ook are
directed. In the third book, we give an example of this in the
explication of the system of the world; for by the propositions
mathematically demonstrated in the former books, we in the third derive
from the celestial phenomena the forces of gravity with which bodies
tend to the sun and the several planets. Then from these forces, by
other propositions which are also mathematical, we deduce the motions of
the planets, the comets, the moon, and the sea.

Upon this subject I had (he says) composed the third book in a popular
method, that it might be read by many, but afterward, considering that
such as had not sufficiently entered into the principles could not
easily discern the strength of the consequences, nor lay aside the
prejudices to which they had been many years accustomed, therefore, to
prevent the disputes which might be raised upon such accounts, I chose
to reduce the substance of this book into the form of Propositions (in
the mathematical way). So that this third book is composed both "in
popular method" and in the form of mathematical propositions.

_Books I and II_

The principle of universal gravitation, namely, "That every particle of
matter is attracted by or gravitates to every other particle of matter
with a force inversely proportional to the squares of their distances,"
is the discovery which characterises the "Principia." This principle the
author deduced from the motion of the moon and the three laws of Kepler;
and these laws in turn Newton, by his greater law, demonstrated to be
true.

From the first law of Kepler, namely, the proportionality of the areas
to the times of their description, Newton inferred that the force which
retained the planet in its orbit was always directed to the sun. From
the second, namely, that every planet moves in an ellipse with the sun
as one of foci, he drew the more general inference that the force by
which the planet moves round that focus varies inversely as the square
of its distance therefrom. He demonstrated that a planet acted upon by
such a force could not move in any other curve than a conic section; and
he showed when the moving body would describe a circular, an elliptical,
a parabolic, or hyperbolic orbit. He demonstrated, too, that this force
or attracting, gravitating power resided in even the least particle; but
that in spherical masses it operates as if confined to their centres, so
that one sphere or body will act upon another sphere or