Hegel and Newtonianism pp 429-438 | Cite as

# A Worm in Newton’s Apple

## Abstract

The early history of Newton’s *Principia* is well known. Its genesis was a summer 1684 visit by Edmund Halley of Oxford to Isaac Newton at Cambridge. Here is a paraphrase of a portion of their reported conversation: “Along what curve would a body travel”, asked Halley, “if it were attracted to a fixed other body by a force inversely proportional to the square of the distance between them?” “A conic section”, was Newton’s immediate reply: “an ellipse, an hyperbola, or a parabola”. “How do you know?” asked Halley. “I’ve worked it out mathematically”, declared Newton. “Remarkable!” cried Halley; “show me the work”. Newton could not then find the required papers, but several weeks later he reproduced his solution and sent the result to the admiring Halley, whose reaction was electric.

## Keywords

Conic Section Centripetal Force Require Paper Planetary Motion Hundredth Anniversary## Preview

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## Notes

- 1.Newton
*Principles*I.Google Scholar - 2.Quoted from Cohen, 1978, p. 131.Google Scholar
- 3.
*Ibid.*reference 2, p. 131.Google Scholar - 4.Weinstock, R. 1992. This paper resurrects proofs by Laplace and Jacobi, and also presents one constructed by the author in February 1991.Google Scholar
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*cum*Corollary 1 of*Principia*Book 1 — with a*correct*presentation of the content of Proposition XVII in the wake of the “standard” misrepresentation repeated, on p. 163, from the first edition!Google Scholar - 11.L. Euler, 1911-.
*Series Secunda, Tomus Primus*, pp. 221–222.Google Scholar - 12.I.B. Cohen 1978, p. 294.Google Scholar
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*Principles*I. pp. 65–66. The uncareful reader might hastily infer the misrepresentation from the*statement*of Proposition XVII: “Supposing the centripetal force to be inversely proportional to the squares of the distances of places from the centre, and that the absolute value of that force is known; it is required to determine the line which a body will describe that is let go from a given place with a given velocity in the direction of a given right line.” But even a cursory examination of the argument that follows quickly reveals what the proposition in fact offers.Google Scholar - 14.See, for example, Truesdell, 1968, pp. 88, 91, 93; R.S. Westfall 1973.Google Scholar
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- 23.I am deeply grateful to Dr Bozidar A. Anicin of the Engineering Faculty, University of Belgrade, for leading me to Rosenberger’s book and its report on pp. 183-184. He had not himself seen the volume; his information on what Rosenberger has to say on the
*Principia*treatment of inverse-square orbits came from a sixty-four-page pamphlet published 1933 in Belgrade by Dr Branislav Petronijevic:*The Laws of Central Motion According to Newton and Others*(in Serbocroatian; title translated by Dr Anicin).Google Scholar