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, knew and followed certain rules, but though this theory be denied or even disproved--if after all these men obtained their results unconsciously--their creations so lend themselves to a geometrical analysis that the claim for the existence of certain canons of proportion, based on geometry, remains unimpeached. [Illustration 67] [Illustration 68] The plane figures principally employed in determining architectural proportion are the circle, the equilateral triangle, and the square--which also yields the right angled isosceles triangle. It will be noted that these are the two dimensional correlatives of the sphere, the tetrahedron and the cube, mentioned as being among the determining forms in molecular structure. The question naturally arises, why the circle, the equilateral triangle and the square? Because, aside from the fact that they are of all plane figures the most elementary, they are intimately related to the body of man, as has been shown (Illustration 45), and the body of man is as it were the architectural archetype. But this simply removes the inquiry to a different field, it is not an answer. Why is the body of man so constructed and related? This leads us, as does every question, to the threshold of a mystery upon which theosophy alone is able to throw 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 façades 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 façades.