, in the same sense that music
is number made audible. A building is an aggregation of the commonest
geometrical forms: parallelograms, prisms, pyramids and cones--the
cylinder appearing in the column, and the hemisphere in the dome.
The plans likewise of the world's famous buildings reduced to their
simplest expression are discovered to resolve themselves into a few
simple geometrical figures. (Illustration 58). This is the "bed rock"
of all excellent design.

[Illustration 60: EGYPTIAN; GREEK; ROMAN; MEDIAEVAL]

[Illustration 61: JEFFERSON'S PEN SKETCH FOR THE ROTUNDA OF THE
UNIVERSITY OF VIRGINIA]

[Illustration 62: APPLICATION OF THE EQUILATERAL TRIANGLE TO THE
ERECHTHEUM AT ATHENS]

[Illustration 63]

[Illustration 64: THE EQUILATERAL TRIANGLE IN ROMAN ARCHITECTURE]

But architecture is geometrical in another and a higher sense than
this. Emerson says: "The pleasure a palace or a