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L’Hôpital's Analyse des infiniments petits

An Annotated Translation with Source Material by Johann Bernoulli

  • Robert E Bradley
  • Salvatore J. Petrilli
  • C. Edward Sandifer

Part of the Science Networks. Historical Studies book series (SNHS, volume 50)

Table of contents

  1. Front Matter
    Pages i-liv
  2. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 1-9
  3. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 11-43
  4. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 61-78
  5. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 79-112
  6. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 113-127
  7. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 129-138
  8. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 151-168
  9. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 187-231
  10. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 233-293
  11. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
    Pages 295-301
  12. Back Matter
    Pages 303-311

About this book

Introduction

This monograph is an annotated translation of what is considered to be the world’s first calculus textbook, originally published in French in 1696. That anonymously published textbook on differential calculus was based on lectures given to the Marquis de l’Hôpital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulli’s lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulli’s notes, in Latin, to l’Hôpital’s text in French. The similarities are remarkable, but there is also much in l’Hôpital’s book that is original and innovative.

This book offers the first English translation of Bernoulli's notes, along with the first faithful English translation of l’Hôpital’s text, complete with annotations and commentary. Additionally, a significant portion of the correspondence between l’Hôpital and Bernoulli has been included, also for the fi rst time in English translation.

This translation will provide students and researchers with direct access to Bernoulli’s ideas and l’Hôpital’s innovations. Both enthusiasts and scholars of the history of science and the history of mathematics will fi nd food for thought in the texts and notes of the Marquis de l’Hôpital and his teacher, Johann Bernoulli.

Keywords

Differential Calculus Differential Geometry History of Calculus Infinitesimal Analysis Johann Bernoulli L’Hôpital Non-standard Analysis

Authors and affiliations

  • Robert E Bradley
    • 1
  • Salvatore J. Petrilli
    • 2
  • C. Edward Sandifer
    • 3
  1. 1.Mathematics and Computer ScienceAdelphi UniversityGarden CityUSA
  2. 2.Mathematics and Computer ScienceAdelphi UniversityGarden CityUSA
  3. 3.NewtownUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17115-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-17114-2
  • Online ISBN 978-3-319-17115-9
  • Series Print ISSN 1421-6329
  • Series Online ISSN 2296-6080
  • Buy this book on publisher's site