are either in motion or at rest.
AXIOM II. Every body is moved sometimes more slowly, sometimes more quickly.
LEMMA I. Bodies are distinguished from one another in respect of motion and rest, quickness and slowness, and not in respect of substance.
Proof.—The first part of this proposition is, I take it, self—evident. That bodies are not distinguished in respect of substance, is plain both from I. v. and I. viii. It is brought out still more clearly from I. xv, note.
LEMMA II. All bodies agree in certain respects.
Proof.—All bodies agree in the fact, that they involve the conception of one and the same attribute (II., Def. i.). Further, in the fact that they may be moved less or more quickly, and may be absolutely in motion or at rest.
LEMMA III. A body in motion or at rest must be determined to motion or rest by another body, which other body has been determined to motion or rest by a third body, and that