Newton's Principia and inverse-square orbits in a resisting medium: A spiral of twisted logic
type: Item
instance of: scholarly article
title: Newton's Principia and inverse-square orbits in a resisting medium: A spiral of twisted logic
zbMATH Open document ID: 0934.01002
author: Robert Weinstock
published in: Historia Mathematica
publication date: 2000-03-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 70M20
zbMATH DE Number: 1248268
zbMATH Keywords: Newton
zbMATH Keywords: inverse-square orbit
zbMATH Keywords: resisting medium
zbMATH Keywords: King-Hele
zbMATH Keywords: Chandraskehar
zbMATH Keywords: Erlichson
MaRDI profile type: Publication
full work available at URL: hmat.1998.2192
OpenAlex ID: W2071386023
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DOI: 10.1006/HMAT.1998.2192
description: scientific article; zbMATH DE number 1248268