How did l'Hôpital's 1696 calculus book shape mathematics?

Published in 1696 by the French mathematician Guillaume de l'Hôpital, the Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes was the first systematic textbook on differential calculus. It popularized Leibniz's infinitesimal calculus and first introduced the limit-evaluating method known as l'Hôpital's rule, which the author learned from his tutor Johann Bernoulli.

What we know

• Guillaume de l'Hôpital published Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes in 1696 as the first systematic exposition and textbook of differential calculus. [2, 3]
• The book included l'Hôpital's rule for calculating limits of indeterminate forms by taking derivatives, a rule l'Hôpital learned from his tutor Johann Bernoulli. [2, 4]
• The treatise treated only differential calculus, while corresponding volumes treating integral calculus were authored by Johann Bernoulli. [3]

Where to go next

• how it workedHow does l'Hôpital's rule work for indeterminate forms?
• whoWho was Johann Bernoulli?
• whenWhat was the first textbook on integral calculus?
• the bigger pictureWhat are the core principles of infinitesimal calculus?
• compared withHow did Leonhard Euler shape modern mathematical notation?
• an unexpected connectionHow did a French nobleman's calculus treatise rely on a Swiss tutor?Although the famous 1696 calculus text bears l'Hôpital's name and was authored by him, its contents including the famous limit rule originated from his private tutor Johann Bernoulli.

Sources

• [1]Guillaume de l'Hôpital (Wikidata Q202279) · CC0 1.0
• [2]Guillaume de l'Hôpital · CC BY-SA 4.0
• [3]Analyse des infiniment petits pour l'intelligence des lignes courbes · CC BY-SA 4.0
• [4]L'Hôpital's rule · CC BY-SA 4.0
• [5]Leonhard Euler · CC BY-SA 4.0

Your path

1. What was the role of a Roman provincial governor?
2. /How are porous media used in energy storage?
3. /How did l'Hôpital's 1696 calculus book shape mathematics?