body with a
force directly proportional to the quantity of matter and inversely as
the square of the distance between their centres, and that their
velocities of mutual approach will be in the inverse ratio of their
quantities of matter. Thus he outlined the universal law.

_The System of the World_

It was the ancient opinion of not a few (writes Newton in Book III.) in
the earliest ages of philosophy that the fixed stars stood immovable in
the highest parts of the world; that under the fixed stars the planets
were carried about the sun; that the earth, as one of the planets,
described an annual course about the sun, while, by a diurnal motion, it
was in the meantime revolved about its own axis; and that the sun, as
the common fire which served to warm the whole, was fixed in the centre
of the universe. It was from the Egyptians that the Greeks derived their
first, as well as their soundest notions of philosophy. It is not to be
denied that Anaxagoras, Democritus and others would have it that the
earth possessed the centre of the world, but it was agreed on both sides
that the motions of the celestial bodies were performed in spaces
altogether free and void of resistance. The whim of solid orbs was[1] of
later date, introduced by Endoxus, Calippus and Aristotle, when the
ancient philosophy began to decline.

As it was the unavoidable consequence of the hypothesis of solid orbs
while it prevailed that the comets must be thrust down below the moon,
so no sooner had the late observations of astronomers restored the
comets to their ancient places in the higher heavens than these
celestial spaces were at once cleared of the encumbrance of solid orbs,
which by these observations were broken to pieces and discarded for
ever.

Whence it was that the planets came to be retained within any certain
bounds in these free spaces, and to be drawn off from the rectilinear
courses, which, left to themselves, they should have pursued, into
regular revolutions in curvilinear orbits, are questions which we do not
know how the ancients explained; and probably it was to give some sort
of satisfaction to this difficulty that solid orbs were introduced.

The later philosophers pretend to account for it either by the action of
certain vortices, as Kepler and Descartes, or by some other principle of
impulse or attraction, for it is most certain that these effects must
proceed from the action of some force or other. This we will call by t