Paris, De Bure, 1826-1829. 4°, 4 volumes, I. (2), II, 357, (3) pages ; II. (2), II, 376, (4) pages ; III. (2), 368, (4) pages [gap in page numbering between 22 and 25] ; IV. (2), 1-54, 49-319, (5) pages ; contemporary half-sheep (spines rubbed, hinges partly split, headcaps a little chipped). Copy of the French mathematician Jacques Philippe Marie Binet ? The first volumes of the mathematical journal founded by Cauchy in 1826. In this important and personal periodical, Cauchy makes fundamental contributions to mathematics with many original theories : the calculus of residues, an astonishing theory of light, the foundation of group theory, and his personal input for the solution of partial differential equations. "In 1826 Cauchy began to publish his Exercises de Mathématiques, which was essentially a mathematical periodical consisting entirely of papers written by himself ; it appeared at approximately monthly intervals until 1830. [.] Some of the work appearing in the Exercices is expository in character, but much of it contains original research. In particular, as we shall see, his main contributions to what he called the calculus of residues are to be found there." (Smithies, Cauchy and the Creation of Complex Function Theory, p. 113.) "[In his Exercices de mathématiques, Cauchy] use, for the first time, the term résidu for the limit, and the term résidu intégral for the sum of all residues in a certain region." (Mitrinovic and Keckic, The Cauchy Method of Residues. Theory and Applications, volume 1, page 331.) "The term itself and the formal definition of a residue are first encountered in the paper 'Sur un nouveau genre de calcul analogue au calcul infinitésimal' (Exercices de Mathématiques, Paris, 1826, volume 1). Here, Cauchy introduces and defines this new concept [.] After this paper Cauchy wrote a large number of other papers placed in this and later volumes of his Exercices de mathématiques, in which he studied the applications of the theory to the computation of integrals, differential equations, the expansion of functions in series and infinite products, theory of equations, and so forth." (Mathematics of the 19th Century, vol. II : Geometry, Analytic Function Theory, p. 132). Bound in contemporary half-sheep, the present copy has a particularity : paper tabs inserted in the volumes, especially the second and fourth. Two of them have printed letterheads : "Imprimerie Bachelier" and "Académie de Paris. Faculté des sciences". Several contain manuscript mathematical annotations or comments, one of which is dated 1851. These tabs show that the first owner was a conscientious reader and a mathematician connected to the University of Paris and the printer Bachelier, who specialised in scientific publications. In addition, the visiting card of "M. Binet Membre de l'institut (Académie des Sciences)" can be found between pages 294 and 295 of the fourth volume. It left a yellow mark on the paper, proving it has remained in this place for a long time, probably since the middle of the 19th century. Given these elements, we may say that the first owner was probably the French mathematician and physicist Jacques Philippe Marie Binet, or someone connected to him in the first half of the 19th century. Binet made pioneering contributions to number theory and the mathematical foundations of matrix algebra in the wake of Cauchy's own research, in particular the Cauchy-Binet formula and Cauchy-Binet theorem. He was also close to Cauchy's political opinions. An interesting association copy. A fifth volume of the Exercices de mathématiques was published in 1830, which is not present here.
