10. MOTION is a continual relinquishing of one place, and acquiring of another; and that place which is relinquished is commonly called the terminus a quo, as that which is acquired is called the terminus ad quem; I say a continual relinquishing, because no body, how little soever, can totally and at once go out of its former place into another, so, but that some part of it will be in a part of a place which is common to both, namely, to the relinquished and the acquired places. | A G B I E
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C H D K F| For example, let any body be in the place A C B D; the same body cannot come into the place B D E F, but it must first be in G H I K, whose part G H B D is common to both the places A C B D, and G H I K, and whose part B D I K, is common to both the places G H I K, and B D E F. Now it cannot be conceived that any thing can be moved without time; for time is, by the definition of it, a phantasm, that is, a conception of motion; and, therefore, to conceive that any thing may be moved without time, were to conceive motion without motion, which is impossible.
What it is to be at rest, to have been moved, and to be moved. No motion to be conceived without the conception of past and future.
11. That is said to be at rest, which, during any time, is in one place; and that to be moved, or to have been moved, which, whether it be now at rest or moved, was formerly in another place than that which it is now in. From which definitions it may be inferred, first, that whatsoever is moved, has been moved; for if it be still in the same place in which it was formerly, it is at rest, that is, it is not moved, by the definition of rest; but if it be in another place, it has been moved, by the definition of moved. Secondly, that what is moved, will yet be moved; for that which is moved, leaveth the place where it is, and therefore will be in another place, and consequently will be moved still. Thirdly, that whatsoever is moved, is not in one place during any time, how little soever that time be; for by the definition of rest, that which is in one place during any time, is at rest.
There is a certain sophism against motion, which seems to spring from the not understanding of this last proposition. For they say, that, if any body be moved, it is moved either in the place where it is, or in the place where it is not; both which are false; and therefore nothing is moved. But the falsity lies in the major proposition; for that which is moved, is neither moved in the place where it is, nor in the place where is not; but from the place where it is, to the place where it is not. Indeed it cannot be denied but that whatsoever is moved, is moved somewhere, that is, within some space; but then the place of that body is not that whole space, but a part of it, as is said above in the seventh article. From what is above demonstrated, namely, that whatsoever is moved, has also been moved, and will be moved, this also may be collected, that there can be no conception of motion, without conceiving past and future time.
A point, a line, superficies, and solid, what they are.
12. Though there be no body which has not some magnitude, yet if, when any body is moved, the magnitude of it be not at all considered, the way it makes is called a line, or one single dimension; and the space, through which it passeth, is called length; and the body itself, a point; in which sense the earth is called a point, and the way of its yearly revolution, the ecliptic line. But if a body, which is moved, be considered as long, and be supposed to be so moved, as that all the several parts of it be understood to make several lines, then the way of every part of that body is called breadth, and the space which is made is called superficies, consisting of two dimensions, one whereof to every several part of the other is applied whole. Again, if a body be considered as having superficies, and be understood to be so moved, that all the several parts of it describe several lines, then the way of every part of that body is called thickness or depth, and the space which is made is called solid, consisting of three dimensions, any two whereof are applied whole to every several part of the third.
But if a body be considered as solid, then it is not possible that all the several parts of it should describe several lines; for what way soever it be moved, the way of the following part will fall into the way of the part before it, so that the same solid will still be made which the foremost superficies would have made by itself. And therefore there can be no other dimension in any body, as it is a body, than the three which I have now described; though, as it shall be shewed hereafter, velocity, which is motion according to length, may, by being applied to all the parts of a solid, make a magnitude of motion, consisting of four dimensions; as the goodness of gold, computed in all the parts of it, makes the price and value thereof.
Equal, great, greater, and less, in bodies and magnitudes, what they are.
13. Bodies, how many soever they be, that can fill every one the place of every one, are said to be equal every one to every other. Now, one body may fill the same place which another body filleth, though it be not of the same figure with that other body, if so be that it may be understood to be reducible to the same figure, either by flexion or transposition of the parts. And one body is greater than another body, when a part of that is equal to all this; and less, when all that is equal to a part of this. Also, magnitudes are equal, or greater, or lesser, than one another, for the same consideration, namely, when the bodies, of which they are the magnitudes, are either equal, or greater, or less, &c.
One and the same body has always one and the same magnitude.