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Science Networks. Historical Studies

L’Hôpital's Analyse des infiniments petits

An Annotated Translation with Source Material by Johann Bernoulli

Authors: Bradley, Robert E, Petrilli, Salvatore J, Sandifer, C. Edward

  • ​Includes the first ever complete English translation of the first Calculus textbook
  • Provides the first English translation of Johann Bernoulli's lessons in Differential Calculus
  • Offers an English translation of substantial portions of the l’Hôpital-Bernoulli correspondence 
  • Presents a historical introduction to l'Hôpital's text and Bernoulli's lessons​ ​
  • Includes a 38-page preface, extensive footnoting, and cross referencing of topics
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Buy this book

eBook $59.99
$129.00 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-3-319-17115-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
$169.00 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-17114-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
$169.00 (listprice)
price for USA
valid through June 30, 2017
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 3, 2016
  • ISBN 978-3-319-34494-2
  • Free shipping for individuals worldwide
About this book

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.

Reviews

“The Analyse des Infiniment Petits (Analysis of the Infinitely Small) treated the differential calculus as a tool ‘for the understanding of curved lines.’ … The result is a truly valuable book: here is the original calculus textbook, with the sources on which it was based, presented in English with an excellent introduction that makes it much easier to follow what is going on. This one is not to be missed!” (Fernando Q. Gouvêa, MAA Reviews, September, 2015)


Table of contents (13 chapters)

  • In Which We Give the Rules of This Calculus

    Bradley, Robert E. (et al.)

    Pages 1-9

  • Use of the Differential Calculus for Finding the Tangents of All Kinds of Curved Lines

    Bradley, Robert E. (et al.)

    Pages 11-43

  • Use of the Differential Calculus for Finding the Greatest And the Least Ordinates, to Which Are Reduced Questions De Maximis & Minimis

    Bradley, Robert E. (et al.)

    Pages 45-59

  • Use of the Differential Calculus for Finding Inflection Points and Cusps

    Bradley, Robert E. (et al.)

    Pages 61-78

  • Use of the Differential Calculus for Finding Evolutes

    Bradley, Robert E. (et al.)

    Pages 79-112

Buy this book

eBook $59.99
$129.00 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-3-319-17115-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
$169.00 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-17114-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
$169.00 (listprice)
price for USA
valid through June 30, 2017
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 3, 2016
  • ISBN 978-3-319-34494-2
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
L’Hôpital's Analyse des infiniments petits
Book Subtitle
An Annotated Translation with Source Material by Johann Bernoulli
Authors
Series Title
Science Networks. Historical Studies
Series Volume
50
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-17115-9
DOI
10.1007/978-3-319-17115-9
Hardcover ISBN
978-3-319-17114-2
Softcover ISBN
978-3-319-34494-2
Series ISSN
1421-6329
Edition Number
1
Number of Pages
LIV, 311
Number of Illustrations and Tables
235 b/w illustrations, 9 illustrations in colour
Topics