Lettres de A[mos] Dettonville contenant Quelques-unes de ses Inventions de Géométrie. Sçavoir La Résolution de tous les Problèmes touchant la Roulette qu il avoit proposez publiquement au mois de Juin 1658. L Égalité entre les Lignes courbes de toutes sortes de Roulettes, & des Lignes Eliptiques. L Égalité entre les Lignes Spirale, & Parabolique, demonstrée à la manière des Anciens. La Dimension d un Solide formé par le moyen d une Spirale autour d un Cone. La Dimension & le Centre de gravité des Triangles Cylindriques. La Dimension et le Centre de gravité de l Escalier. Un Traitté des Trilignes & de leurs Onglets. Un Traitté des Sinus, et des Arcs de Cercle, Un Traitté des Solides Circulaires

PASCAL, Blaise

Verlag: Guillaume Desprez, Paris, 1659

PASCAL S WORK ON INDIVISIBLES - "ONE OF THE MOST BRILLIANT OF HIS GENIUS" (TCHEMERZINE) - THE MARQUESSES OF BUTE COPY. First edition, extremely rare (one of about 120 copies printed), and a fine copy with noble provenance, of one of Pascal s most brilliant works. "Édition originale, extrêmement rare, de la dernière uvre de Pascal, l une des plus éclatantes de son génie" (Lucien Scheler in Tchemerzine, V, pp. 54-55). "Pascal devoted himself during 1658 and the first part of 1659 to the perfection of the theory of indivisibles, an ancestor of the integral calculus. In 1658, after using the method of indivisibles to solve several infinitesimal problems relating to the cycloid, he proposed the problems he had solved as a challenge to other mathematicians, then announced his own superior solutions in four letters published in December 1658 and January 1659 under the pseudonym A. Dettonville. These pamphlets were collected in February 1659 under the above title. The structure of this work is very complex, with the first letter (Lettre de A. Dettonville à Monsieur de Carcavy) containing five separately paginated sections and the remaining three letters (Lettre de A. Dettonville à Monsieur A. D. D. S. …, Lettre de A. Dettonville à Monsieur De Sluze …, and Lettre de A. Dettonville à Monsieur Huggyens ([i.e., Huygens]) appearing in inverse order of their composition" (Norman). In a diagram (fig. 26) in the treatise Traité des Sinus du quart de Cercle, Pascal introduced what Leibniz later called the characteristic triangle and used to establish the differential calculus. Pascal made us of it "to determine the sum of the sines (ordinates) of a portion of the curve, that is, the area under this portion. If Pascal had at this point only been more interested in arithmetic considerations and in the problem of tangents, he might have anticipated the important concept of the limit of a quotient and have discovered the significance of this for the determination of both tangents and quadratures. Had he done this, he would have hit upon the crucial point in the calculus some seven years before Newton and about fourteen years before Leibniz" (Boyer, p. 153). "Cette édition originale ne fut donc tirée qu à 120 exemplaires, le tirage classique de l époque étant d environ 3000" ( Mémoires sur la vie de M. Pascal par Marguerite Périer, sa nièce, p. 40 in Pascal, uvres complètes, Bibliothèques de la Pléiade, N.R.F., 1957 and Tchémerzine, V, 55). ABPC/RBH list six copies, those of Bute (the present copy), Pierre Berge, Macclesfield, Norman, Honeyman, and that of Jean Jacques Amelot, Seigneur de Chaillou (1689-1749). The Berge copy made $118,262 in 2015 ("contemporary vellum, loss to lower board, plates reinforced at folds, second plate detached") and was subsequently offered by a French dealer. Our copy has the 1658 title, sometimes lacking, in addition to that of 1659. OCLC lists three copies in US (Harvard, NYPL, Yale). Provenance: Marquesses of Bute, Luton Park, Bedfordshire (18th-century armorial bookplate; sale Sotheby's, 4 July 1961, lot 413, £800 to Dawson); sale Christie s, 2 June 2004, lot 90, £65,725 ($120,145). According to the testimony of Gilberte Périer, his sister, it was to forget very painful toothache that in 1657 Pascal suddenly resumed his mathematical research, interrupted since his religious conversion late in 1654. According to Pascal himself, the solution to the problem of finding the area of a cycloid (the path travelled by a point on a circle as it rolls along a plane) came to him in his sleep. Initially he wrote nothing of this discovery as he regarded it as a distraction from his work on religion, but his friend the Duke of Roannez pointed out that God may have provided this vision to give more strength to his work against atheists and libertines, because by showing them the depth of his genius they would be less likely to challenge his proofs of religious doctrine. "During 1658 and the first months of 1659 Pascal devot. Bestandsnummer des Verkäufers 5530

Bibliografische Details

Titel: Lettres de A[mos] Dettonville contenant ...
Verlag: Guillaume Desprez, Paris
Erscheinungsdatum: 1659
Auflage: First edition.