Translators’ Preface

Analyse des infiniment petits, pour l’intelligence des lignes courbes was the first textbook of the differential calculus. The title translates as Analysis of the infinitely small, for the understanding of curved lines. It was published anonymously in Paris in 1696, although members of the French mathematical community were well aware that the author was Guillaume François Antoine de l’Hôpital,1 the Marquis of Saint-Mesme (1661–1704). The textbook was successful, as evidenced by the appearance of a posthumous second edition (L’Hôpital 1716), which identified the author.2 Pierre Varignon (1646–1722), who was professor of mathematics at Collège des Quatre-Nations in Paris and a friend of l’Hôpital, created a collection of clarifications and additions to the Analyse. These were published posthumously (Varignon 1725), a few years after the 1716 edition of the Analyse. Later editions of the Analyse included similar commentary and continued to appear throughout the 18th century (L’Hôpital 1768, 1781). Differential and integral calculus are generally considered to have their origins in the works of Sir Isaac Newton (1642–1727) and Wilhelm Gottfried von Leibniz (1646–1716)3 in the late 17th century, although the roots of the subject reach far back into that century and, arguably, even into antiquity. Leibniz first described his new calculus in a cryptic article more than a decade before the publication of the Analyse (Leibniz 1684). For all practical purposes, Leibniz’ early papers were not