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 Magazine, 1840), and in 1852 established a theorem relating to the expression of an eliminant as a determinant. Cayley made a new statement of Bézout's method of elimination and established a general theory of elimination (1852).   ANALYSIS.

Under this head we find it convenient to consider the subjects of the differential and integral calculus, the calculus of variations, infinite series, probability, and differential equations. Prominent in the development of these subjects was Cauchy.

Augustin-Louis Cauchy[78] (1789-1857) was born in Paris, and received his early education from his father. Lagrange and Laplace, with whom the father came in frequent contact, foretold the future greatness of the young boy. At the École Centrale du Panthéon he excelled in ancient classical studies. In 1805 he entered the Polytechnic School, and two years later the École des Ponts et Chaussées. Cauchy left for Cherbourg in 1810, in the capacity of engineer. Laplace's Mécanique Céleste and Lagrange's Fonctions Analytiques were among his book companions there. Considerations of health induced him to return to Paris after three years. Yielding to the persuasions of Lagrange and Laplace, he renounced engineering in favour of pure science. We find him next holding a professorship at the Polytechnic School. On the expulsion of Charles X., and the accession to the throne of Louis Philippe in 1830, Cauchy, being exceedingly conscientious, found himself unable to take the oath demanded of him. Being, in consequence, deprived of his positions, he went into voluntary exile. At Fribourg in Switzerland, Cauchy resumed his studies, and in 1831 was induced by the king of Piedmont to