Usages de l'analyse de Descartes, pour découvrir, sans le secours du calcul differentiel, les propriétés, ou affections principales des lignes géométriques de tous les ordres

GUA DE MALVES, Jean Paul de

Verlag: Paris: Briasson, 1740

First edition of the first publication of de Gua (1710-86), "a work on analytic geometry inspired by both Descartes's 'Géométrie' (1637) and Newton's 'Enumeratio linearum tertii ordinis' (1704). Its principal aim was to develop a theory of algebraic plane curves of any degree (Descartes's 'lignes géométriques') based essentially on algebra. Nevertheless, he drew on infinitesimal methods in order to simplify various calculations and recognized that their use is indispensable, particularly for everything involving the transcendental curves ('mécaniques'). De Gua was especially interested in tangents, asymptotes, and singularities: multiples, points, cusps, and points of inflection. In this area he skillfully used coordinate transformations and systematically made use of an 'algebraic' or 'analytic' triangle, obtained by a 45° rotation of Newton's parallelogram. The use of the latter had been popularized by the 'Enumeratio' and by the commentaries of several of Newton's disciples, among them Brook Taylor, James Stirling, and s'Gravesande. The use of perspective allowed de Gua to associate the different types of points at a finite distance with various infinite branches of curves. Among his other contributions, he explicitly asserted that if a cubic admits three points of inflection, the latter are aligned. He also introduced two new types of cubics into the enumeration undertaken by Newton and Stirling, among others. De Gua's treatise contributed to the rise of the theory of curves in the eighteenth century and partially inspired the subsequent works of Euler (1748), Gabriel Cramer (1750), A. P. Dionis du Séjour, and M. B. Goudin (1756). The fame of this work led to de Gua's election to the Royal Academy of Sciences as adjoint geometer on 18 March 1741, replacing P. C. Le Monnier" (René Taton in DSB). In 1743, thanks to the support of Montesquieu, Buffon and de Maupertuis, he became a Fellow of the Royal Society of London. In 1745, however, following a bitter dispute with the anatomist Antoine Ferrein, de Gua was ousted from the Académie Royale de Sciences. On June 27, 1746, he was named premier éditeur en chef of the French edition of Ephraïm Chamber's 'Cyclopaedia' - the 'Encyclopédie' - but this collaboration lasted only 13 months. The publisher of the present work, Antoine-Claude Brisson, was also a co-editor and bookseller of the 'Encyclopédie'. Shortly after its publication, D'Alembert wrote a mostly praiseworthy review of de Gua's book in the 'Journal des Savants', and he made numerous references to it in the 'Encyclopédie'. 8vo, pp. xxvi, 457, [3], with four folding plates. Contemporary French calf, spine gilt with red lettering-piece, marbled endpapers, red edges (spine ends and corners repaired). Bestandsnummer des Verkäufers ABE-1585573562530

Bibliografische Details

Titel: Usages de l'analyse de Descartes, pour ...
Verlag: Paris: Briasson
Erscheinungsdatum: 1740
Einband: Hardcover
Zustand: Very Good
Auflage: 1st Edition