De l'Hôpital, Bernoulli, and the genesis of Analyse des infiniment petits

Abstract

The Marquis de l'Hôpital's Analyse des infiniment petits (1696) was the first ever calculus textbook. Its introductory chapters were based on Johann Bernoulli's Lectiones de calculo differentialium, a series of lessons written for the Marquis in 1691–92. Bernoulli also assisted with the later chapters, while the Marquis supported him with a stipend during 1694–96. We examine the text and its source material in this paper, which was presented at the research symposium ‘Editing historical mathematics: techniques and traditions since 1900’ at All Soul's College, Oxford, in December 2011. With this in mind he published his Analyse des infiniment petits, a book that was both good and well-written … We may only find fault in that Mr. de l'Hôpital did not make well enough known the debt he owed to Mr. Bernoulli … (Montucla 1798, 397)