"Here then we have all the essentials for the calculus; but only for explicit integral algebraic functions, needing the binomial expansion of Newton, or a general method of rationalization which did not impose too great algebraic difficulties, for their further development; also, on the authority of Poisson, Fermat is placed out of court, in that he also only applied his method to certain special cases. Following the lead of Roberval, Newton subsequently used the third definition of a tangent, and the idea of time as the independent variable, although this was only to insure that one at least of his working variables should increase uniformly. This uniform increase of the independent variable would seem to have been usual for mathematicians of the period and to have persisted for some time; for later we find with Leibniz and the Bernoullis that d(dy/dx) = (d2y/dx2)dx. Barrow also used time as the independent variable in order that, like Newton, he might insure that one of his variables, a moving point or line or superficies, should proceed uniformly; ...Barrow... chose his own definition of a tangent, the second of those given above; and to this choice is due in great measure his advance over his predecessors. For his areas and volumes he followed the idea of Cavalieri and Roberval."