42Nd Boston International Antiquarian Book Fair 16-18 November 2018 - Booth #108
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RARE & IMPORTANT BOOKS & MANUSCRIPTS IN THE HISTORY OF SCIENCE & MEDICINE 42nd Boston International Antiquarian Book Fair 16-18 November 2018 - Booth #108 Flæsketorvet 68 – 1711 København V – Denmark Cell: (+45)27628014 www.sophiararebooks.com Académie Royale des Sciences. A SUPBERB COLLECTION OF HITHERTO UNPUBLISHED MATHEMATICAL TRACTS ACADÉMIE ROYALE DES SCIENCES [AUZOUT, FRENICLE, HUYGENS, MARIOTTE, PICARD, ROBERVAL, RØMER]. Divers ouvrages de mathématique et de physique. Paris: L’Imprimerie Royale, 1693. $15,000 Folio (365 x 240 mm), pp. [viii, last leaf blank], 518, [2, colophon], with numerous woodcut diagrams and illustrations in text. Contemporary mottled calf with the arms of Louis XIV in the centre of each cover (Olivier 2494, fer 10), and with his monogram in each spine compartment, hinges with some wear and top capital chipped, an entirely unrestored copy in its original state. First edition of this superb collection of thirty-one treatises by the leading scientists of seventeenth-century France, almost all of which are published here for the first time. This is one of the earliest important publications of the Académie des Sciences, and one of the most magnificent, and the present copy was probably intended for presentation: it is bound in contemporary calf with the arms of Louis XIV on each cover. Of the eight works by Christiaan Huygens (1629-95) in the present volume, all appear here for the first time except for his treatise on gravity, De la cause de la pesanteur, which was first published three years earlier as an appendix to the Traitéde la lumière. Most of these works were reprinted at The Hague in 1731 in quarto format (in three separate volumes). Founded on 22 December 1666, one of the principal functions of the Académie 2 Académie Royale des Sciences. was to facilitate publication of the works of its members. Frenicle and Roberval by Descartes, his irreconcilable adversary. 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(as was Huygens), and without the assistance of the Académie it is likely that many of their works would have remained unpublished “Roberval was one of the leading proponents of the geometry of infinitesimals, (only two works by Frenicle and two by Roberval were published in their lifetimes). which he claimed to have taken directly from Archimedes, without having known After the death of Frenicle and Roberval in 1675, their books and manuscripts the work of Cavalieri. Moreover, in supposing that the constituent elements of a were entrusted to the astronomer Jean Picard; eight treatises by Huygens were figure possess the same dimensions as the figure itself, Roberval came closer to the also sent to Picard for publication in this collection. After Picard’s death in 1682, integral calculus than did Cavalieri, although Roberval’s reasoning in this matter publication of the works was brought to fruition by Philippe de la Hire. La Hire was not free from imprecision. The numerous results that he obtained in this area also included in the Divers ouvrages five treatises by Picard himself, including are collected in the Divers ouvrages, under the title of Traité des indivisibles. One an unusual 37-page work on dioptrics, one by Mariotte and two each by Auzout of the first important findings was, in modern terms, the definite integration of and Rømer. The most important work in the volume is probably Roberval’s the rational power, which he most probably completed around 1636, although by Traité des indivisibles, composed around the same time as Cavalieri’s Geometria what manner we are not certain. The other important result was the integration indivisibilibus (1635) but independent of it and published here for the first time. of the sine … the most famous of his works in this domain concerns the cycloid. The treatises by Frenicle, a close correspondent of Fermat, treat topics in number Roberval introduced the “compagne” (“partner”) of the original cycloidal curve theory and related fields. See below for a full list of contents. and appears to have succeeded, before the end of 1636, in the quadrature of the latter and in the cubature of the solid that it generates in turning around its base … Gilles Personne de Roberval (1602-75) arrived in Paris in 1628 and put himself in contact with the Mersenne circle. “Mersenne, especially, always held Roberval “On account of his method of the “composition of Movements” Roberval may be in the highest esteem. In 1632 Roberval became professor of philosophy at the called the founder of kinematic geometry. This procedure had three applications— Collège de Maître Gervais. On 24 June 1634, he was proclaimed the winner in the fundamental and most famous being the construction of tangents. “By means the triennial competition for, the Ramus chair (a position that he kept for the of the specific properties of the curved line,” he stated, “examine the various rest of his life) at the Collège Royal in Paris, where at the end of 1655 he also movements made by the point which describes it at the location where you wish succeeded to Gassendi’s chair of mathematics. In 1666 Roberval was one of the to draw the tangent: from all these movements compose a single one; draw the charter members of the Académie des Sciences in Paris … He himself published line of direction of the composed movement, and you will have the tangent of only two works: Traité de méchanique (1636) and Aristarchi Samii de mundi the curved line.” Roberval conceived this remarkably intuitive method during his systemate (1644). A rather full collection of his treatises and letters was published earliest research on the cycloid (before 1636). At first, he kept the invention secret, in the Divers ouvrages de mathématique et de physique par messieurs de I’Académie but he finally taught it between 1639 and 1644; his disciple François du Verdus royale des sciences (1693), but since few of his other writings were published in the recorded his lessons in Observations sur la composition des mouvemens, et sur le following period, Roberval was for long eclipsed by Fermat, Pascal, and, above all, moyen de trouver les touchantes des lignes courbes … In the second place, he also 3 Académie Royale des Sciences. applied this procedure to comparison of the lengths of curves, a subject almost untouched since antiquity … The third application consisted in determining extrema … “Roberval composed a treatise on algebra, De recognitione aequationum, and another on analytic geometry, De geometrica planarum et cubicarum aequationum resolutione. Before 1632, he had studied the “logistica speciosa” of Viète; but the first treatise, which probably preceded Descartes’s Géométrie, contains only the rudiments of the theory of equations. On the other hand, in 1636 he had already resorted to algebra in search of a tangent. By revealing the details of such works, he would have assured himself a more prominent place in the history of analytic geometry, and even in that of differential calculus … “In 1647 [Roberval] wrote to Torricelli: “We have constructed a mechanics which is new from its foundations to its roof, having rejected, save for a small number, the ancient stones with which it had been built” (p. 301) … around 1669, Roberval wrote Projet d’un livre de mechanique traitant des mouvemens composez … Roberval dreamed, certainly with too great temerity, of a vast physical theory based uniquely on the composition of motions” (DSB). Bernard Frenicle de Bessy (1605-75) was an accomplished amateur mathematician who corresponded with Descartes, Huygens, Mersenne and, perhaps most importantly, Fermat. “Frenicle de Bessy is best known for his contributions to number theory. In fact, Fermat, in a letter to Roberval, writes: ‘For some time M Frenicle has given me the desire to discover the mysteries of numbers, an area in which he is highly versed’ … He solved many of the problems posed by Fermat but he did more than find numerical solutions for he also put forward new ideas and posed further questions” (Mactutor). 4 Académie Royale des Sciences. In “Méthode pour trouver la solution des problèmes par les exclusions, Frenicle of his principle of gravitation … says that in his opinion, arithmetic has as its object the finding of solutions in integers of indeterminate problems. He applied his method of exclusion to “In 1673 Picard moved into the Paris observatory and collaborated with Cassini, problems concerning rational right triangles, e.g., he discussed right triangles, the Romer, and, later, Philippe de La Hire on the institution’s regular program of difference or sum of whose legs is given … The most important of these works by observations. He also joined many missions away from the observatory. The first Frenicle is the treatise Des quarrez ou tables magiques. These squares, which are of these enabled him to provide more precise data on the coordinates of various of Chinese origin and to which the Arabs were so partial, reached the Occident French cities (1672-1674); others, conducted from 1679 to 1681 with La Hire, had not later than the fifteenth century. Frenicle pointed out that the number of magic the purpose of establishing the bases of the principal triangulation of a new map squares increased enormously with the order by writing down 880 magic squares of France. The results of these geodesic observations were published in 1693 by La of the fourth order, and gave a process for writing down magic squares of even Hire [pp. 368-370 of the present work]” (DSB). “In 1692 William Molyneux, who order” (DSB). was familiar with [Isaac] Barrow’s Lectiones XVIII, published his Dioptrica nova, which was a practical treatise on lenses and telescopes. He independently arrived In 1666 Jean Picard (1620-82) “was named a founding member of the Académie at Huygens’s rule for images in thin lenses, though in a slightly different form and Royale des Sciences and, even before its opening, participated in several stated less generally.