All bodies together, and each by itself, give off to the surrounding air an infinite number of images which are all-pervading and each complete, each conveying the nature, colour and form of the body which produces it.

We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple and always consonant to itself.

This principle of nature being very remote from the conceptions of Philosophers, I forbore to describe it in that book, least I should be accounted an extravagant freak and so prejudice my Readers against all those things which were the main designe of the book.

The same law takes place in a system, consisting of many bodies, as in one single body, with regard to their persevering in their state of motion or of rest. For the progressive motion, whether of one single body or of a whole system of bodies, is always to be estimated from the motion of the center of gravity.

Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.

Those qualities of bodies that cannot be intended and remitted [i.e., qualities that cannot be increased and diminished] and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.