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 been said that an edition of Euler's complete works would fill 16,000 quarto pages. His mode of working was, first to concentrate his powers upon a special problem, then to solve separately all problems growing out of the first. No one excelled him in dexterity of accommodating methods to special problems. It is easy to see that mathematicians could not long continue in Euler's habit of writing and publishing. The material would soon grow to such enormous proportions as to be unmanageable. We are not surprised to see almost the opposite in Lagrange, his great successor. The great Frenchman delighted in the general and abstract, rather than, like Euler, in the special and concrete. His writings are condensed and give in a nutshell what Euler narrates at great length.

Jean-le-Rond D'Alembert (1717–1783) was exposed, when an infant, by his mother in a market by the church of St. Jean-le-Rond, near the Nôtre-Dame in Paris, from which he derived his Christian name. He was brought up by the wife of a poor glazier. It is said that when he began to show signs of great talent, his mother sent for him, but received the reply, "You are only my step-mother; the glazier's wife is my mother." His father provided him with a yearly income. D'Alembert entered upon the study of law, but such was his love for mathematics, that law was soon abandoned. At the age of twenty-four his reputation as a mathematician secured for him admission to the Academy of Sciences. In 1743 appeared his Traité de dynamique, founded upon the important general principle bearing his name: The impressed forces are equivalent to the effective forces. D'Alembert's principle seems to have been recognised before him by Fontaine, and in some measure by John Bernoulli and Newton. D'Alembert gave it a clear mathematical form and made numerous applications of it. It enabled the laws of motion and the