is indwelling
harmony, rhythm, proportion, which has its basis in geometry and
number, is seen to exist in crystals, flower forms, leaf groups, and
the like, where it is obvious; and in the more highly organized world
of the animal kingdom also; though here the geometry is latent rather
than patent, eluding though not quite defying analysis, and thus
augmenting beauty, which like a woman is alluring in proportion as she
eludes (Illustrations 51, 52, 53).

[Illustration 52: PROPORTIONS OF THE HORSE]

[Illustration 53]

By the true artist, in the crystal mirror of whose mind the universal
harmony is focused and reflected, this secret of the cause and source
of rhythm--that it dwells in a correlation of parts based on an
ultimate simplicity--is instinctively apprehended. A knowledge of it
formed part of the equipment of the painters who made glorious the
golden noon of pictorial art in Italy during the Renaissance. The
problem which preoccupied them was, as Symonds says of Leonardo,
"to submit the freest play of form to simple figures of geometry in
grouping." Alberti held that the painter should above all things have
mastered geometry, and it is known that the study of perspective and
kindred subjects was widespread and popular.

[Illustration 54]

The first painter who deliberately rather than instinctively based
his compositions on geometrical principles seems to have been Fra
Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova,
in Florence. Symonds says of this picture, "Simple figures--the
pyramid and triangle, upright, inverted, and interwoven like the
rhymes of a sonnet--form the basis of the composition. This system was
adhered to by the Fratre in all his subsequent works" (Illustration
54). Raphael, with that power of assimilation which distinguishes
him among men of genius, learned from Fra Bartolommeo this method
of disposing figures and combining them in masses with almost
mathematical precision. It would have been indeed surprising if
Leonardo da Vinci, in whom the artist and the man of science were
so wonderfully 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
perfection of pyramidal composition. It is however in his masterpiece,
The Last Supper, that he combines geometrical symmetry and precision
with perfect naturalness and freedom in the grouping of ind