Proofs and Contexts: the Debate between Bernoulli and Newton on the Mathematics of Central Force Motion

I discuss the confrontation between Isaac Newton and Johann Bernoulli on the study of central force motion. I show that their polemical exchange reveals the different agendas concerning the application of mathematics to natural philosophy endorsed by the group based in Oxford, Cambridge, and London, whose leader was Newton, and the group scattered in Europe, mostly in Basel and Paris, whose main representatives were Leibniz and Bernoulli. I focus on some issues that concern the interpretation of texts in the history of mathematics.