L’Hôpital's Analyse des infiniments petits: An Annotated Translation with Source Material by Johann Bernoulli (Science Networks. Historical Studies Book 50)

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. This monograph is an annotated translation of what is considered to be the worldâ#x80;#x99;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 lâ#x80;#x99;HÃ ́pital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulliâ#x80;#x99;s lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulliâ#x80;#x99;s notes, in Latin, to lâ#x80;#x99;HÃ ́pitalâ#x80;#x99;s text in French. The similarities are remarkable, but there is also much in lâ#x80;#x99;HÃ ́pitalâ#x80;#x99;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 lâ#x80;#x99;HÃ ́pitalâ#x80;#x99;s text, complete with annotations and commentary. Additionally, a significant portion of the correspondence between lâ#x80;#x99;HÃ ́pital 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 Bernoulliâ#x80;#x99;s ideas and lâ#x80;#x99;HÃ ́pitalâ#x80;#x99;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 lâ#x80;#x99;HÃ ́pital and his teacher, Johann Bernoulli 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 First 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 Find Food For Thought In The Texts And Notes Of The Marquis De L'hôpital And His Teacher, Johann Bernoulli. Robert E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer. Includes Bibliographical References And Indexes. Front Matter....Pages i-liv In Which We Give the Rules of This Calculus....Pages 1-9 Use of the Differential Calculus for Finding the Tangents of All Kinds of Curved Lines....Pages 11-43 Use of the Differential Calculus for Finding the Greatest And the Least Ordinates, to Which Are Reduced Questions De Maximis & Minimis ....Pages 45-59 Use of the Differential Calculus for Finding Inflection Points and Cusps....Pages 61-78 Use of the Differential Calculus for Finding Evolutes....Pages 79-112 Use of the Differential Calculus for Finding Caustics by Reflection....Pages 113-127 Use of the Differential Calculus for Finding Caustics by Refraction....Pages 129-138 Use of the Differential Calculus for Finding the Points of Curved Lines That Touch An Infinity of Lines Given in Position, Whether Straight or Curved....Pages 139-149 The Solution of Several Problems That Depend upon the Previous Methods....Pages 151-168 A New Method for Using the Differential Calculus with Geometric Curves, from Which We Deduce the Method of Messrs. Descartes and Hudde....Pages 169-185 Bernoulli’s Lectiones de Calculo Differentialis ....Pages 187-231 Selected Letters from the Correspondence Between the Marquis de L’Hôpital and Johann Bernoulli....Pages 233-293 Fontenelle’s Eulogy for the Marquis de L’Hôpital....Pages 295-301 Back Matter....Pages 303-311 The similarities are remarkable, but there is also much in l'Hopital'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'Hopital's text, complete with annotations and commentary.