The father of Lagrange, luckily perhaps for the fame of his son, was ruined by some unfortunate speculation. The latter used to say, that had he possessed fortune, he should probably never have turned his attention to the science in which he excelled. He was placed at the College of Turin, and applied himself diligently and with enthusiasm to classical literature, showing no taste at first for mathematics. In about a year he began to attend to the geometry of the ancients. A memoir of Halley in the Philosophical Transactions, on the superiority of modern analysis, produced consequences of which the author little dreamed. Lagrange met with it, before his views upon the subject had settled: and immediately, being then only seventeen years old, applied himself to the study of the modern mathematics. Before this change in his studies, according to Delambre[7], after it, according to others, but certainly while very young, he was elected professor at the Royal School of Artillery at Turin. We may best convey some notion of his early proficiency, by stating without detail, that at the age of twenty-three we find him—the founder of an Academy of Sciences at Turin, whose volumes yield in interest to none, and owe that interest principally to his productions,—a member of the Academy of Sciences at Berlin, an honour obtained through the medium of Euler, who shortly after announced him to Frederic of Prussia as the fittest man in Europe to succeed himself,—and settling, finally, a most intricate question[8] of mathematics, which had given rise to long discussions between Euler and D’Alembert, then perhaps the two first mathematicians in Europe. He had previously extended the method of Euler for the solution of what are called _isoperimetrical problems_, and laid the foundation for the _Calculus of Variations_, the most decided advance, in our opinion, which any one has made since the death of Newton. Footnote 7: Éloge de Lagrange, Mémoires de l’Institut. 1812. Footnote 8: The admissibility of discontinuous functions into the integrals of partial differential equations. In 1764 he gained the prize proposed by the Academy of Sciences for an Essay on the Libration of the Moon; and in 1766, that for an Essay on the Theory of the Satellites of Jupiter. In the former of these we find him, for the first time, using the _principle of virtual velocities_, which had hitherto remained almost a barren truth, but which he afterwards made, in conjunction with the principle known after the name of D’Alembert, the foundation of the whole of mechanical science.