The second edition (1808) of Legendre's highly influential Essai sur la th?orie des nombres.Adrien-Marie Legendre (17521833), one of the great French mathematicians active in the Revolutionary period, made important contributions to number theory, statistics, mathematical analysis and algebra. The second, much improved, edition (1808) of his highly influential Essai sur la th?orie des nombres is offered here.Adrien-Marie Legendre (17521833), one of the great French mathematicians active in the Revolutionary period, made important contributions to number theory, statistics, mathematical analysis and algebra. The second, much improved, edition (1808) of his highly influential Essai sur la th?orie des nombres is offered here.Adrien-Marie Legendre (17521833), one of the great French mathematicians active in the Revolutionary period, made important contributions to number theory, statistics, mathematical analysis and algebra. He taught at the ?cole Militaire, where he was a colleague of Laplace, and made his name with a paper on the trajectory of projectiles which won a prize of the Berlin Academy in 1782, and brought him to the attention of Lagrange. In 1794 he published El?ments de g?om?trie, which remained a textbook for over 100 years. The first edition of his Essai sur la th?orie des nombres was published in 1798, and the much improved second edition, which is offered here, in 1808. In it Legendre had taken account of criticism by Gauss of the mathematical proofs in the first edition, though he was bitter at the manner in which his younger rival had claimed credit for some of his solutions.Pr?face; Introduction; Part I. Exposition de diverses m?thodes et propositions relatives ? l'analyse ind?termin?e; Part II. Propri?t?s g?n?rales des nombres; Part III. Th?orie des nombres consid?r?s comme d?composables en trois carr?s; Part IV. M?thodes et recherches diverses; Part V. Usage de l'analyse ind?termin?e dans la r?solution de l'?quation; Tables.