1. The next things in order to be treated of are MOTION and MAGNITUDE, which are the most common accidents of all bodies. This place therefore most properly belongs to the elements of geometry. But because this part of philosophy, having been improved by the best wits of all ages, has afforded greater plenty of matter than can well be thrust together within the narrow limits of this discourse, I thought fit to admonish the reader, that before he proceed further, he take into his hands the works of Euclid, Archimedes, Apollonius, and other as well ancient as modern writers. For to what end is it, to do over again that which is already done? The little therefore that I shall say concerning geometry in some of the following chapters, shall be such only as is new, and conducing to natural philosophy. I have already delivered some of the principles of this doctrine in the eighth and ninth chapters; which I shall briefly put together here, that the reader in going on may have their light nearer at hand. First, therefore, in chap. VIII. art. 10, _motion_ is defined to be _the continual privation of one place, and acquisition of another_. Secondly, it is there shown, that _whatsoever is moved is moved in time_. Thirdly, in the same chapter, art. 11, I have defined _rest to be when a body remains for some time in one place_. Fourthly, it is there shown, that _whatsoever is moved is not in any determined place_; as also that the same _has been moved, is still moved, and will yet be moved_; so that in every part of that space, in which motion is made, we may consider three times, namely, the _past_, the _present_, and _future time_. Fifthly, in art. 15 of the same chapter, I have defined _velocity_ or _swiftness to be motion considered as power, namely, that power by which a body moved may in a certain time transmit a certain length_; which also may more briefly be enunciated thus, _velocity is the quantity of motion determined by time and line_. Sixthly, in the same chapter, art. 16, I have shown that _motion is the measure of time_. Seventhly, in the same chapter, art. 17, I have defined motions to be equally swift, when in equal times equal lengths are transmitted by them. Eighthly, in art. 18 of the same chapter, _motions_ are defined to be _equal, when the swiftness of one moved body, computed in every part of its magnitude, is equal to the swiftness of another, computed also in every part of its magnitude_. From whence it is to be noted, that _motions equal to one another, and motions equally swift_, do not signify the same thing; for when two horses draw abreast, the motion of both is greater than the motion of either of them singly; but the swiftness of both together is but equal to that of either.