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Could anyone, please, point the exact place in "Principia Mathematica" where Newton explicitly stated the expression for the gravitational force between two particles? I mean the fact that it is proportional to the product of their masses and the inverse square of the distance between them. The closest thing I've found is Propositional 75, Theorem 35, Corollary 1 [Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999]:

"The attractions of spheres toward other homogeneous spheres are as the attracting spheres [i.e., as the masses of the attracting spheres] divided by the squares of the distances of their own centers from the centers of those that they attract."

But this statement is about spheres, not particles. And also only about the proportionality to the mass of the attracting sphere, not the attracted one.

Also this answer What was Newton's statement of the universal law of gravitation? points some propositionals, but they eather do not account all proportionalities, or not general enough (stated only for planets etc.)

So, what (and where) is the most general form of the law present in this book?

Андрей Кокорев
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    People did not state "the most general form" in the style of Bourbaki in Newton's times. General principles were generated inductively, and the readers were expected to transfer them from examples given to other examples. Theorem VII with its Corollary 2 are the closest you'll get in Principia:"That there is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain... The force of gravity towards the several equal particles of any body is reciprocally as the square of the distance of places from the particles". – Conifold Oct 16 '22 at 06:27

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