14. One and the same body is always of one and the same magnitude. For seeing a body and the magnitude and place thereof cannot be comprehended in the mind otherwise than as they are coincident, if any body be understood to be at rest, that is, to remain in the same place during some time, and the magnitude thereof be in one part of that time greater, and in another part less, that body's place, which is one and the same, will be coincident sometimes with greater, sometimes with less magnitude, that is, the same place will be greater and less than itself, which is impossible. But there would be no need at all of demonstrating a thing that is in itself so manifest, if there were not some, whose opinion concerning bodies and their magnitudes is, that a body may exist separated from its magnitude, and have greater or less magnitude bestowed upon it, making use of this principle for the explication of the nature of rarum and densum.
Velocity, what it is.
15. Motion, in as much as a certain length may in a certain time be transmitted by it, is called VELOCITY or swiftness: &c. For though swift be very often understood with relation to slower or less swift, as great is in respect of less, yet nevertheless, as magnitude is by philosophers taken absolutely for extension, so also velocity or swiftness may be put absolutely for motion according to length.
Equal, greater, and less, in times, what they are.
16. Many motions are said to be made in equal times, when every one of them begins and ends together with some other motion, or if it had begun together, would also have ended together with the same. For time, which is a phantasm of motion, cannot be reckoned but by some exposed motion; as in dials by the motion of the sun or of the hand; and if two or more motions begin and end with this motion, they are said to be made in equal times; from whence also it is easy to understand what it is to be moved in greater or longer time, and in less time or not so long; namely, that that is longer moved, which beginning with another, ends later; or ending together, began sooner.
Equal, greater, and less, in velocity, what.
17. Motions are said to be equally swift, when equal lengths are transmitted in equal times; and greater swiftness is that, wherein greater length is passed in equal time, or equal length in less time. Also that swiftness by which equal lengths are passed in equal parts of time, is called uniform swiftness or motion; and of motions not uniform, such as become swifter or slower by equal increasings or decreasings in equal parts of time, are said to be accelerated or retarded uniformly.
Equal, greater, and less, in motion, what.
18. But motion is said to be greater, less, and equal, not only in regard of the length which is transmitted in a certain time, that is, in regard of swiftness only, but of swiftness applied to every smallest particle of magnitude; for when any body is moved, every part of it is also moved; and supposing the parts to be halves, the motions of those halves have their swiftness equal to one another, and severally equal to that of the whole; but the motion of the whole is equal to those two motions, either of which is of equal swiftness with it; and therefore it is one thing for two motions to be equal to one another, and another thing for them to be equally swift. And this is manifest in two horses that draw abreast, where the motion of both the horses together is of equal swiftness with the motion of either of them singly; but the motion of both is greater than the motion of one of them, namely, double. Wherefore motions are said to be simply equal to one another, when the swiftness of one, computed in every part of its magnitude, is equal to the swiftness of the other computed also in every part of its magnitude: and greater than one another, when the swiftness of one computed as above, is greater than the swiftness of the other so computed; and less, when less. Besides, the magnitude of motion computed in this manner is that which is commonly called FORCE.
That which is at rest will always be at rest, except it be moved by some external thing.