L’Hôpital's Analyse des infiniments petits: An Annotated by Robert E Bradley

By Robert E Bradley

This monograph is an annotated translation of what's thought of to be the world’s first calculus textbook, initially released in French in 1696. That anonymously released textbook on differential calculus used to be in response to lectures given to the Marquis de l’Hôpital in 1691-2 by means of the good Swiss mathematician, Johann Bernoulli. within the Nineteen Twenties, a replica of Bernoulli’s lecture notes was once chanced on in a library in Basel, which offered the chance to check Bernoulli’s notes, in Latin, to l’Hôpital’s textual content in French. The similarities are striking, yet there's additionally a lot in l’Hôpital’s e-book that's unique and innovative.

This publication deals the 1st English translation of Bernoulli's notes, in addition to the 1st trustworthy English translation of l’Hôpital’s textual content, whole with annotations and observation. also, a good portion of the correspondence among l’Hôpital and Bernoulli has been integrated, additionally for the fi rst time in English translation.

This translation will offer scholars and researchers with direct entry to Bernoulli’s rules and l’Hôpital’s options. either fans and students of the background of technology and the background of arithmetic will fi nd meals for concept within the texts and notes of the Marquis de l’Hôpital and his instructor, Johann Bernoulli.

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Extra resources for L’Hôpital's Analyse des infiniments petits: An Annotated Translation with Source Material by Johann Bernoulli

Example text

Cissoid of Diocles The word cissoid derives from the Ancient Greek word for ivy. In modern sources, the Cissoid of Diocles is defined by considering a circle, a tangent line at some point B on its circumference and the pole F diametrically opposite to B. In figure 14, only the semi-circle FNB is given, with the tangent line Bb. From the pole F , a straight line FN is drawn through the circle at N to the tangent line, and the point M is taken so that FM D Nb. The Cissoid of Diocles is then the curve FMA, which is the locus of all such points M .

139 9 The Solution of Several Problems That Depend upon the Previous Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 10 A New Method for Using the Differential Calculus with Geometric Curves, from Which We Deduce the Method of Messrs. Descartes and Hudde . . . . . . . . . . . . . . . . . . . . . 169 3 4 xlv xlvi Contents 11 Bernoulli’s Lectiones de Calculo Differentialis . .

305 Analysis of the Infinitely Small For the Understanding of Curved Lines1 Guillaume François Antoine, Marquis de l’Hôpital 1 Analyse des infiniment petits, pour l’intelligence des lignes courbes, Imprimerie Royale, Paris, 1696. L’Hôpital’s Preface The analysis that we explain in this work assumes common analysis, but it is very different. Ordinary analysis considers only finite magnitudes. This analysis reaches all the way to infinity itself. It compares infinitely small differences of finite magnitudes; it uncovers the ratios among these differences; and in this way it makes known the ratios among finite magnitudes, which are as though infinite when compared to the infinitely small.

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