COSMOS, VOL. II - World eBook Library

CELESTIAL SPACES. 737
discoveries by means of the
Calculus. Intellectual labour
invention of the Infinitesimal
shows itself in all its exalted
grandeur, where, instead of requiring external material
means, it derives its light exclusively from the sources opened
to pure abstraction, by the mathematical development of
thought. There dwells an irresistible charm, venerated by
all antiquity, in the contemplation of mathematical truths,
in the everlasting revelations of time and space, as they
reveal themselves in tones, numbers, and lines.* The im-
provement of an intellectual instrument of research analysis
lias powerfully accelerated the reciprocal fructification of
ideas, which is no less important than the rich abundance of
their creations. It has opened to the physical contemplation of
the universe new spheres of immeasurable extent, in the ter-
restrial and celestial regions of space, revealed both in the
periodic fluctuations of the ocean, and in the varying perturbations
of the planets.
* Willielm von Humboldt, Cfesammefo Werlce, Bd. i. s. 11.