Analyse des infiniment petits, pour l'intelligence des lignes courbes … Seconde edition.

L'HÔPITAL, Guillaume François Antoine, marquis de.

Edité par Paris, François Montalant, 1715., 1715

A propos de cet article

4to, pp.xv, [1], 162, 165 181, [1] (i.e.wanting leaf X2, pp.163 164); with 11 folding engraved plates illustrating 156 diagrams, engraved vignette to title, initials, head- and tailpieces; two marginal tears to title (not touching text), final plate detached, small marginal hole to last leaf and plate, occasional light marginal dampstaining and other small marks, some toning; overall good in contemporary mottled calf, spine gilt in compartments, gilt lettering-piece, edges stained red, marbled pastedowns, small fragments from a medieval musical manuscript visible to joints; upper joint partly split, spine with small losses and partly detached, some wear to boards, corners, and edges, free endpapers wanting; with marginal annotations in a later eighteenth-century hand to 137pp. of text and to 4 plates, with occasional marginal diagrams.Second edition (first 1696) of l'Hôpital's famous Analyse, the first textbook on differential calculus, inspired by the work of Leibniz and the Bernoulli brothers, this copy profusely annotated by an anonymous but proficient eighteenth-century mathematician. 'Following the classical custom, the book starts with a set of definitions and axioms … Following the axioms, the basic rules of the differential calculus are given and exemplified. The second chapter applies these rules to the determination of the tangent to a curve in a given point … The third chapter deals with maximum-minimum problems and includes examples drawn from mechanics and from geography. Next comes a treatment of points of inflection and of cusps. This involves the introduction of higher-order differentials, each supposed infinitely small compared to its predecessor. Later chapters deal with evolutes and with caustics' (DSB). The rule named after L'Hôpital (for finding the limiting value of a fraction whose numerator and denominator tend to zero) is given in chapter nine. The extraordinary marginal annotations in this copy by a later eighteenth-century reader display a remarkable engagement with l'Hôpital's work, comprising critical and explanatory text, detailed mathematical formulae, and occasional diagrams. The popularity of the Analyse prompted several commentaries, such as Jean-Pierre de Crousaz's Commentaire (1721) and Pierre Varignon's Eclaircissemens (1725), and the marginalia here are very much in the same spirit, although evidently not copied from either of these works. The annotator sometimes employs the first person, as if drafting their own commentary or recording that of a teacher e.g.'we will see what to think of these general rules' (p.63); 'it seems to me that the rule should be presented in this way …' (p.66). He is certainly not uncritical: 'the author, for greater clarity, should have said for example …' (p.105); 'this equation of the BCD curve proves as well as that of our author that this curve is of the 3rd kind' (p.137). The final page contains a rant regarding faults in the printing, our annotator expressing his opinion that the editor was 'the worst kind of scamp' ('le pire polison'). There are references to Descartes ('ce grand homme' pp.21 22), to Varignon (p.103), and to the astronomer Nicolas-Louis de Lacaille (1713 1762) (p.138). Language: French.

N° de réf. du vendeur H6522

Détails bibliographiques

• Titre: Analyse des infiniment petits, pour l'intelligence des lignes courbes … Seconde edition.
• Éditeur: Paris, François Montalant, 1715.
• Date de parution: 1715