ROBERVAL, HUYGENS, FRENICLE, et al. [ACADEMIE ROYALE des SCIENCES]
Divers ouvrages de mathématique et de physique.
Paris: L’Imprimerie Royale, 1693.
First edition of this superb collection of thirty-one treatises by the leading scientists of seventeenth-century France, all but one of which are published here for the first time.
There are nine treatises by Gilles Personne de Roberval (1602-75), comprising the principal corpus of his published works. Of particular importance is his Traité des indivisibles, composed around the same time as Cavalieri’s Geometria (1635) but independent of it and published here for the first time. “Roberval was one of the leading proponents of the geometry of infinitesimals, which he claimed to have taken directly from Archimedes, without having known of the work of Cavalieri. Moreover, in supposing that the constituent elements of a figure possess the same dimensions as the figure itself, Roberval came closer to the integral calculus than did Cavalieri... The numerous results that he obtained in this area are collected in the Divers Ouvrages, under the title of Traité des indivisibles... The most famous of his works in this domain concerns the cycloid” (DSB XI.487). The volume also contains Roberval’s foundation work on kinematic geometry, and his treatise on the composition of movements. “On account of his method of ‘composition of movements’ Roberval may be called the founder of kinematic geometry. This construction has three applications – the fundamental and most famous being the construction of tangents...” (ibid.).
The collection also contains four treatises by the accomplished amateur mathematician Bernard Frenicle de Bessy (ca. 1605-75), a close correspondent of Fermat, who made significant contributions of his own to number theory and related fields. These treatises include the tract on his method of calculation by exclusion, which gives applications to problems concerning right-angled triangles whose sides are integers, e.g. he discussed right-angles triangles the sum or difference of whose legs is given. There are also two treatises on magic squares. “The most important of these works of Frenicle is the treatise “Des quarrez ou tables magiques”. These squares, which are of Chinese origin and to which the Arabs were so partial, reached the Occident not later then the fifteenth century. Frenicle pointed out that the number of magic squares increased enormously with the order by writing down 880 magic squares of the fourth order, and gave a process for writing down magic squares of even order” (DSB V.159).
After the death of Frenicle and Roberval in 1675, their books and manuscripts were entrusted to the astronomer Jean Picard. Eight treatises by Huygens were also sent to Picard expressly for publication in this collection, including De la cause de la pesanteur, Construction d’un problème d’optique and his Démonstration de l’equilibre de la balance. The volume also contains five treatises by Picard himself, including an unusual 37-page work on dioptrics, one by Mariotte and two by Rømer. One of the Auzout contributions is a description of his micrometer – the only treatise in this collection which was published previously.
This is one of the earliest important publications of the Académie des Sciences, and one of the most magnificent. Founded on 22 December 1666, one of the principal functions of the Académie was to facilitate publication of the works of its members. Frenicle and Roberval were founding members (as was Huygens), and without the assistance of the Académie it is likely that many of their works would have remained unpublished (only one work by Frenicle and two by Roberval were published in their lifetimes).
Folio, pp. [viii, last leaf blank], 518, [2, colophon], with numerous woodcut diagrams and illustrations in text. Contemporary calf.