Newton on the equiangular spiral: An addendum to Erlichson's account
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.
scientific article; zbMATH DE number 636026