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Gua De Malves, Jean Paul De

Gua De Malves, Jean Paul De

(b. near Carcassonne, France, ca. 1712; d. Paris, France, 2 June 1786)

mathematics, mineralogy, economics.

Very little is known of de Gua’s life, and even the precise date and place of his birth are not established. According to Condorcet, he was struck by the contrast between the opulence of his first years and the privation that followed the ruin of his parents, Jean de Gua, baron of Malves, and Jeanne de Harrugue, in the wake of the bankruptcy of John Law in 1720. He planned an ecclesiastical career; while it seems that he never became a priest, this training nevertheless permitted him to obtain several benefices and pensions. After a stay in Italy he appears to have participated for a few years in the activities of the short-lived Société des Arts, a sort of scientific and technical academy founded in 1729 by Louis de Bourbon-Condé, prince of Clermont. In any case, he gradually acquired a thorough grounding in science.

De Gua’s first publication (1740) was 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. He presented several mathematical memoris, two of which, published at the time, deal with the number of roots of an algebraic equation according to their nature and sign and with the famous rule of Descartes. However, on 3 June 1745, following a dispute de Gua renounced the pursuit of a normal academic career and requested that his modest position of associate be made honorary. Although he continued his scientific research, he seems to have moved away from the study of mathematics during this period. Not until the time of the reorganization of 23 April 1785 did he resume his place at the Academy, this time as a pensioner in the new class of natural history and mineralogy, which was closer to his new interests. Moreover, it seems that the contents of the several mathematical memoirs on spherical trigonometry and the geometry of polyhedra that he subsequently published in the Histoire of the Academy for 1783 date for the most part from the 1740’s.

The career of de Gua was marked by several incidents which certainly resulted, at least in part, from difficulties inherent in his personality. His stay at the Collège Royal (Collège de France) was abnormally brief. Appointed on 30 June 1742 to the chair of Greek and Latin philosophy, which was vacant following the death of Joseph Privat de Molières, de Gua actually filled this post until 26 July 1748, when he resigned; he was replaced by P. C. Le Monnier. Like his predecessors and his successor, de Gua gave to his instruction an orientation having no connection with the official title of the chair; he dealt successively with Newtonian epistemology, differential and integral calculus, the principles of mathematics, arithmetic, and the philosophy of Locke—without, however, publishing anything based on his teaching.

Another incident took place during the same period. In 1745 the publisher A. F. Le Breton had joined with the Paris booksellers A. C. Briasson, M. A. David, and L. Durand for the purpose of publishing a much enlarged French version of the famous Cyclopaedia of Ephraim Chambers. Apparently appreciating de Gua’s wide-ranging abilities, they made him responsible for the scientific material in the edition in a contract signed on 27 June 1746 in the presence of Diderot and d’Alembert, who acted both as witnesses and as consultants. The agreement was annulled on 3 August 1747. On 16 October 1747 de Gua, who had meanwhile mortgaged his other income to repay a portion of the advances be had received from the booksellers, was replaced by d’Alembert and Diderot as director of this project, which was to become the celebrated Encyclopèdie.

De Gua next turned his attention to philosophy and political economy, translating works by George Berkeley and Matthew Decker, as well as a debate in the House of Commons that he introduced with a long “Avant-propos” on the problem of the interest rate on loans. At the same time he was actively interested in prospecting for gold in Languedoc and addressed several memoirs on this subject to the government. Having obtained, in 1764, an exploitation permit valid for twenty years, he undertook an unsuccessful venture that partially ruined him. In 1764 he published a work on mineral prospecting and composed the first six volumes of a series of mémoires périodiques on subjects in philosophy, science, economics, and so on; the series was never published—for lack, it seems, of official authorization. De Gua also was interested in lotteries, but beginning in the 1760’s he specialized in mineralogy and conchology, which explains his change of sections at the Academy in 1785.

This disordered scientific activity and a taste for the unusual give to de Gua’s work a special character. The interest of his first mathematical writings evokes regrets that he did not persevere in this direction.


I. Original Works. Among de Gua’s writings are Usages de l’analyse de Descartes pour découvrir, sans le secours du calcul différentiel, les propriétés, du affections principales des lignes géométriques de tous les ordres (Paris, 1740); five mathematical memoirs in Histoire de l’Academie royale des sciences: “Démonstration de la règle de Descartes…,” 72–96, and “Recherches des nombres des racines réelles ou imaginaires…,” 435–494, in the volume for 1741 (Paris, 1744) and “Trigonométrique sphérique, déduite trés brièvement, …”, 291–343, “Diverses mesures, en partie neuves, des aires sphériques et des angles solides....,” 344–362, and “Propositions neuves.... sur le tèttaédre…,” 363–402, in the volume for 1783 (Paris, 1786); and Projet d’ouverture et d’exploitation de minières et mines d’or et d’autres métaux aux environs du Cézé du Gardon, de l’Eraut [sic] et d’autres rivières du Languedoc, du Comté de Foix, du Rouergue etc. (Paris, 1764). He translated several works from English into French: George Berkeley, Dialogues entre Hylas et Philonaüs contre les sceptiques et les athées (Amsterdam, 1750); Matthew Decker, Essai sur les causes du déclin du commerce étranger de la Grande Bretagne, 2 vols. (n.p., 1757); and Discours pour et contre la réduction de l’intérest naturel de l’argent, qui ayant été prononcés; en 1737, dans la Chambre des communes du parlement de la Grande Bretagne, occasion nèrent en ce pays la réduction de 4 à 3% . . . (Wesel— Paris, 1757)— “Avantpropos du traducteur,” pp. i-clxviii, is by de Gua. With J. B. Romé de l’Isle he edited Catalogue systèmatique et raisonné descuriosités de la nature et de l’art, qui composent le cabinet de M. Davila... (Paris, 1767), for which he wrote I, pt. 2, 71–126: “Coquilles marines.”

II. Secondary Literature. On de Gua or his work, see the following (listed chronologically): the éloge of M. J. A. N. Condorcet, read 15 Nov. 1786, in Histoire de l’Academié royale des sciences pour l’année 1786 (Paris, 1788), pt. 1, 63–76; X, de Feller, ed., Dictionnaire historique, IV (Paris, 1808), 238; J. J. Weiss, in Michaud. ed., Biographie universelle, XVIII (Paris, 1817), 575–576, also in new ed., XVIII (Paris, 1857), 1–2; J. M. Quérard, La France littéraire, III (Paris, 1829), 494–495; Guyot de Fére, in F. Hoefer, ed., Nouvelle biographic générale, XXII (Paris, 1859), col. 278; Poggendorif, I, 967–968; Intermédiare des mathématiciens, VIII (1901), 158, and XI (1904), 148–149; P. Sauerbeck, “Einleitung in die analytische Geometric der höheren algehraïschen Kurven nach der Methoden von Jean-Paul de Gua de Malves. Ein Beitrag zur Kurvendiskussion,” in Abhandlungen zur Geschichte der mathematischen Wissenschaften, 15 (1902), 1–166; G. Loria, “Da Descartes e Fermat a Monge e Lagrange. Contributo alla storia della geometria analitica,” in Atti dell Accademia nazionale dei Lincei. Memorie, classe di scienze fisiche, matematiche e naturale, 5th ser., 14 (1923), 777–845; N. Nielsen, Géomètres français du XVIIIe siécle (Copenhagen Paris, 1935), pp. 195–200: L. P. May, “Documents nouveaux sur l’Encyclopédie,” in Revue de synthèse, 15 (1938), 5–30; G. Loria, Scoria delle matematiche (Milan, 1950), pp. 668–689, 739–740, 758, 851; and C. B. Boyer, History of Analytic Geometry (New York, 1956), pp. 174–175, 184, 194.

RenÉ Taton

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