The calculus according to S. F. Lacroix (1765-1843)

Silvestre François Lacroix (Paris. 1765 - ibid., 1843) was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous book is a monumental Traité du calcul différentiel et du calcul intégral (three large volumes, 1797-1800; a second edition appeared in 1810-1819) - an encyclopaedic appraisal of 18th-century calculus. He also published many textbooks, one of which is closely associated to this large Traité: the Traité élémentaire du calcul différentiel et du calcul intégral (first edition in 1802; four more editions in Lacroix's lifetime; four posthumous editions).
Although most historians acknowledge the great influence of Lacroix's large Traité in early 19th-century mathematics it has not been thoroughly studied. This thesis is a contribution for correcting this omission. The focus is on its first edition, but the second edition and the Traité élémentaire, are also addressed.
The thesis starts with a short biography of Lacroix, followed by an overview of the first edition of the large Traité. Next corne five chapters where particular aspects are analyzed in detail: the foundations of the calculus, analytic and differential geometry, approximate integration and conceptions of the integral, types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions), and three aspects related to finite differences and series (the use of subscript indices, types of solutions of finite difference equations, and mixed difference equations); for all these aspects Lacroix's treatment is compared to the 18th-century background, and to his likely sources. Then we examine how the large Traité was adapted to a textbook - the Traité élémentaire, we take a look at the second edition of the large Traité, and conclude the body of the thesis with some final remarks.

Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy awarded by Middlesex University.