First Theory of Functions of a Real Variable. Lagrange, Joseph Louis (1736-1813). Théorie des fonctions analytiques, contenant les principes du calcul différentiel. . . . Paris: Imprimérie de la République, An V [1797/98]. 4to (271 x 215 mm). Uncut and partly unopened. Original limp boards, title in ink on spine, minor soiling at foot of spine. Light toning, otherwise a very fine, crisp copy. FIRST EDITION, second issue. Lagrange was born in Turin of mixed Italian and French descent, and spent the first 30 years of his life in his native city. He began devoting himself exclusively to mathematics when he was 17; within a year he had published his first mathematical paper and begun a fruitful correspondence with Leonhard Euler, who at the time was working in Berlin as Director of Mathematics at the Berlin Academy. While in Turin Lagrange founded the Turin Academy of Sciences and published a number of papers in its journal; his mathematical work during this time helped to establish the calculus of variations. In 1766, upon Euler's return to St. Petersburg, Lagrange agreed to take over Euler's position at the Berlin Academy. He spent the next twenty years in Berlin where he made a number of fundamental contributions to algebra, number theory and celestial mechanics; during this time he also wrote his landmark Mécanique analytique (1788), which 'transformed mechanics into a branch of mathematical analysis' (O'Connor and Robertson). In 1787 Lagrange moved to Paris where he became a member of the French Academy of Sciences; in the following decade he was appointed professor of mathematics at the École Polytechnique. His lectures on the differential calculus at the École Polytechnique form the basis of his Théorie des fonctions analytiques. Lagrange's Théorie des fonctions analytiques contains the first theory of functions of a real variable. 'In it Lagrange intended to show that power series expansions are sufficient to provide differential calculus with a solid foundation. Today mathematicians are partially returning to this conception in treating the formal calculus of series. . . . Completed by convergence considerations, [Lagrange's work] dominated the study of the functions of a complex variable throughout the nineteenth century' (Dictionary of Scientific Biography). The book is divided into three parts: the first deals with the general theory of functions; the second with applications to geometry; and the third with applications to mechanics. Lagrange's work on differential calculus provided a starting point for the researches of Cauchy, Jacobi and Weierstrass. In the H. F. Norman catalogue, it is stated that there were two issues of the present work, both published in the same year: A version with 276 pages, forming Vol. III of the ninth cahier of the J. de l'École Polytechnique; and a separate edition with 277 pages. Later research has shown this to be incorrect: There are in fact two separate issues of the Théorie des fonctions analytiques -Version A, with 276 pages, and Version B, with 277-as well as the journal issue. Version B is the true first edition: This is revealed by the 8-page index that appears at the beginning of both A and B, which refers to the 'Conclusion' on pp. 276-277. Since Version A does not have a page 277, it is clear that the index must have been prepared for Version B, making B the earlier issue. Version B's priority is confirmed by the fact that, in Version A the errata listed in Version B have been corrected. The journal printing of Lagrange's work is also Version B. O'Connor, J. J., and E. F. Robertson, Joseph Louis Lagrange, MacTutor History of Mathematics; Web. 12 Apr. 2011; Dictionary of Scientific Biography; Norman 1258. For further information on this lot please visit Bonhams.com For further information about this lot please visit the lot listing