[L'HOSPITAL, Guillaume Franois Antoine de, Marquis de Saint-Mesme (1661-1704)]. Analyse des infiniment petits, pour l'intelligence des lignes courbes. Paris: l'Imprimerie Royale, 1696.
4o (250 x 189 mm). Title engraving of French royal arms, 11 numbered folding engraved plates by N. Bercy, engraved allegorical head-pieces, one signed Le Pautre, engraved initials, one engraved tail-piece by G. Audran, woodcut tailpieces by Vincent Le Sueur. Initial blank leaf removed. (Some foxing, occasional browning, edges somewhat dust-soiled.) Contemporary ?English blind-tooled speckled calf (rebacked, board edges rubbed). Provenance: English purchase inscription on front free endpaper ("3 shill"), a few early marginal reader's marks.
FIRST EDITION OF THE FIRST TEXTBOOK OF THE DIFFERENTIAL CALCULUS. The Marquis de L'Hospital was the first mathematician to learn the calculus from one of its earliest practitioners, Jean Bernoulli, who spent several months at L'Hospital's estate in 1692 instructing him in the new method, knowledge of which had previously been confined to Leibniz, Newton, and Bernoulli and his brother Jacques. The following year L'Hospital proved his mastery of the calculus by solving a problem posed by Bernoulli, and he was quickly elected honorary member of the Acadmie des Sciences. Aside from a few brief articles in the Leipzig Acta Eruditorum, no explanation of the calculus had yet been published, and L'Hospital's Analyse was immediately recognized as a significant contribution to mathematics. The book circulated widely and went through many editions; it brought the differential notation into general use in France and helped disseminate it throughout Europe.
L'Hospital freely acknowledged his debt to Bernoulli and Leibniz in his preface, which gives a short history of the development of the calculus in the preceding century, including the beginnings of the Newton-Leibniz controversy. Nonetheless, after L'Hospital's death Bernoulli complained that he had not been sufficiently credited for some of the fundamental concepts of the calculus, a dispute that has never been wholly resolved. Babson, Supplement, p. 30; Norman 1345.