To find the magnitude of F 2 (r) from the original central force F 1 (r), Newton calculated their difference F 2 (r) − F 1 (r) using geometry and the definition of centripetal acceleration. In Proposition 44 of his Principia, he showed that the difference is proportional to the inverse cube of the radius, specifically by the formula given above, which Newtons writes in terms of the two constant areal velocities, h 1 and h 2