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Johann Bernoulli, John Keill and the inverse problem of central forces. (English) Zbl 0836.01003

This paper addresses the controversy caused by Johann Bernoulli’s affirmation in 1710 that Sir Isaac Newton had not rigorously proved that conic sections, having a focus at the force centre, were necessarily orbits for a body accelerated by an inverse square law force. In particular, the author concentrates on two papers by John Keill in which the results on central forces produced by British Newtonian mathematicians were summarised and their methods defended. The aim of the paper is to redress the balance in which the prevailing view is that British mathematics, in particular in dynamics was sidelined in view of the criticism of Bernoulli and his continental contemporaries.

MSC:

01A45 History of mathematics in the 17th century
70-03 History of mechanics of particles and systems

Biographic References:

Bernoulli, Johann; Keill, John
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[4] Sir Isaac NewtonMathematical Principles of Natural Philosophy, and,System of the WorldBerkeley1962 48 49 translated into English by Andrew Motte in 1729, revised by Florian Cajori 5th imp. What Newton means here is that one has to makeQapproach toPas a limit. All the statements are valid in this limiting situation, when the arePQis ’nascent’ or ’vanishing’. Newton’s theory of ’limits of prime and ultimate ratios’ was developed in Section 1, Book 1.
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