Adrien Marie Legendre, 1798

LEGENDRE, Adrien Marie (1752–1833). Essai sur la théorie des nombres. Paris, Duprat, an VI [1798].

First edition of one of the fundamental works in the history of number theory, containing Legendre’s discovery of the law of quadratic reciprocity, described by Gauss as the "gem of arithmetic." Although Legendre had first given a demonstration of this law in the Mémoires of the Academy of Sciences, Paris, 1785, his presentation was incomplete and only fully developed in the present work. This work also contains his researches on Fermat’s last theorem and the group of integers which can be represented as sums of three squares. This work also demonstrates him as a precursor of analytic number theory, with his law on the distribution of prime numbers. See DSB VIII pp. 135-143. Norman 1325, Parkinson p. 231.

Quarto (257 x 190 mm). Half-title, one leaf errata, table at rear. Contemporary French tree calf, spine gilt with geometric patterns and caduceuses (extremities rubbed, small loss at head of spine).