  A fundamental contrast between Newton's mathematical theory of motion under centripetal forces and the mathematical theories of motion developed by Galileo and Huygens is that Newton's is generic.  Galileo and Huygens examined one kind of force, uniform gravity, with a goal of deriving testable consequences. Newton's theory covers not only forces that vary as 1/r2, for which the Principia is famous, but also forces that vary as r, as 1/r3, and even as any arbitrary function of r. At the end of Section 11 he gives a reason, quoted earlier: