Newton on the equiangular spiral: An addendum to Erlichson's account
type: Item
instance of: scholarly article
title: Newton on the equiangular spiral: An addendum to Erlichson's account
zbMATH Open document ID: 0804.01003
published in: Historia Mathematica
publication date: 1995-01-22T00:00:00Z
review text: The author discusses a flaw in Newton's proof of Proposition IX of Book I of the Principia. The figure for Proposition IX in the first two editions of the Principia differs from that in the third edition. But the basic error remains: the assumption without proof of the similarity of all segments of the spiral with the same central angle. By 1671 Newton had proved this assumption by an integration. In Proposition IX it would thus appear that he either simply presented as known an analytic result now familiar to himself, or hoped that his readers would consider it as valid for infinitesimal segments.
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 636026
zbMATH Keywords: Newton
zbMATH Keywords: spiral
author: Curtis Wilson
MaRDI profile type: Publication
full work available at URL: hmat.1994.1018
OpenAlex ID: W2059847316
cites work: Newton's solution to the equiangular spiral problem and a new solution using only the equiangular property
cites work: Q5650623
cites work: Q3304892
cites work: Q5519096
cites work: D'Alembert versus Euler on the precession of the equinoxes and the mechanics of rigid bodies
DOI: 10.1006/HMAT.1994.1018
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description: scientific article; zbMATH DE number 636026