Orbital motion and force in Newton’s Principia\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{Principia}$$\end{document}; the equivalence of the descriptions in Propositions 1 and 6 [Book Review]

Archive for History of Exact Sciences 68 (2):179-205 (2014)
  Copy   BIBTEX

Abstract

In Book 1 of the Principia, Newton presented two different descriptions of orbital motion under the action of a central force. In Prop. 1, he described this motion as a limit of the action of a sequence of periodic force impulses, while in Prop. 6, he described it by the deviation from inertial motion due to a continuous force. From the start, however, the equivalence of these two descriptions has been the subject of controversies. Perhaps the earliest one was the famous discussion from December 1704 to 1706 between Leibniz and the French mathematician Pierre Varignon. But confusion about this subject has remained up to the present time. Recently, Pourciau has rekindled these controversies in an article in this journal, by arguing that “Newton never tested the validity of the equivalency of his two descriptions because he does not see that his assumption could be questioned. And yet the validity of this unseen and untested equivalence assumption is crucial to Newton’s most basic conclusions concerning one-body motion” (Pourciau in Arch Hist Exact Sci 58:283–321, 2004, 295). But several revisions of Props. 1 and 6 that Newton made after the publication in 1687 of the first edition of the Principia reveal that he did become concerned to provide mathematical proof for the equivalence of his seemingly different descriptions of orbital motion in these two propositions. In this article, we present the evidence that in the second and third edition of the Principia, Newton gave valid demonstrations of this equivalence that are encapsulated in a novel diagram discussed in Sect. 4.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,122

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Isaac Newton’s ‘Of Quadrature by Ordinates’.Naoki Osada - 2013 - Archive for History of Exact Sciences 67 (4):457-476.
Investigations of the coordinates in Ptolemy’s Geographike Hyphegesis Book 8.Christian Marx - 2012 - Archive for History of Exact Sciences 66 (5):531-555.
On Jacobi’s transformation theory of elliptic functions.Alberto Cogliati - 2014 - Archive for History of Exact Sciences 68 (4):529-545.
On the bounded quasi‐degrees of c.e. sets.Roland Sh Omanadze - 2013 - Mathematical Logic Quarterly 59 (3):238-246.
Shelah's strong covering property and CH in V [r ].Esfandiar Eslami & Mohammad Golshani - 2012 - Mathematical Logic Quarterly 58 (3):153-158.
Hierarchies of ineffabilities.Toshimichi Usuba - 2013 - Mathematical Logic Quarterly 59 (3):230-237.

Analytics

Added to PP
2020-02-03

Downloads
7 (#1,254,960)

6 months
1 (#1,241,711)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Newton's early computational method for dynamics.Michael Nauenberg - 1994 - Archive for History of Exact Sciences 46 (3):221-252.
Curvature in Newton's dynamics.J. Bruce Brackenridge & Michael Nauenberg - 2002 - In I. Bernard Cohen & George E. Smith (eds.), The Cambridge Companion to Newton. Cambridge University Press. pp. 85--137.
Proposition 10, Book 2, in the Principia, revisited.Michael Nauenberg - 2011 - Archive for History of Exact Sciences 65 (5).

Add more references