The 42nd meeting of the ORESME Reading Group will be held on Friday-Saturday, February 21-22, 2020, at Northern Kentucky University. We shall once more support plans for a Read the Masters event, our second, at MAA MathFest 2020 in Philadelphia this coming August. In an effort to choose a selection that will have wide appeal and accessibility for a general audience at MathFest, we’ve selected for our reading the first few lectures from the Résumé des leçons … sur le calcul infinitésimal of Augustin-Louis Cauchy (1789-1857), his 1823 calculus course at l’École Royale Polytechnique, wherein he presents his definition of a limit for the first time and uses it to define both continuity and the notion of a derivative. We will use the original French edition from Cauchy's Ouevres and a new English translation by Dennis M. Cates now available as an e-book from Springer.
We shall take up
- Résumé des leçons données a l’École Royale Polytechnique sur le calcul infinitésimal. Calcul différentiel. Série 2, Tome 4, 13-25.
- Chapters 1, 2 and 3 from Dennis M. Cates, Cauchy’s Calcul Infinitésimal: an annotated English translation, Springer, 2019. vii-xxiv, 1-15.
As an additional reference, Cates had earlier published a calculus textbook that used Cauchy's work as the primary source. Here are his analyses of this text:
- Dennis M. Cates. A Guide to Cauchy's Calculus: A Translation and Analysis of Calcul Infinitésimal. Fairview Academic Press, 2012. Title pages, Lecture One Analysis (pp. 40-52), Lecture Two Analysis (pp. 59-67), Lecture Three Analysis (pp. 75-90).
Submissions from 2019
Cauchy's Calcul Infinitésimal. First, Second, Third Lectures., Dennis M. Cates
Submissions from 2012
Submissions from 1823
Oeuvres complètes d'Augustin Cauchy, Résumé des leçons […] sur le Calcul Infinitésimal, Augustin-Louis Cauchy