Our design (writes Newton in his preface) not respecting arts but philosophy, and our subject not manual but natural powers, we consider those things which relate to gravity, levity, elastic force, the resistance of fluids and the like forces, whether attractive or impulsive; and, therefore, we offer this work as the mathematical principles of philosophy, for all the difficulty of philosophy seems to consist in this--from the phenomena of motions to investigate the forces of nature, and from these forces to demonstrate the other phenomena, and to this end the general propositions in the first and second book 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.