In the first edition of the Principia, published in 1687, Isaac Newton stated his second law of motion in a concise form,1
where motion is defined as “velocity and the quantity of matter [mass] jointly,” which we call momentum. This formulation remained unchanged in the second (1713) and third (1726) editions of the Principia, and in each of these editions Newton gave it a precise mathematical form for velocity-independent central forces in Prop. 1 and Prop. 6, Book 1, followed by numerous examples that further clarified the content of his law.3 In Book 2, Newton applied the second law to resistance forces due to a dense medium, which depend on the velocity of the moving body,4 and in Book 3, he applied it to gravitational forces that satisfy the inverse-square dependence on distance to obtain the solutions of outstanding planetary problems which stimulated mathematical astronomy...
