  We explore Leibniz's understanding of the differential calculus, and argue
that his methods were more coherent than is generally recognized. The
foundations of the historical infinitesimal calculus of Newton and Leibniz have
been a target of numerous criticisms. Some of the critics believed to have
found logical fallacies in its foundations. We present a detailed textual
analysis of Leibniz's seminal text Cum Prodiisset, and argue that Leibniz's
system for differential calculus was free of contradictions.
