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**Lacroix and the calculus.**
*(English)*
Zbl 1141.01006

Science Networks. Historical Studies 35. Basel: Birkhäuser (ISBN 978-3-7643-8637-5/hbk). xiv, 468 p. (2008).

Silvestre François Lacroix (1765–1843) is most famous for his textbooks, in particular for his Traité élémentaire du calcul différentiel et du calcul intégral, which first appeared in 1802 and continued being used even after Cauchy’s groundbreaking transformation of the fundaments of analysis. Lacroix’s Traité is the main topic of the present book: after a short biography of Lacroix and an overview of the Traité, the author presents the principles of the calculus in the late 18th century (infinitesimals vs. limits) and discusses the foundations of calculus given by Lacroix. The next few chapters discuss certain sections of the Traité: analytic and differential geometry, the conception of the integral, differential equations, difference equations and series. Chapter 8 discusses the abridged version of the Traité, which was used as a textbook, and in Chapter 9 the changes in the second edition of the Traité are studied.

The appendix contains two short memoirs by Lacroix, comments by Lacroix himself on his Traité, syllabi of his courses at the École Polytechnique, and “biographical data on a few obscure characters”.

The present book will be invaluable for everyone interested in the development of calculus and its foundations in the early 19th century.

The appendix contains two short memoirs by Lacroix, comments by Lacroix himself on his Traité, syllabi of his courses at the École Polytechnique, and “biographical data on a few obscure characters”.

The present book will be invaluable for everyone interested in the development of calculus and its foundations in the early 19th century.

Reviewer: Franz Lemmermeyer (Jagstzell)

### MSC:

01A50 | History of mathematics in the 18th century |

01A55 | History of mathematics in the 19th century |

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |

01A70 | Biographies, obituaries, personalia, bibliographies |