Abstract
Everyone's heard of the L'Hospital rule. Less is known, however, of the book in which it is enunciated, and almost nothing is known of the Marquis de l'Hospital, even in educated circles.
We first see the rule in §163 of the Analysis of the Infinitesimal for the Understanding of Curved Lines - and its author (like everything else of substance in the book) is the Marquis's private tutor, Johann Bernoulli. The Analysis of the Infinitesimal was published in 1696 and marks a milestone in the history of mathematics.
It is the first comprehensive treatment of differential calculus to bring the new method from heights accessible only to a select few into the hands of the general learned public, with all the consequences that the promotion of infinitesimals had for the mathematical investigation of nature and the further development of science and technology. The Marquis de l'Hospital and the Analysis of the Infinitesimal is devoted to the philosophical, social and generally spiritual circumstances of the work's creation, as well as to the dark and long-hidden story of its two creators, Guillaume de l'Hospital and Johann Bernoulli.
Together with an introductory study on the personality of the Marquis de l'Hospital and the first history of the infinitesimal calculus, it also consists of a translation of the Analysis of the Infinitesimal, accompanied by a detailed historical-critical commentary.