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Newton explained the inverse square law in Principia. On looking through an English translation, though, I'm having difficulty pulling out a single quote that is Newton's clearest statement of the idea that point particles attracts all point particles with a force that is inversely proportional to the square of the distance and proportional to each of the masses.

I see proofs of the shell theorem that state that the force between a point and a sphere obeys this law, and I see proofs that if we start by assuming an inverse square law, we get conic section orbits. But the book is very large and difficult to read; I simply can't find the best passage stating the universal gravitational law in Newton's own words. What is the best passage to use?

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Chrandrasekhar's Newton's Principia for the Common Reader p. 370:

104. Proposition VII: the universal law of gravitation

We have now reached the climactic point of Philosphie naturalis Principia Mathematica. After establishing the preceding propositions, particularly, Propositions IV and VI, Newton, at long last, is ready to enunciate his law of gravitation. Let him speak.

Proposition VII. Theorem VII
That there is a power of gravity pertaining to all bodies, proportional to the several quantities of matter which they contain.

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    $\begingroup$ That doesn't seem to mention the inverse square law. $\endgroup$ Commented Feb 18, 2021 at 13:35
  • $\begingroup$ @MarkEichenlaub It is mentioned in Corollary 2 to Proposition V, but only for planets rather than all bodies:"The force of gravity which tends to any one planet is reciprocally as the square of the distance of places from that planet's centre". Proposition VII then extends it to all bodies and adds the proportionality to their masses. $\endgroup$
    – Conifold
    Commented Jun 21, 2022 at 6:27

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