‎HEMENT Félix‎
‎LES INFINIMENT PETITS‎

‎Analyse des infiniment petits, pour l'intelligence des lignes courbes. Par Mr. le Marquis De L’Hospital. Seconde Edition. 1715 / Relié avec - bound-up with: 2) M. (Edmund) Stone: Analise des infiniment petits, comprenant le calcul intégral dans toute son étendue, avec son application aux Quadratures, Cubatures, Centres de Gravité, de Percussion, & de toutes sortes de Courbes. Servant de suite aux infiniment petits de ... L’Hôpital (sic): Traduit en François par M. Rondet, Maître de Mathématiques. (avec une préface de P. Castel) 1735.‎

‎1) A Paris, Chez François Montalant, / 2) A Paris, Julien-Michel Gandouin et Pierre-François Giffart, 1715 / 1735, in-4°, XV (+ 1 table) + 181 p. (+ 1 privilège) + 11 planches gravées dépl. / 2) CIV (=104 p.) + 162 p. + 1 f. (fautes à corriger) + 4 planches gravées dépl., petite tache d’eau marginale au début de l’ouvrage (sans gravité), reliure en plein veau d’époque, dos à 5 nerfs richement orné en or, tranches rouges, gardes en papier dominoté originales, bel exemplaire en parfait état.‎

‎1) Seconde édition après l’édition originale du premier manuel de calcul différentiel, impr. à Paris, par l’Imprimerie Royale, en 1696. La seconde édition est purgée de ses fautes typographiques. Cette oeuvre principale de Guillaume de L'Hospital, à la fois précise et simple d'utilisation, fut longtemps une référence dans son domaine, et connut un vif succès à travers le XVIIIe siècle.2) Première édition en français du traité de Edmund Stone, publié en 1730 en anglais. Très rare.1) Second edition of this textbook (first edition printed in 1696: “the influence of which dominated most of the eighteenth century” (Boyer).“The «Analyse des infiniment petits» was the first textbook of the differential calculus. The existence of several commentaries on it attests its popularity. ... L'Hospital was a major figure in the early development of the calculus on the continent of Europe. He advanced its cause not only by his scientific works but also by his many contacts, including correspondance with Leibniz, with Jean Bernoulli, and with Huygens. Fontenelle tells us that it was L'Hospital who introduced Huygens to the new calculus” (DSB).The «Analyse des infiniment petits» “includes the original publication of ideas originated and developed by Leibniz and the Bernoullis. ... (for example) the ninth chapter of this textbook contains what is now know as ‘L'Hospital's rule’ for finding the limiting value of a fraction whose numerator and denominator tend to zero; however, this rule was actually the work of Bernoulli, who included it in his letter to L'Hospital of 22 July 1694” (Norman).2) Very rare first French edition, first published in 1730 in the English language.‘Edmund Stone was born sometime around 1700, the son of a gardener of the Duke of Argyll. He first learned to read at the age of eight and was completely self-taught. He mastered both French and Latin in order to read mathematical works. At the age of eighteen, Stone came to the attention of the duke when the latter found Stone's copy of Newton's Principia in his grounds and assumed that it had been removed from his library. Impressed by the young man, the duke "placed him in a position which afforded him opportunity to pursue his studies".Stone translated works of the Marquis de l'Hospital on conic sections (1720) and Bion on scientific instruments (1723). In 1725, he was admitted as a fellow of the Royal Society in 1725 and published A New Mathematical Dictionary. In 1730, he published The Method of Fluxions, both direct and Inverse: the first part is a translation and reworking in Newtonian notation of De l'Hospital's Analyse des infinement petits (in fact, written by Johann Bernoulli), and the second part is Stone's own.In 1736, he independently found two species of lines of the third order which had been overlooked by Newton and Stirling, but these had been discovered by others a few years earlier. He also published some other mathematical works.Following the death of the Duke of Argyll in 1743, Stone's situation deteriorated and he spent the latter part of his life in poverty’.Article on Edm. Stone by: Alex D D Craik, University of St Andrews. Barbier I/167f; DSB VIII/304-5; Poggendorff I/1146-7; Norman Collection 1345; cf. Cantor III/222 ff. und 244 ff.; Honeyman Collection 2006-7; Boyer 460-1; Struik 312-3; Kline 383; Hoefer NBG XXI/101ff; Quérard: La France Littéraire IX, 271; Poggendorff 1/II 1018. Image disp.‎

‎Eclaircissemens sur l'analyse des infiniment petits -- EDITION ORIGINALE -- BEL EXEMPLAIRE‎

‎P., Rollin, 1725, un volume in 4 (23,5 cm X 18,5 cm), relié en pleine basane, dos orné de fers dorés (reliure de l'époque), (habiles restaurations à un mors), (4), 118pp., (1), 6 PLANCHES dépliantes‎

‎---- EDITION ORIGINALE ---- TRES RARE ---- BEL EXEMPLAIRE ---- "Fully occupied by his teaching duties and his responsibilities as an academician, Varignon had no leisure to prepare works for publication... From the papers he left at his death, most of which are now lost, his disciples assembled several posthumous works : Nouvelle mécanique, Eclaircissements sur l'analyse des infiniment petits (1725) and Elémens de mathématiques (1731). His intense pedagogical activity, extending over more than thirty years, constituted his chief contribution to the progress of science and was the source of his fame. By inaugurating a chair devoted specifically to mathematics at the Collège Mazarin, he joined the handful of men who were then teaching advanced mathematics... In working with the model of falling bodies, Varignon encountered difficulties in obtaining acceleration as a second derivative. This problem had the advantage, however, of obliging him to reassess calculus. His acceptance of the new procedures occurred between 1692 and 1695, and he was among those who gave the most favorable reception to the publication of L'Hospital's Analyse des infiniment petits. The Eclaircissemens is composed of critical notes that Varignon, as professor, considered necessary in presenting L'Hospital's pioneering work to young mathematicians - further evidence of his constructive role in the movement to transform the operations used in mathematics. But Varignon accomplished even more : in 1700-1701 he refuted Rolle's arguments against the new calculus, challenged the cabal that had formed within the Academy, and obliged Leibniz to furnish a more precise account of his ideas. Leibniz, to be sure, did not give him all the aid desired. Nevertheless, he encouraged Varignon to cease debating principles and to start developing mechanical applications of the new mathematics. The questions that Varignon subsequently treated show how faithfully he followed Leibniz' advice. In his course at the Collège Royal for 1722-1723, Varignon planned to discuss the foundations of infinitesimal calculus but was able to do no more than outline his ideas. Although he died before he could present what was undoubtedly the core of a lifetime's experience, that experience had already borne fruit". (DSB XIII)**5158/ARM3-5159/ARB3‎

‎Analyse des infiniment petits pour l'intelligence des lignes courbes‎

‎P., Montalant, 1716, un volume in 4 relié en plein veau, dos orné de fers dorés (reliure de l'époque), (un mors très légèrement fendu sur 2 cm, petite épidermure à un mors, plats légèrement frottés), 16pp., 182pp., 11 PLANCHES DEPLIANTES‎

‎---- BON EXEMPLAIRE ---- Seconde édition ---- "THE FIRST TEXTBOOK OF THE DIFFERENTIAL CALCULUS". (DSB) ---- "L'hospital was a major figure in the early development of the calculus on the continent... For several generations after his death, his fame was based on his book Analyse des infiniment petits pour l'intelligence des lignes courbes...". (DSB VIII pp. 304/305) ---- "G.F.A. L'Hospital (1661/1704), a pupil of Johann Bernoulli, has already been mentioned as taking part in the challenges issues by Leibniz and the Bernoullis. He helped powerfully in making the calculus of Leibniz better known to the mass of mathematicians by the publication of a treatise thereon, the Analyse des infiniment petits. This contains the method of finding the limiting value of a fraction whose two terms tend toward zero at the same time, due to Johann Bernoulli". (Cajori p. 224)**8080/ARB4‎

‎ANALYSE des Infiniment Petits Par le Marquis De l'Hôpital, Suivie d'un nouveau Commentaire pour l'intelligence des endroits les plus difficiles de cet Ouvrage. Par l'Auteur du Guide des jeunes Mathématiciens dans l'étude des Leçons de Mathématique de M. l'Abbé de la Caille.‎

‎ A Avignon, chez la Veuve Girard & François Seguin, Imp. Libraires, près la place St. Didier. Se trouve à Paris, chez Jean Desaint, Libraire, chez Charles Saillant, Libraire, chez Joseph Panckoucke, Libraire, chez Durand Neveu, Libraire, 1768, 1 volume in-8 de 205x130x35 mm environ, 1f.blanc, faux-titre, titre, xxxj-380 pages, 8 planches dépliantes, 1f. blanc, plein veau marbré cognac, dos à nerfs portant titres dorés, orné de caissons à fleurons et motifs dorés, gardes marbrées, tranches rouges. Quelques notes manuscrites au dos de la première garde de couleurs et p. 263, coiffes arasées, coins dénudés, cuir frotté craquelé par endroits et épidermé, petites taches p. 6, mouillure de la p. 49 à la fin du volume.‎

‎Guillaume François Antoine de L'Hôpital (1661-1704), parfois orthographié de L'Hospital, marquis, est un mathématicien français. Il est connu pour la règle qui porte son nom : la règle de L'Hôpital, qui permet de calculer la valeur d'une limite pour une fraction où le numérateur et le dénominateur tendent tous deux vers zéro. Il est aussi l'auteur du premier livre en français sur le calcul différentiel : Analyse des infiniment petits pour l'intelligence des lignes courbes. Publié en 1696, ce texte s'appuie sur les leçons que lui a données Jean Bernoulli, pendant l'hiver 1691-1692, sur le calcul différentiel inventé par Gottfried Wilhelm Leibniz en 1684. Merci de nous contacter à l'avance si vous souhaitez consulter une référence au sein de notre librairie.‎

‎ANALYSE DES INFINIMENTS PETITS et ECLAIRCISSEMENTS SUR L'ANALYSE DES INFINIMENT PETITS‎

‎Acl.1988.In-8 toilé.Réedition de l'édition de 1696.181 p.2 pls. Réédition de l'édition de 1725.99 p.6 pls.TBE.‎