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Proofs and contexts: the debate between Bernoulli and Newton on the mathematics of central force motion. (English) Zbl 1335.01016

Rowe, David E. (ed.) et al., A delicate balance: global perspectives on innovation and tradition in the history of mathematics. A Festschrift in honor of Joseph W. Dauben. Cham: Birkhäuser/Springer (ISBN 978-3-319-12029-4/hbk; 978-3-319-36594-7/pbk; 978-3-319-12030-0/ebook). Trends in the History of Science, 67-102 (2015).
The author examines the debate between Johann Bernoulli and Isaac Newton on the inverse problem of central forces by means of studying their respective solutions. The work of the two men gave rise to polemical exchanges between the two groups surrounding Newton and Bernoulli, respectively. The inverse problem concerns a body moving in space without resistance which is acted upon by a central force. If the initial position and velocity are known, the trajectory has to be computed. The author starts with a controversy in modern times when Weinstock in 1982 [Zbl 0737.01006] published his opinion that Newton had not solved this problem at all and had aroused many opposing replies. As in the case of Bernoulli and Newton it was not quite clear in the 1980s who was right or wrong. Many historians claim that it was Bernoulli who solved the problem properly, many others take Newton’s side. The author examines the methodology of Newton and Bernoulli in detail and concludes that both scientists could not arrive at a common solution because they were already separated by one generation. Newton was a scientist of the 17th century while Bernoulli’s methods and ideas were already rooted in the 18th century. The paper gives deep insight into a famous controversy which even today is worth thinking about.
For the entire collection see [Zbl 1320.01005].

MSC:

01A50 History of mathematics in the 18th century
01A45 History of mathematics in the 17th century

Biographic References:

Bernoulli, Johann; Newton, Isaac

Citations:

Zbl 0737.01006
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Full Text: DOI

References:

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