Abstract
L’Hôpital met Bernoulli in November 1691 and almost immediately hired him as a tutor, to teach him the new calculus. In 1691–92, Bernoulli gave him lessons on the subject, including handwritten notes. Bernoulli kept copies of these notes for himself and long after the publication of the Analyse, he published the second part of these notes, on the integral calculus. However, his notes on the differential calculus, which form the basis of the first four chapters of l’Hôpital’s Analyse, remained unknown until a copy was discovered in Basel in 1922. These notes, originally written in Latin, appear here for the first time in English translation. When compared to the corresponding chapters of the Analyse, we see clearly that Bernoulli provided the major results and the structure for that portion of l’Hôpital’s book, but that l’Hôpital also contributed significantly, especially as a lucid expositor. This chapter contains the full text of Bernoulli’s lessons on the differential calculus, including reproductions of the hand drawn figures.