‎GUA DE MALVES (J.P. de)‎
‎Usage de l'analyse de DESCARTES pour découvrir, sans le secours du calcul différentiel, les propriétés ou affections principales des lignes géométriques de tous les ordres -- EDITION ORIGINALE‎

‎P., Briasson, 1740, un volume in 8 relié en pleine basane, dos orné de caissons et fers dorés, filets dorés sur les plats, tranches rouges (reliure de l'époque), (coiffes légèrement usées et un coin légèrement émoussé), 26pp., 457pp., 3pp. non chiffrées, 4 PLANCHES DEPLIANTES‎

Reference : 7986

‎---- EDITION ORIGINALE ---- "DE GUA's first treatise (1740) contributed to the rise of the theory of curves in the eighteenth century and partially inspired the subsequent works of Euler, Cramer, A.P. Dionis du Séjour and M.B. Goudin. 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. The principal aim of this work, inspired by both Descartes's Géométrie and Newton's Enumeratio linearum tertii ordinis, was to develop a theory of algebraic plane curves of any degree 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. De Gua was especially interested in tangents, asymptotes and singularities (multiples, points, cusps and pints 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 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". (DSB V pp. 566/568)**7986/ARB4-2470/ARM4‎