A Mysterious Copy of Lacroix’s Traité Élémentaire de Calcul Différentiel et de Calcul Intégral: A Mathematical Treasure

Sylvestre François Lacroix (1765–1843) was a prolific and highly successful author of mathematical textbooks in the late 18th and early 19th centuries. One of his most significant publications was the 1790-page Traité du Calcul Différentiel et du Calcul Intégral (Treatise on Differential Calculus and Integral Calculus), published in three volumes between 1797 and 1800. In 1802 Lacroix, by then a professor at the École Polytechnique in Paris, published an abridged version in a single volume, entitled Traité Élémentaire de Calcul Différentiel et de Calcul Intégral (Elementary Treatise of Differential Calculus and Integral Calculus). The three parts of the shorter book, on differential calculus, integral calculus, and differences and series, corresponded to the respective contents of the three volumes of the original work. Its main goal was “to make the 18th-century calculus, in all its details, much more easily accessible and fruitful to the 19th-century mathematicians” [Domingues 2005, p. 291].

Figure 1. Title page of Lacroix's textbook. All photographs of
Lacroix’s Traité Élémentaire de Calcul Différentiel et de Calcul Intégral
that appear in this article depict the author’s copy and were taken by the author.

Like many of Lacroix’s other textbooks, the Traité Élémentaire was very successful, going through nine editions between 1802 and 1881, and receiving English, German, Italian, and Portuguese translations within the first few decades of its initial publication. Of course, it was the English translation of 1816, published by Charles Babbage, John Herschel and George Peacock, that would have the most celebrated impact, as it helped introduce the European differential and functional notation to a British audience, in preference to the old Newtonian fluxional symbols that by then had become a barrier to mathematical discourse between British mathematicians and their continental counterparts.

Figure 2. Front cover of author's copy of Lacroix's textbook.

The pictures above are of my copy of the 4th edition from 1828. As will become clear, the date of this edition is significant to our story. It was clearly brand new when it received its very attractive leather binding, featuring the insignia of the “University of London” along with its date of foundation: “1827.” The university was in fact founded in 1826 as the “London University,” retaining this title until it received its current name, University College London (UCL), in 1836. At the time of its foundation, it was the first such institution to have been established in England since Oxford and Cambridge in the Middle Ages, and it attracted controversy for its liberal admissions policy under which non-Anglicans were permitted a university-level education for the first time in England.