Legendre, Adrien Marie

Legendre, Adrien Marie

Legendre, Adrien Marie (ädrēăNˈ märēˈ ləzhäNˈdrə), 1752–1833, French mathematician. He is noted especially for his work on the theory of numbers, on which he wrote an essay (1798) containing the law of quadratic reciprocity as well as several supplements, all later incorporated in a definitive work, Théorie des nombres (1830). The results of his long study of elliptic integrals appeared in Traité des fonctions elliptiques (3 vol., 1825–32). He invented independently of C. F. Gauss, and was the first to state in print (1806), the method of least squares, and he collaborated in drawing up centesimal trigonometric tables. He taught at the École militaire, Paris, and at the École normale and was associated with the bureau of longitudes from 1812. His Éléments de géométrie (1794, tr. 1867) was an influential textbook.
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Legendre, Adrien Marie


Born Sept. 18, 1752, in Paris; died there Jan. 10, 1833. French mathematician. Member of the Paris Academy of Sciences (1783).

Legendre substantiated and developed the theory of geodetic measurements and was the first to discover (1805–06) the method of least squares and use it in calculations. He introduced what are now called the Legendre polynomials and the Legendre transformation and studied Euler’s integrals of the first and second kind. Legendre proved that elliptic integrals are reducible to canonical forms and found their expansions into series and compiled tables of their values. He gave the first systematic and complete exposition of the contemporary theory of numbers. In the calculus of variations he established an existence test for extremums. Legendre wrote a well-known textbook of geometry, in which he unsuccessfully attempted to prove the parallel postulate.


Traité des fonctions elliptiques et des intégrales Culériennes, vols. 1–3. Paris, 1825–28.
Théorie des nombres, 4th ed. vols. 1–2. Paris, 1855.
In Russian translation:
Osnovaniia geometrii and trigonometrii St. Petersburg, 1837.


Wileitner, H. Istoriia matematiki ot Dekarta do sereediny 19 stoletia, 2nd ed. Moscow, 1966. (Translated from German.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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