Analyse des infiniment petits, pour l'intelligence des lignes courbes. [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

[L'HÔPITAL (or L'HOSPITAL), Guillaume François Antoine, Marquis de.]

Edité par L?imprimerie Royale; Jean Boudot, Paris, 1700

A propos de cet article

THE FIRST BOOKS ON DIFFERENTIAL AND INTEGRAL CALCULUS. A fine sammelband comprising the first editions of the first books on the differential and integral calculus, respectively. "In France it was through the Oratorian circle of Nicolas Malebranche 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), 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 and Charles René Reyneau in 1708. The spread and acceptance of the Leibnizian calculus was transferred in this way to the wide public" (Landmark Writings, p. 56). "The importance of L'Hospital's work lay in its dissemination throughout Europe of the concepts and early development of the calculus, whose cause L'Hospital advanced as well through his many contacts; these included Christiaan Huygens, who is reputed to have learned the calculus from L'Hospital" (DSB). Bernoulli's lectures also covered integral calculus, but L'Hospital dropped plans to write a continuation to his Analyse des infiniment petits dealing with this subject "in deference to Leibniz, who had let him know that he had similar intentions" (ibid.). Leibniz never wrote such a text, however, and Bernoulli's lectures on integral calculus remained unpublished until they appeared in his Opera (1742). The task of completing L'Hospital's book was instead taken up by Carré, a pupil of Malebranche and assistant to Pierre Varignon, from whom he probably learnt calculus. "Following the classical custom, his Analyse des infiniment petits 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" (ibid.). The tenth and final chapter of the Analyse discusses the methods of Descartes and Johann Hudde. The companion work by Carré is "the first treatise on the integral calculus in any language, which is here applied to the determination of the area of superficies [surfaces] and solids and their centres of gravity, problems of percussion, oscillation, etc." (Sotheran). On this last topic, the determination of the centres of oscillation of solids, Carré made a significant error. This was known to Bernoulli but not publicized at the time, and so was propagated into several later calculus texts, such as Charles Hayes' Treatise on Fluxions (1704) and Edmund Stone's The Method of Fluxions, both Direct and Inverse (1730). Both works are rare on the market: ABPC/RBH list four copies of L'Hospital's book since the Norman copy, which realised $6,325 in 1998; and only two copies of Carré's work in the last half century. "Differential and integral calculus are generally considered to have their origins in the works of Newton and Leibniz in the late 17th century, although the roots of the subject reach far back into that century and, arguably, even into antiquity. Leibniz first described his new c.

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Détails bibliographiques

• Titre: Analyse des infiniment petits, pour l'intelligence des lignes courbes. [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
• Éditeur: L?imprimerie Royale; Jean Boudot, Paris
• Date de parution: 1700
• Édition: First edition.
• État de la jaquette: Hardcover
• Catalogues du vendeur:
  • Mathematics, Analysis, Algebra