The swan song of indivisibles. Integral calculus in Pascal's last scientific work. With a preface by François De Gandt (Q2782608)

In 1658, Blaise Pascal issued a set of seven short treatises which together amounted to an essay on the cycloid. He treated eighteen problems, in more or less detail, using the method of indivisibles. Preceding the calculus of Newton and Leibniz, they involve a geometric rendition of the key ideas which the modern reader negotiates with difficulty. This study, a revised version of a 1995 monograph issued by IREM at Besançon, has the goal of explaining Pascal's process, fleshing out the details and providing the intellectual setting for his work. A significant part of the book analyzes the sums of indivisibles exploited by Pascal and how they correspond to the artifacts of modern integration theory. Other chapters treat the calculation of a volume of a solid of revolution as an example; the interrelations between circles and cycloids; the ``October'' problems and the philosophical links with \textit{Pensées}. In particular, the paradoxes of the infinite are for the heart rather than the reason, and the hierarchies of the infinite reflect those of flesh, spirit and love. NEWLINENEWLINENEWLINEThe appendices summarize the contents of the seven treatises, place Pascal's work in the context of 17th century mathematics (relying on work of Pierre Costabel) and review properties of the cycloid known to Pascal's contemporaries.