CHAPTER VII.

OF PLACE AND TIME.

1. Things that have no existence, may nevertheless be understood and computed.—2. What is Space.—3. Time.—4. Part.—5. Division.—6. One.—7. Number.—8. Composition.—9. The whole.—10. Spaces and times contiguous, and continual.—11. Beginning, end, way, finite, infinite.—12. What is infinite in power. Nothing infinite can be truly said to be either whole, or one; nor infinite spaces or times, many.—13. Division proceeds not to the least.

1. In the teaching of natural philosophy, I cannot begin better (as I have already shewn) than from privation; that is, from feigning the world to be annihilated. But, if such annihilation of all things be supposed, it may perhaps be asked, what would remain for any man (whom only I except from this universal annihilation of things) to consider as the subject of philosophy, or at all to reason upon; or what to give names unto for ratiocination's sake.

I say, therefore, there would remain to that man ideas of the world, and of all such bodies as he had, before their annihilation, seen with his eyes, or perceived by any other sense; that is to say, the memory and imagination of magnitudes, motions, sounds, colours, &c. as also of their order and parts. All which things, though they be nothing but ideas and phantasms, happening internally to him that imagineth; yet they will appear as if they were external, and not at all depending upon any power of the mind. And these are the things to which he would give names, and subtract them from, and compound them with one another. For seeing, that after the destruction of all other things, I suppose man still remaining, and namely that he thinks, imagines, and remembers, there can be nothing for him to think of but what is past; nay, if we do but observe diligently what it is we do when we consider and reason, we shall find, that though all things be still remaining in the world, yet we compute nothing but our own phantasms. For when we calculate the magnitude and motions of heaven or earth, we do not ascend into heaven that we may divide it into parts, or measure the motions thereof, but we do it sitting still in our closets or in the dark. Now things may be considered, that is, be brought into account, either as internal accidents of our mind, in which manner we consider them when the question is about some faculty of the mind; or as species of external things, not as really existing, but appearing only to exist, or to have a being without us. And in this manner we are now to consider them.

2. If therefore we remember, or have a phantasm of any thing that was in the world before the supposed annihilation of the same; and consider, not that the thing was such or such, but only that it had a being without the mind, we have presently a conception of that we call space: an imaginary space indeed, because a mere phantasm, yet that very thing which all men call so. For no man calls it space for being already filled, but because it may be filled; nor does any man think bodies carry their places away with them, but that the same space contains sometimes one, sometimes another body; which could not be if space should always accompany the body which is once in it. And this is of itself so manifest, that I should not think it needed any explaining at all, but that I find space to be falsely defined by certain philosophers, who infer from thence, one, that the world is infinite (for taking space to be the extension of bodies, and thinking extension may encrease continually, he infers that bodies may be infinitely extended); and, another, from the same definition, concludes rashly, that it is impossible even to God himself to create more worlds than one; for, if another world were to be created, he says, that seeing there is nothing without this world, and therefore (according to his definition) no space, that new world must be placed in nothing; but in nothing nothing can be placed; which he affirms only, without showing any reason for the same; whereas the contrary is the truth: for more cannot be put into a place already filled, so much is empty space fitter than that, which is full, for the receiving of new bodies. Having therefore spoken thus much for these men's sakes, and for theirs that assent to them, I return to my purpose, and define space thus: SPACE is the phantasm of a thing existing without the mind simply; that is to say, that phantasm, in which we consider no other accident, but only that it appears without us.

3. As a body leaves a phantasm of its magnitude in the mind, so also a moved body leaves a phantasm of its motion, namely, an idea of that body passing out of one space into another by continual succession. And this idea, or phantasm, is that, which (without receding much from the common opinion, or from Aristotle's definition) I call Time. For seeing all men confess a year to be time, and yet do not think a year to be the accident or affection of any body, they must needs confess it to be, not in the things without us, but only in the thought of the mind. So when they speak of the times of their predecessors, they do not think after their predecessors are gone, that their times can be any where else than in the memory of those that remember them. And as for those that say, days, years, and months are the motions of the sun and moon, seeing it is all one to say, motion past and motion destroyed, and that future motion is the same with motion which is not yet begun, they say that, which they do not mean, that there neither is, nor has been, nor shall be any time: for of whatsoever it may be said, it has been or it shall be, of the same also it might have been said heretofore, or may be said hereafter, it is. What then can days, months, and years, be, but the names of such computations made in our mind? Time therefore is a phantasm, but a phantasm of motion, for if we would know by what moments time passes away, we make use of some motion or other, as of the sun, of a clock, of the sand in an hour-glass, or we mark some line upon which we imagine something to be moved, there being no other means by which we can take notice of any time at all. And yet, when I say time is a phantasm of motion, I do not say this is sufficient to define it by; for this word time comprehends the notion of former and latter, or of succession in the motion of a body, in as much as it is first here then there. Wherefore a complete definition of time is such as this, TIME is the phantasm of before and after in motion; which agrees with this definition of Aristotle, time is the number of motion according to former and latter; for that numbering is an act of the mind; and therefore it is all one to say, time is the number of motion according to former and latter; and time is a phantasm of motion numbered. But that other definition, time is the measure of motion, is not so exact, for we measure time by motion and not motion by time.

4. One space is called part of another space, and one time part of another time, when this contains that and something besides. From whence it may be collected, that nothing can rightly be called a PART, but that which is compared with something that contains it.

5. And therefore to make parts, or to part or DIVIDE space or time, is nothing else but to consider one and another within the same; so that if any man divide space or time, the diverse conceptions he has are more, by one, than the parts he makes; for his first conception is of that which is to be divided, then of some part of it, and again of some other part of it, and so forwards as long as he goes on in dividing.

But it is to be noted, that here, by division, I do not mean the severing or pulling asunder of one space or time from another (for does any man think that one hemisphere may be separated from the other hemisphere, or the first hour from the second?) but diversity of consideration; so that division is not made by the operation of the hands but of the mind.

6. When space or time is considered among other spaces or times, it is said to be ONE, namely one of them; for except one space might be added to another, and subtracted from another space, and so of time, it would be sufficient to say space or time simply, and superfluous to say one space or one time, if it could not be conceived that there were another. The common definition of one, namely, that one is that which is undivided, is obnoxious to an absurd consequence; for it may thence be inferred, that whatsoever is divided is many things, that is, that every divided thing, is divided things, which is insignificant.

7. NUMBER is one and one, or one one and one, and so forwards; namely, one and one make the number two, and one one and one the number three; so are all other numbers made; which is all one as if we should say, number is unities.

8. To COMPOUND space of spaces, or time of times, is first to consider them one after another, and then altogether as one; as if one should reckon first the head, the feet, the arms, and the body, severally, and then for the account of them all together put man. And that which is so put for all the severals of which it consists, is called the WHOLE; and those severals, when by the division of the whole they come again to be considered singly, are parts thereof; and therefore the whole and all the parts taken together are the same thing. And as I noted above, that in division it is not necessary to pull the parts asunder; so in composition, it is to be understood, that for the making up of a whole there is no need of putting the parts together, so as to make them touch one another, but only of collecting them into one sum in the mind. For thus all men, being considered together, make up the whole of mankind, though never so much dispersed by time and place; and twelve hours, though the hours of several days, may be compounded into one number of twelve.

9. This being well understood, it is manifest, that nothing can rightly be called a whole, that is not conceived to be compounded of parts, and that it may be divided into parts; so that if we deny that a thing has parts, we deny the same to be a whole. For example, if we say the soul can have no parts, we affirm that no soul can be a whole soul. Also it is manifest, that nothing has parts till it be divided; and when a thing is divided, the parts are only so many as the division makes them. Again, that a part of a part is a part of the whole; and thus any part of the number four, as two, is a part of the number eight; for four is made of two and two; but eight is compounded of two, two, and four, and therefore two, which is a part of the part four, is also a part of the whole eight.

10. Two spaces are said to be CONTIGUOUS, when there is no other space betwixt them. But two times, betwixt which there is no other time, are called immediate, as A B, B C.|A      B     C| And any two spaces, as well as times, are said to be CONTINUAL, when they have one common part, as A C, B D, where the part B C is common; |A   B   C   D| and more spaces and times are continual, when every two which are next one another are continual.

11. That part which is between two other parts, is called a MEAN; and that which is not between two other parts, an EXTREME. And of extremes, that which is first reckoned is the BEGINNING, and that which last, the END; and all the means together taken are the WAY. Also, extreme parts and limits are the same thing. And from hence it is manifest, that beginning and end depend upon the order in which we number them; and that to terminate or limit space and time, is the same thing with imagining their beginning and end; as also that every thing is FINITE or INFINITE, according as we imagine or not imagine it limited or terminated every way; and that the limits of any number are unities, and of these, that which is the first in our numbering is the beginning, and that which we number last, is the end. When we say number is infinite, we mean only that no number is expressed; for when we speak of the numbers two, three, a thousand, &c. they are always finite. But when no more is said but this, number is infinite, it is to be understood as if it were said, this name number is an indefinite name.

12. Space or time is said to finite in power, or terminable, when there may be assigned a number of finite spaces or times, as of paces or hours, than which there can be no greater number of the same measure in that space or time; and infinite in power is that space or time, in which a greater number of the said paces or hours may be assigned, than any number that can be given. But we must note, that, although in that space or time which is infinite in power, there may be numbered more paces or hours than any number that can be assigned, yet their number will always be finite; for every number is finite. And therefore his ratiocination was not good, that undertaking to prove the world to be finite, reasoned thus; If the world be infinite, then there may be taken in it some part which is distant from us an infinite number of paces: but no such part can be taken; wherefore the world is not infinite; because that consequence of the major proposition is false; for in an infinite space, whatsoever we take or design in our mind, the distance of the same from us is a finite space; for in the very designing of the place thereof, we put an end to that space, of which we ourselves are the beginning; and whatsoever any man with his mind cuts off both ways from infinite, he determines the same, that is, he makes it finite.

Of infinite space or time, it cannot be said that it is a whole or one: not a whole, because not compounded of parts; for seeing parts, how many soever they be, are severally finite, they will also, when they are all put together, make a whole finite: nor one, because nothing can be said to be one, except there be another to compare it with; but it cannot be conceived that there are two spaces, or two times, infinite. Lastly, when we make question whether the world be finite or infinite, we have nothing in our mind answering to the name world; for whatsoever we imagine, is therefore finite, though our computation reach the fixed stars, or the ninth or tenth, nay, the thousandth sphere. The meaning of the question is this only, whether God has actually made so great an addition of body to body, as we are able to make of space to space.

13. And, therefore, that which is commonly said, that space and time may be divided infinitely, is not to be so understood, as if there might be any infinite or eternal division; but rather to be taken in this sense, whatsoever is divided, is divided into such parts as may again be divided; or thus, the least divisible thing is not to be given; or, as geometricians have it, no quantity is so small, but a less may be taken; which may easily be demonstrated in this manner. Let any space or time, that which was thought to be the least divisible, be divided into two equal parts, A and B. I say either of them, as A, may be divided again. For suppose the part A to be contiguous to the part B of one side, and of the other side to some other space equal to B. This whole space, therefore, being greater than the space given, is divisible. Wherefore, if it be divided into two equal parts, the part in the middle, which is A, will be also divided into two equal parts; and therefore A was divisible.

CHAPTER VIII.

OF BODY AND ACCIDENT.

1. Body defined.—2. Accident defined.—3. How an accident may be understood to be in its subject.—4. Magnitude, what it is.—5. Place, what it is, and that it is immovable.—6. What is full and empty.—7. Here, there, somewhere, what they signify.—8. Many bodies cannot be in one place, nor one body in many places.—9. Contiguous and continual, what they are.—10. The definition of motion. No motion intelligible but with time.—11. 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.—12. A point, a line, superficies and solid, what they are.—13. Equal, greater, and less in bodies and magnitudes, what they are.—14. One and the same body has always one and the same magnitude.—15. Velocity, what it is.—16. Equal, greater, and less in times, what they are.—17. Equal, greater, and less, in velocity, what.—18. Equal, greater, and less, in motion, what.—19. That which is at rest, will always be at rest, except it be moved by some external thing; and that which is moved, will always be moved, unless it be hindered by some external thing.—20. Accidents are generated and destroyed, but bodies not so.—21. An accident cannot depart from its subject.—22. Nor be moved.—23. Essence, form, and matter, what they are.—24. First matter, what.—25. That the whole is greater than any part thereof, why demonstrated.

1. Having understood what imaginary space is, in which we supposed nothing remaining without us, but all those things to be destroyed, that, by existing heretofore, left images of themselves in our minds; let us now suppose some one of those things to be placed again in the world, or created anew. It is necessary, therefore, that this new-created or replaced thing do not only fill some part of the space above mentioned, or be coincident and coextended with it, but also that it have no dependance upon our thought. And this is that which, for the extension of it, we commonly call body; and because it depends not upon our thought, we say is a thing subsisting of itself; as also existing, because without us; and, lastly, it is called the subject, because it is so placed in and subjected to imaginary space, that it may be understood by reason, as well as perceived by sense. The definition, therefore, of body may be this, a body is that, which having no dependance upon our thought, is coincident or coextended with some part of space.

2. But what an accident is cannot so easily be explained by any definition, as by examples. Let us imagine, therefore, that a body fills any space, or is coextended with it; that coextension is not the coextended body: and, in like manner, let us imagine that the same body is removed out of its place; that removing is not the removed body: or let us think the same not removed; that not removing or rest is not the resting body. What, then, are these things? They are accidents of that body. But the thing in question is, what is an accident? which is an enquiry after that which we know already, and not that which we should enquire after. For who does not always and in the same manner understand him that says any thing is extended, or moved, or not moved? But most men will have it be said that an accident is something, namely, some part of a natural thing, when, indeed, it is no part of the same. To satisfy these men, as well as may be, they answer best that define an accident to be the manner by which any body is conceived; which is all one as if they should say, an accident is that faculty of any body, by which it works in us a conception of itself. Which definition, though it be not an answer to the question propounded, yet it is an answer to that question which should have been propounded, namely, whence does it happen that one part of any body appears here, another there? For this is well answered thus: it happens from the extension of that body. Or, how comes it to pass that the whole body, by succession, is seen now here, now there? and the answer will be, by reason of its motion. Or, lastly, whence is it that any body possesseth the same space for sometime? and the answer will be, because it is not moved. For if concerning the name of a body, that is, concerning a concrete name, it be asked, what is it? the answer must be made by definition; for the question is concerning the signification of the name. But if it be asked concerning an abstract name, what is it? the cause is demanded why a thing appears so or so. As if it be asked, what is hard? The answer will be, hard is that, whereof no part gives place, but when the whole gives place. But if it be demanded, what is hardness? a cause must be shewn why a part does not give place, except the whole give place. Wherefore, I define an accident to be the manner of our conception of body.

3. When an accident is said to be in a body, it is not so to be understood, as if any thing were contained in that body; as if, for example, redness were in blood, in the same manner, as blood is in a bloody cloth, that is, as a part in the whole; for so, an accident would be a body also. But, as magnitude, or rest, or motion, is in that which is great, or which resteth, or which is moved, (which, how it is to be understood, every man understands) so also, it is to be understood, that every other accident is in its subject. And this, also, is explicated by Aristotle no otherwise than negatively, namely, that an accident is in its subject, not as any part thereof, but so as that it may be away, the subject still remaining; which is right, saving that there are certain accidents which can never perish except the body perish also; for no body can be conceived to be without extension, or without figure. All other accidents, which are not common to all bodies, but peculiar to some only, as to be at rest, to be moved, colour, hardness, and the like, do perish continually, and are succeeded by others; yet so, as that the body never perisheth. And as for the opinion that some may have, that all other accidents are not in their bodies in the same manner that extension, motion, rest, or figure, are in the same; for example, that colour, heat, odour, virtue, vice, and the like, are otherwise in them, and, as they say, inherent; I desire they would suspend their judgment for the present, and expect a little, till it be found out by ratiocination, whether these very accidents are not also certain motions either of the mind of the perceiver, or of the bodies themselves which are perceived; for in the search of this, a great part of natural philosophy consists.

4. The extension of a body, is the same thing with the magnitude of it, or that which some call real space. But this magnitude does not depend upon our cogitation, as imaginary space doth; for this is an effect of our imagination, but magnitude is the cause of it; this is an accident of the mind, that of a body existing out of the mind.

5. That space, by which word I here understand imaginary space, which is coincident with the magnitude of any body, is called the place of that body; and the body itself is that which we call the thing placed. Now place, and the magnitude of the thing placed, differ. First in this, that a body keeps always the same magnitude, both when it is at rest, and when it is moved; but when it is moved, it does not keep the same place. Secondly in this, that place is a phantasm of any body of such and such quantity and figure; but magnitude is the peculiar accident of every body; for one body may at several times have several places, but has always one and the same magnitude. Thirdly in this, that place is nothing out of the mind, nor magnitude any thing within it. And lastly, place is feigned extension, but magnitude true extension; and a placed body is not extension, but a thing extended. Besides, place is immovable; for, seeing that which is moved, is understood to be carried from place to place, if place were moved, it would also be carried from place to place, so that one place must have another place, and that place another place, and so on infinitely, which is ridiculous. And as for those, that, by making place to be of the same nature with real space, would from thence maintain it to be immovable, they also make place, though they do not perceive they make it so, to be a mere phantasm. For whilst one affirms that place is therefore said to be immovable, because space in general is considered there; if he had remembered that nothing is general or universal besides names or signs, he would easily have seen that that space, which he says is considered in general, is nothing but a phantasm, in the mind or the memory, of a body of such magnitude and such figure. And whilst another says: real space is made immovable by the understanding; as when, under the superficies of running water, we imagine other and other water to come by continual succession, that superficies fixed there by the understanding, is the immovable place of the river: what else does he make it to be but a phantasm, though he do it obscurely and in perplexed words? Lastly, the nature of place does not consist in the superficies of the ambient, but in solid space; for the whole placed body is coextended with its whole place, and every part of it with every answering part of the same place; but seeing every placed body is a solid thing, it cannot be understood to be coextended with superficies. Besides, how can any whole body be moved, unless all its parts be moved together with it? Or how can the internal parts of it be moved, but by leaving their place? But the internal parts of a body cannot leave the superficies of an external part contiguous to it; and, therefore, it follows, that if place be the superficies of the ambient, then the parts of a body moved, that is, bodies moved, are not moved.

6. Space, or place, that is possessed by a body, is called full, and that which is not so possessed, is called empty.

7. Here, there, in the country, in the city, and other the like names, by which answer is made to the question where is it? are not properly names of place, nor do they of themselves bring into the mind the place that is sought; for here and there signify nothing, unless the thing be shewn at the same time with the finger or something else; but when the eye of him that seeks, is, by pointing or some other sign, directed to the thing sought, the place of it is not hereby defined by him that answers, but found out by him that asks the question. Now such shewings as are made by words only, as when we say, in the country, or in the city, are some of greater latitude than others, as when we say, in the country, in the city, in such a street, in a house, in the chamber, in bed, &c. For these do, by little and little, direct the seeker nearer to the proper place; and yet they do not determine the same, but only restrain it to a lesser space, and signify no more, than that the place of the thing is within a certain space designed by those words, as a part is in the whole. And all such names, by which answer is made to the question where? have, for their highest genus, the name somewhere. From whence it may be understood, that whatsoever is somewhere, is in some place properly so called, which place is part of that greater space that is signified by some of these names, in the country, in the city, or the like.

8. A body, and the magnitude, and the place thereof, are divided by one and the same act of the mind; for, to divide an extended body, and the extension thereof, and the idea of that extension, which is place, is the same with dividing any one of them; because they are coincident, and it cannot be done but by the mind, that is by the division of space. From whence it is manifest, that neither two bodies can be together in the same place, nor one body be in two places at the same time. Not two bodies in the same place; because when a body that fills its whole place is divided into two, the place itself is divided into two also, so that there will be two places. Not one body in two places; for the place that a body fills being divided into two, the placed body will be also divided into two; for, as I said, a place and the body that fills that place, are divided both together; and so there will be two bodies.

9. Two bodies are said to be contiguous to one another, and continual, in the same manner as spaces are; namely, those are contiguous, between which there is no space. Now, by space I understand, here as formerly, an idea or phantasm of a body. Wherefore, though between two bodies there be put no other body, and consequently no magnitude, or, as they call it, real space, yet if another body may be put between them, that is, if there intercede any imagined space which may receive another body, then those bodies are not contiguous. And this is so easy to be understood, that I should wonder at some men, who being otherwise skilful enough in philosophy, are of a different opinion, but that I find that most of those that affect metaphysical subtleties wander from truth, as if they were led out of their way by an ignis fatuus. For can any man that has his natural senses, think that two bodies must therefore necessarily touch one another, because no other body is between them? Or that there can be no vacuum, because vacuum is nothing, or as they call it, non ens? Which is as childish, as if one should reason thus; no man can fast, because to fast is to eat nothing; but nothing cannot be eaten. Continual, are any two bodies that have a common part; and more than two are continual, when every two, that are next to one another, are continual.

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.

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.

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.

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.

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.

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.

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.