LACROIX, Sylvestre François (1765–1843). Traité du calcul différentiel et du calcul intégral.— [Vol III:] Traité des différences et des series. Faisant suite au Traité du calcul différentiel et du calcul intégral. Paris: J.B.M. Duprat, 1797-1800.

First edition, the author’s copy in fine contemporary red morocco, with proof errata corrected by Lacroix and numerous annotations and emendations to the text in his hand, probably made in preparation for the second, revised edition.

Lacroix’s masterly summation of the fields of integral and differential calculus, including the Traité des différences et des séries which formed a supplement to the main work, "in which he “united all the scattered methods, harmonized them, developed them, and joined his own ideas to them ... This monumental work constituted a clear picture of mathematical analysis, documented and completely up to date. While Lacroix followed Euler on many points, he incorporated the various advances made since the middle of the eighteenth century. The treatise is a very successful synthesis of the works of Euler, Lagrange, Laplace, Monge, Legendre, Poisson, Gauss, and Cauchy" (DSB). Lacroix also coins the term "analytic geometry" in this work and and proposes it as a distinct field of mathematical research. The manuscript revisions are likely made in preparation for the second edition, published 1810-1819.

Three volumes, quarto (290 x 209mm). Half-titles in volume II & III, the latter bound at the end, 9 folding plates and tables, 4pp. proof errata at the end of vol. I with ink corrections, pp.97-100 of vol. II reproduced at the end of the volume incorporating corrections to errata (minor spotting). Full red morocco by Champy, sides with double fillet gilt borders enclosing gilt floral roll and inner double fillet panel, spine decoratively gilt, silk endleaves, all edges gilt (endleaves and extremities slightly rubbed). Provenance: an early inscription at the front of volume one identifies this as a presentation from Lacroix's editor to the author – the author (manuscript emendations).