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The third book of Isaac Newton's rigourously established the case for heliocentrism by integrating observations and Kepler's laws. It is structured around two main hypotheses: first, that the cosmos has a static centre located at the centre of planetary motion, and second, that if the Earth itself moved, this would concord with observational data. The first hypothesis directly mentions the possibility of having the Earth as a centre, even if all the propositions claim that the correct centre is the Sun. The Minim Friars Thomas Le Seur (1703-1770) and François Jacquier (1711-1788), along with their editor Jean-Louis Calandrini, chose to collaborate and publish their influential commentary in Geneve [Newton I. 1822 . vol. 4. Glasgow, Scotand: Duncan]-probably to avoid the Catholic prohibition on promoting heliocentrism. This article examines key contributions by these commentators, highlighting their strong scientific focus and commitment to strengthening heliocentric principles in astronomy. It also discusses the educational aim evident in many extensive notes, especially on propositions that stress the transition from geo-heliocentric to heliocentric perspectives (notably propositions 4, 13, 14 and 16).This article is part of the theme issue 'Newton, , Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.
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http://dx.doi.org/10.1098/rsta.2023.0281 | DOI Listing |
Philos Trans A Math Phys Eng Sci
July 2025
Institute of Philosophical Studies, University of Italian Switzerland, Lugano, Ticino, Switzerland.
In physics, all dynamical equations that describe fundamental interactions are second-order differential equations in the time derivatives. In the literature, this property is traced back to a result obtained by Ostrogradski in the mid-nineteenth century, which is the technical basis of a theorem for higher-order theories. In this work, we review the connection of symmetry properties with the order of dynamical equations, before reconsidering Ostrogradski's result.
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July 2025
University of Udine, Udine, Italy.
Identical systems, or 'entities', are 'indistinguishable' in quantum mechanics (QM), and the 'symmetrization postulate' rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis of the historical development of QM attributes the origin of quantum statistics, in particular, 'Bose-Einstein statistics', to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose-Einstein statistics in the combination of words in large texts, as a consequence of the 'entanglement' created by the meaning carried by words when they combine in human language.
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July 2025
History Faculty, University of Oxford, Oxford, England, UK.
The named editors of the annotated edition of Newton's , François Jacquier and Thomas Le Seur, saw their painstaking enterprise as a decisive means to making the great polymath's work more accessible. As this article makes clear, the Genevan edition was above all a collaborative enterprise, resting crucially on the contributions of the two Genevan mathematicians Jean-Louis Calandrini and Gabriel Cramer, both of whose expertise complemented and, in some respects, exceeded that of the two Minim priests based in Rome, while also being attuned to contemporary scientific discussion involving the foremost scientific figures of the time, such as Euler, Clairaut, d'Alembert and the Bernoulli. Focusing in particular on the debate over Newton's theory of the Moon, the article reveals the importance of Calandrini's and Cramer's scientific networks for understanding the production and reception of the Geneva edition.
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July 2025
Department of Physics and Astronomy, Bishop's University Faculty of Arts and Science, Sherbrooke, Quebec, Canada.
Analogies occurring in the literature between spherically symmetric General Relativity and Newtonian physics are discussed, focusing on gravito-electromagne-tism (which contains Newtonian gravity as its 'electrostatics'). In spherical symmetry, the gravitoelectric potential contains the Misner-Sharp-Hernandez mass, to which the Hawking quasilocal mass reduces in this situation. It is shown that, according to observers defined rather naturally, the Hawking energy receives contributions from the electric part of the Weyl curvature but not from its magnetic part, making it 'Newtonian' in a well-defined sense.
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July 2025
Department of Industrial Engineering, University of Rome Tor Vergata, Roma, Lazio, Italy.
Newtonian mechanics is still successful today for the development of systems both in the industrial fields and in the services of human well-being. This paper presents the use of Newtonian mechanics both in terms of biomechanics and the design of motion assisting devices in the physiotherapy field for applications in the rehabilitation and exercise of elderly users. The analysis of the requirements for motion assistance of human limbs is conducted with specific reference to the characteristics of movement and action with typically Newtonian Mechanics models.
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