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Mémoire sur la Théorie des Nombres, présenté à l'Académie des Sciences le 31 Mai 1830.[Paris: Didot, 1840]. First edition.
Extremely rare separately-paginated offprint of Cauchy's great memoir on number theory, which treats the theory of congruences and reciprocity, but using an approach based on the theory of indeterminate equations rather than the arithmetic method used by Gauss in Disquisitiones Arithmeticae. Although it was read to the Academy in May 1830, the memoir remained unpublished until 1840 owing to Cauchy's self-imposed exile following the revolution of July 1830.

Cauchy's work in number theory has been overlooked by most historians in favour of his work in analysis, but it is now beginning to be reappraised (see Boucard). In 1829 he published a brief paper with the same title as the present memoir but occupying only 17 pages (Bulletin des sciences mathématiques, physiques et chimiques, t. 12, pp. 205-221). His main purpose was to study equations of the form pm = x2 + ny2, where n is a divisor of p - 1. In the first part of the paper he treats the case in which n is a prime number, and in the remaining three sections the case in which n is composite. He sketches a proof of the law of quadratic reciprocity (the "gem of arithmetic," first proved in the Disquisitiones), and indicates that his methods enable him to discover an infinity of other reciprocity laws. The paper read to the Academy on 31 May 1830 is a further development of the 1829 paper. When it was finally published as the present memoir, it was accompanied by 14 'notes', comprising more than 350 pages, providing explanations and generalizations of the material.

For a very detailed analysis of this memoir, see J. Boucard, "Un "rapprochement curieux de l'algèbre et de la théorie des nombres": études sur l'utilisation des congruences en France de 1801 à 1850", Université Pierre et Marie Curie, 2011 (institut.math.jussieu.fr/theses/2011/jboucard/these_residus_congruences4.pdf).

This is a separately-paginated offprint of the paper published in Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. 17, pp. 249-768 (reprinted in Oeuvres complètes, éd. Académie des Sciences, 1ère sér., t. 3, Paris: Gauthier-Villars, 1882-1974, pp. 5-450). We have located only one other copy (Free University of Brussels); not in OCLC.. Large 4to, pp 524, contemporary half-calf, spine lettered in gilt

      [Bookseller: Sophia Rare Books]
Last Found On: 2013-05-02           Check availability:      Antikvariat    

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