This statement correctly represents the general course of the facts,
though requiring allowances in the detail. Mathematics, for example,
from the very beginning of its cultivation, can hardly at any time have
been in the theological state, though exhibiting many traces of the
metaphysical. No one, probably, ever believed that the will of a god
kept parallel lines from meeting, or made two and two equal to four; or
ever prayed to the gods to make the square of the hypothenuse equal to
more or less than the sum of the squares of the sides. The most devout
believers have recognized in propositions of this description a class of
truths independent of the devine omnipotence. Even among the truths
which popular philosophy calls by the misleading name of Contingent the
few which are at once exact and obvious were probably, from the very
first, excepted from the theological explanation. M. Comte observes,
after Adam Smith, that we are not told in any age or country of a god of
Weight. It was otherwise with Astronomy: the heavenly bodies were
believed not merely to be moved by gods, but to be gods themselves: and
when this theory was exploded, there movements were explained by
metaphysical conceptions; such as a tendency of Nature to perfection, in
virtue of which these sublime bodies, being left to themselves, move in
the most perfect orbit, the circle.
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