No well-organized intellect can fail to perceive that a
sublime and immortal Truth underlies these speculations. Undoubtedly, in
the straight line, in the conic sections, in the innumerable composite
curves of the mathematician, lie the germs of all these symbolic
expressions. But the artist, whose lines of Beauty vary continually with
the emotions which produce them, who feels in his own human heart the
irresistible impulse which gives an exquisite balance and poise to those
lines, cannot allow that the _spirit_ of his compositions is governed by
the exact and rigid formula; of the philosopher to any greater extent
or in any other manner than as the numbers of the poet are ruled by the
grammar of his language. These formulae may be applied as a curious test
to ascertain what strange sympathies there may be between such lines and
the vast organic harmonies of Nature and the Universe; but they do not
enter into the soul of their creation any more than the limitations of
counterpoint and rhythm laid their incubus on the lyre of Apollo. The
porches where Callicrates, Hermogenes, and Callimachus walked were
guarded by no such Cerberus as the disciples of Plato encountered at the
entrance of the groves of the Academy,--
"[Greek: Oudeis ageometraetos eisito],"
"Let no one ignorant of Geometry enter here";
but the divine Aphrodite welcomed all mankind to the tender teachings of
the Wild Acanthus, the Honeysuckle, and the Sea-Shell, and all the deep
utterances of boundless Beauty.
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