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 here—such as probabilities, finite differences, ascending continued fractions, elliptic integrals. Everywhere his wonderful powers of generalisation and abstraction are made manifest. In that respect he stood without a peer, but his great contemporary, Laplace, surpassed him in practical sagacity. Lagrange was content to leave the application of his general results to others, and some of the most important researches of Laplace (particularly those on the velocity of sound and on the secular acceleration of the moon) are implicitly contained in Lagrange's works.

Lagrange was an extremely modest man, eager to avoid controversy, and even timid in conversation. He spoke in tones of doubt, and his first words generally were, "Je ne sais pas." He would never allow his portrait to be taken, and the only ones that were secured were sketched without his knowledge by persons attending the meetings of the Institute.

Pierre Simon Laplace (1749–1827) was born at Beaumont-en-Auge in Normandy. Very little is known of his early life. When at the height of his fame he was loath to speak of his boyhood, spent in poverty. His father was a small farmer. Some rich neighbours who recognised the boy's talent assisted him in securing an education. As an extern he attended the military school in Beaumont, where at an early age he became teacher of mathematics. At eighteen he went to Paris, armed with letters of recommendation to D'Alembert, who was then at the height of his fame. The letters remained unnoticed, but young Laplace, undaunted, wrote the great geometer a letter on the principles of mechanics, which brought the following enthusiastic response: "You needed no introduction; you have recommended yourself; my support is your due." D'Alembert secured him a position at the École Militaire of Paris as professor of