The Catenary, or How Differential Calculus Appeared on the Public Square

This chapter attempts to define, by means of an example, a manner of doing history of sciences, a manner which is particularly internalist and that must be completed by works of another type. My aim is not to impose a particular manner; on the contrary, I am deeply convinced of the fact that history of sciences is in its essence interdisciplinary and that it must be done by several hands and in several manners. Our predecessors have pinned up the great texts and described the results obtained, translating them in a modern language and controlling their accuracy along the way. This manner of doing history, which I will qualify as a posteriori, is indispensable but should be completed by an a priori reading of those texts. I mean by that to give an account of the manner in which a text could have been sought and understood by its author with the knowledge and vocabulary he might have had in his time. The example I have chosen is only of interest from this last point of view because its aim is to compare different ways to arrive at the same scientific result.