Sylvestre François Lacroix
He was born in Paris, and was raised in a poor family who still managed to obtain a good education for their son. Lacroix's path to mathematics started with the novel Robinson Crusoe. That gave him an interest in sailing and thus navigation too. At that point geometry captured his interest and the rest of mathematics followed. He had courses with Antoine-René Mauduit at College Royale de France and Joseph-Francois Marie at Collége Mazaine of University of Paris. In 1879 he obtained some lunar observations of Pierre Charles Le Monnier and began to calculate the variables of lunar theory. The next year he followed some lectures of Gaspard Monge.
In 1782 at the age of 17 he became an instructor in mathematics at the École de Gardes de la Marine in Rochefort. Monge was the students' examiner and Lacroix's supervisor there until 1795. Returning to Paris, Condorcet hired Lacroix to fill in for him as instructor of gentlemen at a Paris lycée. In 1787 he began to teach at École Royale Militaire de Paris and he married Marie Nicole Sophie Arcambal.
It was the best of times and the worst of times: Lavoisier had opened inquiry into "new chemistry", a subject Lacroix studied with Jean Henri Hassenfratz. He also joined Societe Philomatique de Paris which provided a journal in which to communicate his findings. On the other hand, Paris was in the grip of the Reign of Terror. In 1794 Lacroix became director of the Executive Committee for Public Instruction. In this position he promoted École Normale and the system of Écoles Centrales. In 1795 he taught at École Central des Quatres-Nations.
The first volume Traité du Calcul Différentiel et du Calcul Intégral was published in 1897. Legendre predicted that it "will make itself conspicuous by the choice of methods, their generality, and the rigor of the demonstrations." In hindsight Ivor Grattan-Guinness observed:
- The Traite is by far the most comprehensive work of its kind for that time. The extent of its circulation is not known and it may not have been very large...But it is as well known as any other treatise of its time, and certainly more worth reading than any other, especially for the emerging generation.
In 1799 he became professor of analysis at École Polytechnique.
Lacroix was the author of at least 17 biographies contributed to Biographie Universalle compiled by Louis Gabriel Michaud.
In 1809 he was admitted to Faculté des Sciences de Paris.
In 1812 he began teaching at the Collège de France, and was appointed chair of mathematics in 1815.
When a second edition of the Traité du Calcul Différentiel et du Calcul Intégral was published in three volumes in 1810, 1814, and 1819, Lacroix renewed the text:
- New material, recording many of the advances made during the new century, were introduced throughout the text, which was rounded off by a long list of 'Corrections and additions' and a splendid 'Table of contents'. In addition, the structure of the work was changed somewhat, especially the third volume on series and differences. But the general impression is still that the main streams and directions of the calculus had been amplified and enriched, rather than changed in any substantial way.
During his career he produced a number of important textbooks in mathematics. Translations of these books into the English language were used in British universities, and the books remained in circulation for nearly 50 years.
- Traité du Calcul Différentiel et du Calcul Intégral, Chez Courcier, Paris, 1797-1800.
- 1802: Traité Élémentaire du Calcul Différentiel et du Calcul Intégral, link from HathiTrust.
- Revised and re-published several times; the 9th edition appeared in 1881.
- 1804: Complément des Élémens d'algèbre, a l'usage de l'École Centrale des Quatre-Nations, Chez Courcier, Paris, Fifth edition (1825) from Internet Archive.
- 1814: Eléments de Géométrie à l'usage de l'Ècole Central des Quatre-Nations, 10th edition, link from Hathi Trust.
- 1816: Traité élémentaire de calcul des probabilités, Paris, Mallet-Bachelier, link from HathiTrust.
- 1816: Essais sur L'Enseignement en Général, et sur celui des Mathématiques en Particulier, Libraire pur les Mathématiques, link from Internet Archive
- quoted in Grattan-Guinness (1990) page 140
- I. Grattan Guinness (1990) page 183
- I. Grattan-Guinness (1990) page 267
- For example, John Farrar's translation Elements of Algebra, 3rd edition, 1831 Boston
- S.F. Lacroix (1861) Traité du Calcul Différentiel ed du Calcul Intégral, Premier Tome, 6th edition
- Charles Babbage - MacTutor History of Mathematics
- João Caramalho Domingues (2008) Lacroix and The Calculus, Science Networks: Historical Studies, v. 35, Birkhäuser ISBN 978-3-7643-8638-2 .
- Ivor Grattan-Guinness (1990) Convolutions in French Mathematics, 1800 — 1840, §2.5.4 Lacroix: scientific educator, pp 113,4, Science Networks: Historical Studies v. 2, Birkhauser ISBN 3-7643-2240-3 .
- O'Connor, John J.; Robertson, Edmund F., "Sylvestre François Lacroix", MacTutor History of Mathematics archive, University of St Andrews.