The Rule of Three 
extremities of an equilateral triangle it makes 
tor beauty of proportion. 
An ancient and notable example occurs in 
the pyramids of Egypt, the sides of which, in 
their original condition, were it is believed 
equilateral triangles. It is a demonstrable 
fact that certain geometrical intersections give 
tration from the Como edition of Vitruvius, 
published in Milan about 1521, which 
shows a vertical section of the Milan cathe¬ 
dral, together with the system of equilateral 
triangles which determined its principal 
proportions. The architects of the Italian 
Renaissance, inheriting the Roman tra- 
the proportions of the Greek orders. The 
perfect little Erectheum of the Athenian 
acropolis would seem to have been pro¬ 
portioned by means of the equilateral triangle, 
both in general, and in detail. The same 
figure, in conjunction with the square and 
the circle was employed by the Romans in 
designing triumphal arches, basilicas, and 
baths. The vescia piscis, consisting of two 
arcs of a circle enclosing a double equilateral 
triangle was often used during the Middle 
Ages in laying out the plans of churches and 
cathedrals. It is scarcelv an exaggeration 
to say that an entire system of window 
tracery was based upon the circle and the 
equilateral triangle. That the latter figure 
was a determining factor in the proportion¬ 
ing of Gothic buildings is sufficiently proven 
(if such proof were needed) by the accom¬ 
panying facsimile reproduction of an illus- 
dition in such matters, constantly recog¬ 
nized this essential principle of monumental 
design. 
There is abundant evidence in support of 
the theory that the builders of antiquity, 
the masonic guilds of the Middle Ages, and 
the architects of the Italian Renaissance 
followed certain geometrical rules of propor¬ 
tion ; but even though this theory be denied 
or disproven,—if after all these men ob¬ 
tained their results working unconsciously 
and at hap-hazard,—the fact of the existence 
of such rules remains unchanged for, as has 
been well said, “ the artist follows the rules 
without knowing them.” Laws of beauty 
there are, of which this Rule of Three is 
one, which are “ dependent on the nature of 
human intelligence”—deep as the foundation 
of the world. 
Claude Trap do?/. 
