Newton's Principia and inverse-square orbits in a resisting medium: A spiral of twisted logic (Q1277360)

Not everything that mathematicians write is correct, not every argument is logical: there have been several well-known recent instances concerning Riemann and Fermat: Homer nods. Therefore we expect to find flaws in Dirichlet, Kelvin, Gauss, and Euler, as well as Newton. Proposition XV/Theorem XII in Book Two of Newton's \textit{Principia} purports to find the spiral path of a body attracted by a central force with an inverse-square law through a medium which retards it in proportion to the square of its speed. Detailed reasons are given to support the conclusion that Newton's argument is illogical; the illogicality is presented in detail. Like Weierstrass's complaint against Dirichlet's and Kelvin's method of proof, Weinstock gives a counterexample to the method of Newton's proof. The commentaries on Newton by King-Hele, Chandrasekhar and Erlichson are reviewed in similar style.