Lacroix and the Calculus 



João Caramalho Domingues, Silvestre François Lacroix (Paris, 1765  ibid., 1843) was a most influential mathematical book author. His most famous work is the threevolume Traité du calcul différentiel et du calcul intégral (17971800; 2nd ed. 18101819)  an encyclopedic appraisal of 18thcentury calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix's large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18thcentury calculus, and the way it is reflected in Lacroix's account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix's large Traité was adapted for teaching into a shorter, textbook version  the Traité élémentaire de calcul différentiel et de calcul intégral (1802; several later editions). This adaptation is also analysed. Lacroix and the Calculus should appeal to historians and mathematicians interested in the history of the calculus (and especially in the background to Cauchy and Bolzano) and in its teaching in the late 18th and early 19th centuries. Contents

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