attraction for both of them follow the same law as to distance as is
given by the planetary motions round the sun? It has been stated that
in this way the first conception of universal gravitation arose.[1]

Quite the most important event in the whole history of physical
astronomy was the publication, in 1687, of Newton's _Principia
(Philosophiae Naturalis Principia Mathematica)_. In this great work
Newton started from the beginning of things, the laws of motion, and
carried his argument, step by step, into every branch of physical
astronomy; giving the physical meaning of Kepler's three laws, and
explaining, or indicating the explanation of, all the known heavenly
motions and their irregularities; showing that all of these were
included in his simple statement about the law of universal
gravitation; and proceeding to deduce from that law new irregularities
in the motions of the moon which had never been noticed, and to
discover the oblate figure of the earth and the cause of the
tides. These investigations occupied the best part of his life; but he
wrote the whole of his great book in fifteen months.

Having developed and enunciated the true laws of motion, he was able
to show that Kepler's second law (that equal areas are described by
the line from the planet to the sun in equal times) was only another
way of saying that the centripetal force on a planet is always
directed to the sun. Also that Kepler's first law (elliptic orbits
with the sun in one focus) was only another way of saying that the
force urging a planet to the sun varies inversely as the square of the
distance. Also (if these two be granted) it follows that Kepler's
third law is only another way of saying that the sun's force on
different planets (besides depending as above on distance) is
proportional to their masses.