Newton's mature dynamics: Revolutionary or reactionary?

Summary

By a simple revision of Newton's diagram for Proposition 6 of the third edition of the Principia, one can see directly how the mathematics of uniform circular motion have been employed to solve the Kepler problem of elliptical planetary motion in Proposition 11. Newton strove initially to build his dynamics on the linear kinematics of Galileo; and, in this utilization of uniformly accelerated linear motion to solve more complicated problems, he can be seen as revolutionary. But he could not escape completely from the coils of celestial circularity, and in his utilization of uniform circular motion to solve problems of elliptical motion, he can be seen as reactionary. The key to understanding Newton's mature dynamics resides in the discussion of the alternate dynamics ratio, as presented here in section six.