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Combining Proportions to get Newton's Law of Universal Gravitation

I've read a little on the history of Newton's Law of Gravitation and noticed that the formula can be separated into 3 distinct parts that lead to the end result of $F_g = G \frac{m_1 m_2}{r^2}$; the ...
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Lorentz force law in Newtonian relativity

I know that in special relativity Electric and Magnetic fields mix together in different reference frames, but my question is about classical mechanics. It seems weird to me is that the Lorentz Force ...