Continuity in nature and in mathematics: Du Châtelet and Boscovich

In the mid-eighteenth century, it was usually taken for granted that all curves described by a single mathematical function were continuous, which meant that they had a shape without bends and a well-defined derivative. In this paper I discuss arguments for this claim made by two authors, Emilie du Châtelet and Roger Boscovich. I show that according to them, the claim follows from the law of continuity, which also applies to natural processes, so that natural processes and mathematical functions have a shared characteristic of being continuous. However, there were certain problems with their argument, and they had to deal with a counterexample, namely a mathematical function that seemed to describe a discontinuous curve.