In the same year (1823) that Simpson’s work was reprinted, *Resume Des Lecons Donnees a L’Ecole Royale Polytechnique: Calcul Infinitesimal* by Augustin-Louis Cauchy was published in France (Cauchy 1823). This book is what we would nowadays call a textbook of Analysis rather than an introduction to the calculus. In many respects it resembles contemporary textbooks; for instance, the first and second derivative tests are stated with care and precision. However, *Resume* does not deal with any applications, as is customary in a book on Analysis, making it a work quite different from Simpson’s. One of the strengths of *Doctrine* is precisely the number and variety of applications, which help to motivate the reader and render it a masterpiece of mathematical exposition.

In hindsight we can see that Simpson opted for the right course by avoiding extensive discussions on the foundations of Calculus, which no one was able to put on a solid base during Simpson’s lifetime, and instead concentrating on the usefulness of the techniques invented by

*Editor’s Note: This article was published in 2005.*