I was reading about the first contributes that will bring the Birth of Calculus with Newton and Leibniz, and in particular the initial problem of finding the tangent of a curve in each point. Roberval started from Archimedes's spiral considering then a cycloid and saying that the tangent is simply the vector sum of both the contributes of speed. Then Newton introduces his method of fluxions defining fluents as objects made by moving geometric elements but it seems that he just used what Roberval already described to define its concept of tangent in each point. What are the differences between what these guys said?
Thank you