NEWTON TO COTES

London, 28 March 1713

Sir

I had your [letter] of Feb 18th, and the difficulty you mention which lies in these words “And since, by the third law of motion, every attraction is mutual” is removed by considering that as in geometry the word “hypothesis” is not taken in so large a sense as to include the axioms and postulates, so in experimental philosophy it is not to be taken in so large a sense as to include the first principles or axioms which I call the laws of motion. These principles are deduced from phenomena and made general by induction: which is the highest evidence that a proposition can have in this philosophy. And the word “hypothesis” is here used by me to signify only such a proposition as is not a phenomenon nor deduced from any phenomena but assumed or supposed without any experimental proof. Now the mutual and mutually equal attraction of bodies is a branch of the third law of motion and how this branch is deduced from phenomena you may see in the end of the corollaries of the laws of motion, page 22. If a body attracts another body contiguous to it and is not mutually attracted by the other: the attracted body will drive the other before it and both will go away together with an accelerated motion in infinitum, as it were by a self-moving principle, contrary to the first law of motion, whereas there is no such phenomenon in all nature.