Roger Cotes edited the second edition of the Principia. In the process of its preparation he and
From a Letter
to
I had yours of Feb 18th, and
the difficulty you mention which lies in these words “Et cum Attractio omnis
mutua sit” [“since 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 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 Phaenomena, 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 Phaenomenon 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
Phaenomena you may see at the end of the Corollaries of the Laws of Motion,
pag. 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 phaenomenon in all nature.