Abstract

In this paper, I intend to document the ongoing quarrelQuarrel on the cycloid in order to analyse the diverse mathematical ways of the scientific revolution, and the judgments mathematicians gave about their reasons to improve some processes as well as to publish or not, and possibly to improve on their predecessors or rivals. What is particularly fascinating in the story as told is that Johann Bernoulli[aut]Bernoulli Jacob considered the case of the cycloid to be obsolete, due to the completely new Calculus. Therefore, the focus on Torricelli[aut]Torricelli and Roberval, which was maintained by many authors, had far from obvious purposes that I wish to investigate by looking at various testimonies. In fact, this taking the opportunity of the republication of Torricelli’s[aut]TorricelliOpera geometricaOpera geometrica, I too confront the history of science as done by mathematicians and by historians, both for methods, results, and posterity. As I consider so many reactions to this quarrelQuarrel, I have mostly appended original translations in English of various documents in the form of annexes. Because of the important number of letters quoted, and of original sources, I have introduced some lists just before the annexes. The bibliography is at the end of the paper.