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 of Bernoulli," which are in fact (though not so considered by him) the coefficients of $$\scriptstyle{\frac{x^n}{n!}}$$ in the expansion of $\scriptstyle{(e^x-1)^{-1}}$.|undefined Of his collected works, in three volumes, one was printed in 1713, the other two in 1744.

John Bernoulli (1667–1748) was initiated into mathematics by his brother. He afterwards visited France, where he met Malebranche, Cassini, De Lahire, Varignon, and de l'Hospital. For ten years he occupied the mathematical chair at Gröningen and then succeeded his brother at Basel. He was one of the most enthusiastic teachers and most successful original investigators of his time. He was a member of almost every learned society in Europe. His controversies were almost as numerous as his discoveries. He was ardent in his friendships, but unfair, mean, and violent toward all who incurred his dislike—even his own brother and son. He had a bitter dispute with James on the isoperimetrical problem. James convicted him of several paralogisms. After his brother's death he attempted to substitute a disguised solution of the former for an incorrect one of his own. John admired the merits of Leibniz and Euler, but was blind to those of Newton. He immensely enriched the integral calculus by his labours. Among his discoveries are the exponential calculus, the line of swiftest descent, and its beautiful relation to the path described by a ray passing through strata of variable density. He treated trigonometry by the analytical method, studied caustic curves and trajectories. Several times he was given prizes by the Academy of Science in Paris.

Of his sons, Nicholas and Daniel were appointed professors of mathematics at the same time in the Academy of St. Petersburg. The former soon died in the prime of life; the latter returned to Basel in 1733, where he assumed the chair of experimental philosophy. His first mathematical