The contemplation of the various steps by which mankindhas come into possession of the vast stock of mathematicalknowledge can hardly fail to interest the mathematician. Hetakes pride in the fact that his science, more than any other, is an exact science, and that hardly anything ever done inmathematics has proved to be useless. The chemist smilesat the childish efforts of alchemists, but the mathematicianfinds the geometry of the Greeks and the arithmetic of theHindoos as useful and admirable as any research of to-day. Heis pleased to notice that though, in course of its development, mathematics has had periods of slow growth, yet in the mainit has been pre-eminently a progressive scienc
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