The contemplation of the various steps by which mankind has come into possession of the vast stock of mathematical knowledge can hardly fail to interest the mathematician. He takes pride in the fact that his science, more than any other, is an exact science, and that hardly anything ever done in mathematics has proved to be useless. The chemist smiles at the childish eorts of alchemists, but the mathematician nds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any