  Among those who resisted this confusion between “physical explanations” and “mathematical explanations” was the Jesuit Louis Castel. In “Vrai système de physique générale de M. Isaac Newton” (Paris, 1734), he discussed Principia’s proposition XIII of Book III (on Kepler’s law of areas). He granted that the proposition connected mathematically the inverse square law to the ellipticity of the course of the planets. However, he objected that “the one is not the cause, the reason of the other” (Castel 1734, 97) and that Newton had not provided any physical explanation, only a mathematical one. Indeed “physical reasons are necessary reasons of entailment, of linkages, of mechanism. In Newton, there is none of this kind.” (Castel 1734, 121)