Analyse des infiniment petits, pour l’intelligence des lignes courbes. Paris: L’imprimerie Royale, 1696. [Bound with :] CARRÉ, Louis. Methode pour la mesure des surfaces, la dimension des solides, leurs centres de pesanteur, de percussion et d'oscillation, par l'application du calcul intégral.

Paris: L’imprimerie Royale / Jean Boudot, 1696/1700.

A fine sammelband comprising the first editions of the first books on the differential and integral calculus, respectively.

“It was through his wide network of acquaintances in various European countries that Leibniz put into effect all his strategies for the spread of his analysis. The presence first of Jacob Hermann, the favourite pupil of Jacob Bernoulli, and then of Nicolaus I Bernoulli, the nephew of the Bernoulli brothers, as professors of mathematics in Padua was one outlet ... In France it was through the Oratorian circle of Nicolas Malebranche (1638–1715) that Johann Bernoulli introduced in 1691 the Leibnizian calculus. His lessons to the Marquis de l’Hôpital led to the draft of the first treatise of differential calculus (1696) [first offered work], and it was under the influence of Malebranche that some years later appeared the first works on the integral calculus by Louis Carré in 1700 [second offered work] and Charles René Reyneau in 1708. The spread and acceptance of the Leibnizian calculus was transferred in this way to the wide public, through the manuals and textbooks written for students at universities or ecclesiastical colleges.” (Landmark Writings in Western Mathematics, p.56).

“Following the classical custom, [the first work] starts with a set of definitions and axioms... The difference (differential) is defined as the infinitely small portion by which a variable quantity increases or decreases continuously. Of the two axioms, the first postulates that quantities which differ only by infinitely small amounts may be substituted for one another, while the second states that a curve may be thought of as a polygonal line with an infinite number of infinitely small sides such that the angle between adjacent lines determines the curvature of the curve. Following the axioms, the basic rules of the differential calculus are given and exemplified. The second chapter applies these rules to the determination of the tangent to a curve in a given point... The third chapter deals with maximum-minimum problems and includes examples drawn from mechanics and geography. Next comes a treatment of points of inflection and cusps. This involves the introduction of higher-order differentials, each supposed infinitely small compared to its predecessor. Later chapters deal with evolutes and with caustics. L’Hospital’s rule is given in chapter 9” (DSB VIII: 304).

Jean Bernoulli complained that he had not been given enough credit for his contributions, but L’Hospital himself, in the introduction to the book, does acknowledge his debt to both the Bernoulli brothers and to Leibniz: “Je reconnois devoir beaucoup aux lumieres de Mrs Bernoulli, surtout a celles du jeune presentement Professeur a Groningue. Je me suis servi sans façon de leurs découvertes & de celles de M. Leibniz.”

Born into a noble family, L’Hospital (1661-1704) abandoned a military career due to poor eyesight to pursue his interest in mathematics. He was a member of Malebranche’s circle in Paris and it was there that in 1691 he met the young Jean Bernoulli, who was visiting France and agreed to supplement his Paris talks on calculus with private lectures to l'Hospital at his estate at Oucques. In 1693, l'Hospital was elected to the Academy of Sciences, and served twice as its vice-president. By contrast, Carré (1663-1711) came from a humble family. He studied theology for three years in Paris before taking a secretarial position with Malebranche, who introduced him to mathematics. Two years after publishing the present work he was appointed surveyor to the Academy of Sciences, and in 1706 he became resident engineer.

I. Honeyman 2006 & 2007; Norman 1345; Sotheran, First Supplement, 1411; not in Macclesfield. II. Macclesfield 481; Poggendorff I, 383-384; Sotheran I, 704.

Two works bound in one volume, 4to (251 x 186 mm), pp. [xviii], 181, [3], with 11 folding engraved plates; pp. [xii], 115, [1, blank] and 4 folding engraved plates. Old signature cut from first title and expertly repaired. Contemporary French calf, spine gilt with red lettering-piece. Fine copies.

Item #2848

Price: $15,000.00