The _Principia_ consists of three books. The first and second, which occupy three-fourths of the work, are entitled _On the Motion of Bodies_, and the third bears the title _On the System of the World_. The two first books contain the mathematical principles of philosophy, namely, the laws and conditions of motions and forces; and they are illustrated with several philosophical _scholia_ which treat of some of the most general and best-established points in philosophy, such as the density and resistance of bodies, spaces void of matter, and the motion of sound and light. The object of the third book is to deduce from these principles the constitution of the system of the world; and this book has been drawn up in as popular a style as possible, in order that it may be generally read. The great discovery which characterizes the _Principia_ is that of the principle of universal gravitation, as deduced from the motion of the moon, and from the three great facts or laws discovered by Kepler. This principle is: _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_. From the first law of Kepler, namely, the proportionality of the areas to the times of their revolution, Newton inferred that the force which kept the planet in its orbit was always directed to the sun; and from the second law of Kepler, that every planet moves in an ellipse with the sun in one of its foci, he drew the still more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance from the focus. As this law was true in the motion of satellites round their primary planets Newton deduced the equality of gravity in all the heavenly bodies toward the sun, upon the supposition that they are equally distant from its centre; and in the case of terrestrial bodies he succeeded in verifying this truth by numerous and accurate experiments. By taking a more general view of the subject Newton demonstrated that a conic section was the only curve in which a body could move when acted upon by a force varying inversely as the square of the distance; and he established the conditions depending on the velocity and the primitive position of the body, which were requisite to make it describe a circular, an elliptical, a parabolic, or a hyberbolic orbit.