IsisCB Explore

Article ID: CBB001321045

Orbital Motion and Force in Newton's Principia; the Equivalence of the Descriptions in Propositions 1 and 6 (2014)

Nauenberg, Michael (Author)

Archive for History of Exact Sciences
Volume: 68
Pages: 179--205
Publication date: 2014
Language: English

Outside Links

WorldCat

Google Scholar

JSTOR

Motion (physical) Proof Orbital motion (quantum) Mathematics and its relationship to science Forces 18th century 17th century Varignon, Pierre Newton, Isaac Leibniz, Gottfried Wilhelm von

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.

...More

Citation URI

data.isiscb.org/p/isis/citation/CBB001321045

This citation is part of the Isis database.

Citations Indexes

Similar Citations

Chapter Smith, George E.; (2012)
How Newton's Principia Changed Physics (/p/isis/citation/CBB001500352/)

Article Christophe Schmit; (2015)
Les dynamiques de Jean-Jacques Dortous de Mairan (/p/isis/citation/CBB695462531/)

Article Nauenberg, Michael; (2003)
Kepler's Area Law in the Principia: Filling in some Details in Newton's Proof of Proposition 1 (/p/isis/citation/CBB000410830/)

Chapter Huggett, Nick; (2012)
What Did Newton Mean by “Absolute Motion”? (/p/isis/citation/CBB001500345/)

Chapter Garber, Daniel; (2012)
Leibniz, Newton and Force (/p/isis/citation/CBB001500339/)

Article Mathieu Gibier; (2019)
Dynamique et pneumatique : Leibniz face aux expériences paradoxales de Huygens (/p/isis/citation/CBB962675218/)

Article François Duchesneau; (2019)
Le recours aux principes architectoniques dans la Dynamica de Leibniz (/p/isis/citation/CBB978969993/)

Article Janiak, Andrew; (2010)
Substance and Action in Descartes and Newton (/p/isis/citation/CBB001221446/)

Article Adwait A. Parker; (2020)
Newton on active and passive quantities of matter (/p/isis/citation/CBB738730801/)

Article Meli, Domenico Bertoloni; (2006)
Inherent and Centrifugal Forces in Newton (/p/isis/citation/CBB000670062/)

Article Belkind, Ori; (2013)
Leibniz and Newton on Space (/p/isis/citation/CBB001320865/)

Article Dyck, Maarten Van; Verelst, Karin; (2013)
“Whatever Is Neither Everywhere Nor Anywhere Does Not Exist”: The Concepts of Space and Time in Newton and Leibniz (/p/isis/citation/CBB001320861/)

Book Khamara, Edward J.; (2006)
Space, Time, and Theology in the Leibniz-Newton Controversy (/p/isis/citation/CBB000741545/)

Chapter Marius Stan; (2017)
Newton’s Concepts of Force among the Leibnizians (/p/isis/citation/CBB491004939/)

Chapter Watkins, Eric; (2001)
Kant on Extension and Force: Critical Appropriations of Leibniz and Newton (/p/isis/citation/CBB000101472/)

Article Katherine Brading; Marius Stan; (2021)
How Physics Flew the Philosophers' Nest (/p/isis/citation/CBB008141627/)

Chapter Niccolò Guicciardini; (2015)
Proofs and Contexts: the Debate between Bernoulli and Newton on the Mathematics of Central Force Motion (/p/isis/citation/CBB805053813/)

Article Nauenberg, M.; (2010)
The Early Application of the Calculus to the Inverse Square Force Problem (/p/isis/citation/CBB001021999/)

Article Daniel Garber; (2019)
La dynamique de Leibniz est-elle compatible avec sa monadologie ? (/p/isis/citation/CBB392397811/)

Article Kochiras, Hylarie; (2013)
Causal Language and the Structure of Force in Newton's System of the World (/p/isis/citation/CBB001320795/)