LEGENDRE Adrien-Marie Essai sur la théorie des nombres.

DSB, VIII, 142; En français dans le texte, 200.

First edition.

One of the fundamental works in the development of number theory; it contains Legendre’s (1752-1833) discovery of the law of quadratic reciprocity, described by Gauss as a ‘gem of arithmetic’.

Although Legendre had first given a demonstration of this law in the Mémoires of the Paris Academy of Sciences in 1785, his presentation was incomplete and was only fully developed in the present work. This book also contains Legendre’s research on Fermat’s last theorem and the group of integers which can be represented as the sum of three squares.

Legendre “in both the theory of elliptic function and number theory… raised questions that were fruitful subjects on investigation for mathematicians of the 19th century” (DSB).

Fine copy.