The Rule of Three 
rhis system was adhered to by the Fratre in 
all his subsequent works.” Raphael, with that 
power of assimilation which distinguishes him 
among men of genius, learned from Fra 
Bartolommeo this meth¬ 
od of disposing figures, 
and combining them in 
masses with almost math¬ 
ematical precision, and 
the equilateral triangle 
was one of his favorite 
devices. This even a 
cursory study of his 
works will show. 
It would have been 
indeed suprising if Leon¬ 
ardo da Vinci, in whom 
the artist and the man of 
science were so wonder¬ 
fully united had not been 
greatly preoccupied with 
the mathematics of the 
art of painting. His 
Madonna of the Rocks, 
and Virgin on the lap of 
Saint Anne,in the Louvre, 
exhibit the very perfec¬ 
tion of pyramidal compo¬ 
sition. It is, however, 
in his masterpiece, the 
Last Supper, that he 
combines geometrical 
symmetry and precision 
with perfect naturalness 
and freedom in the group¬ 
ing of individually inter¬ 
esting and dramatic fig¬ 
ures. I'he twelve apos¬ 
tles are distributed in 
four groups of three each 
about the figure of Christ, 
which, artfullv isolated 
from the others, is ex¬ 
actly contained within a 
well defined equilateral 
triangle; while from the head of this figure, 
t.e.y from the apex of the triangle, the simple 
perspective lines of the room radiate. 
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 
may be traced not only in the false senti¬ 
ment and affectation of the period, but also 
in the abandonment by the artists of those 
obscurely geometrical 
arrangements and group¬ 
ings which, in the work 
of the great masters, so 
satisfies the eye and 
haunts the memory of 
the beholder. 
Architecture is the 
most closely related of all 
the arts to geometry. 
Indeed, in a certain 
sense, architecture is ge¬ 
ometry made concrete 
and ponderable. As Em¬ 
erson says, “The pleasure 
a palace or a temple gives 
the eye is that an order 
and method has been 
communicated to stones, 
so that they speak and 
geometrize, become ten¬ 
der or sublime with ex¬ 
pression.” Over and 
above its obvious geom¬ 
etry, every truly great 
and beautiful work of 
architecture is harmoni¬ 
ously proportioned, both 
as a whole and as to its 
parts, by reason of these 
being in a manner co-in¬ 
cident with certain simple 
symmetrical figures of 
geometry. These, 
though invisible to the 
sight, and not consciously 
present in the mind of 
the beholder, serve to co¬ 
ordinate the entire fabric 
into one memorable 
whole. Chief among such 
figures, by reason of its peculiar properties 
and perfection, 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 musical sounds. It may be 
stated as a general rule, that whenever three 
important points in any architectural compo¬ 
sition approximately coincide with the three 
THE/ EQUILATERAL TRIANGLE IN 
ROMAN ARCHITECTURE 
A SECTION OF THE/ PANTHEON. ROME/ 
