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Did Newton believe in infinitely small particle theory of matter? Because when he talks about axis of rotation, which is locus of the centers of the circles of the rotating body and particle on the axis does not rotate for that they must have no size. For that, I think he had to considered matter made of infinitely small particles with no size at all.

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  • $\begingroup$ Do you have any reference source for the idea that any historical person asked such a question or made any inference about particles on the rotation-axis of a rotating body? Is there any reason to connect such a question or inference with Newton? $\endgroup$ – terry-s Dec 19 '18 at 14:10
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    $\begingroup$ Geometers talked about lines that have no breadth since the Pythagoreans. That did not mean that they believed in infinitely small particles either. People always distinguished between physical properties and mathematical idealizations. $\endgroup$ – Conifold Dec 19 '18 at 22:01
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About Newton's theory of matter, see Newton's Atomism :

The key sources of Newton's stance on atomism in his published work are Querie 31 of his Opticks (1704), and a short piece on acids. Atomistic views also make their appearance in the Principia, where Newton claimed “the least parts of bodies to be—all extended, and hard and impenetrable, and moveable, and endowed with their proper inertia”

See also :

and


We have to take into account that Newton's Principia is mainly a book of mathematical physics (the first one).

See Def.VIII :

For the quantity of motion arises from the celerity multiplied by the quantity of matter; and the motive force arises from the accelerative force multiplied by the same quantity of matter. For the sum of the actions of the accelerative force, upon the several particles [emphasis added] of the body, is the motive force of the whole.

Thus, bodies are made of "particles" (or "corpuscles") and nothing more than this is postulated in the treatise to manage the laws of motion and mutual attraction of bodies.

But see Scholium to Lemma XI :

Those things which have been demonstrated of curved lines, and the surfaces which they comprehend, may be easily applied to the curved surfaces and contents of solids. These Lemmas are premised to avoid the tediousness of deducing involved demonstrations ad absurdum, according to the method of the ancient geometers. For demonstrations are shorter by the method of indivisibles; but because the hypothesis of indivisibles seems somewhat harsh, and therefore that method is reckoned less geometrical, I chose rather to reduce the demonstrations of the following Propositions to the first and last sums and ratios of nascent and evanescent quantities, that is, to the limits of those sums and ratios, and so to premise, as short as I could, the demonstrations of those limits. For hereby the same thing is performed as by the method of indivisibles; and now those principles being demonstrated, we may use them with greater safety.

Therefore if hereafter I should happen to consider quantities as made up of particles, or should use little curved lines for right ones, I would not be understood to mean indivisibles [emphasis added], but evanescent divisible quantities; not the sums and ratios of determinate parts, but always the limits of sums and ratios; and that the force of such demonstrations always depends on the method laid down in the foregoing Lemmas.

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  • $\begingroup$ Are you saying that any of these sources have anything about the size of the supposed particles (whether infinitely small or otherwise) or about any considerations that relate them to rotating bodies? $\endgroup$ – terry-s Dec 19 '18 at 15:54

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