Traites de Calcul Differentiel et de Calcul Integral . . .
by BOSSUT, Charles (1730-1814).
Paris:: Imprimerie de la republique, ., 1798. 2 volumes. 8vo. , lxxx, 520, ; , 564, 6] pp. 8 folding plates. Contemporary full mottled calf, with 2 gilt-stamped spine labels per volume [original: red; recent: black], edges all marbled; rebacked in cloth, with original gilt-stamped spine mounted, new marbled endleaves, extremities worn. Very clean copy. First edition of the author's textbooks on differential calculus and integral calculus, writing after the influence of Euler and after the French Revolution. He includes three chapters on approximation of integrals, with a goal "to express integrals as infinite series. Bossut uses continued division, the binomial formula, the method of undetermined coefficients, and Bernoulli series. Although there is no attempt at evaluation of errors, there is much more concern with the practical issues of convergence than in [Euler I]." – João Caramalho Domingues, p. 158. "Bossut presented his algebraization of the infinitesimal calculus as an adaptation of Euler's concept of calculating with differences and zeros: ["I suppose differentials to be zeros or quantities which are evanescent and indeterminate, between which there can exit certain ratios which are the same as those between finite quantities." [Bossut, vol. I, p. lxxx, trans. by Gert Schubring)]. For Bossut also, the concept of function was the starting point and foundational concept. The calculus of differences was a simplified version of the presentations in Euler and de Prony. Bossut formulated the transition from finite differences to differentials without reflecting on limit processes or the existence of limits. For this, he continued basing himself on the infiniment petits, which he, however, explicitly called a hypothese, which led to important shortcuts. . ." – Gert Schubring, Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying The Development Of Analysis In 17th-19th Century France And Germany . . ., Springer, (2006). Bossut (1730-1814) entered the Jesuit College at 14 years of age as a student of Pere Beraud, himself a skilled mathematician whose pupils included Jean-Etienne Montucla (1725-1799) and Joseph Jerôme Lalande (1832-1807). His important for the history of science lies in the role he played as a major contributor to European education in science. He taught mathematics and mechanics, pioneered research in hydrodynamics while holding the chair of that discipline at the Louvre. Bossut "was one of the few whom d'Alembert took as students, and as such he was admitted as a correspondent to the Academie des Sciences" in 1753. – DSB, II, pp. 334-5. See: João Caramalho Domingues, Lacroix and the Calculus, (2008), page 3.
(Inventory #: S13219)
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