Various Works

  of continuity except rotatory motion: consequently neither

  alteration nor increase admits of continuity. We need now say no

  more in support of the position that there is no process of change

  that admits of infinity or continuity except rotatory locomotion.

  9

  It can now be shown plainly that rotation is the primary locomotion.

  Every locomotion, as we said before, is either rotatory or rectilinear

  or a compound of the two: and the two former must be prior to the

  last, since they are the elements of which the latter consists.

  Moreover rotatory locomotion is prior to rectilinear locomotion,

  because it is more simple and complete, which may be shown as follows.

  The straight line traversed in rectilinear motion cannot be

  infinite: for there is no such thing as an infinite straight line; and

  even if there were, it would not be traversed by anything in motion:

  for the impossible does not happen and it is impossible to traverse an

  infinite distance. On the other hand rectilinear motion on a finite

  straight line is if it turns back a composite motion, in fact two

  motions, while if it does not turn back it is incomplete and

  perishable: and in the order of nature, of definition, and of time

  alike the complete is prior to the incomplete and the imperishable

  to the perishable. Again, a motion that admits of being eternal is

  prior to one that does not. Now rotatory motion can be eternal: but no

  other motion, whether locomotion or motion of any other kind, can be

  so, since in all of them rest must occur and with the occurrence of

  rest the motion has perished. Moreover the result at which we have

  arrived, that rotatory motion is single and continuous, and

  rectilinear motion is not, is a reasonable one. In rectilinear

  motion we have a definite starting-point, finishing-point,

  middle-point, which all have their place in it in such a way that

  there is a point from which that which is in motion can be said to

  start and a point at which it can be said to finish its course (for

  when anything is at the limits of its course, whether at the

  starting-point or at the finishing-point, it must be in a state of

  rest). On the other hand in circular motion there are no such definite

  points: for why should any one point on the line be a limit rather

  than any other? Any one point as much as any other is alike

  starting-point, middle-point, and finishing-point, so that we can

  say of certain things both that they are always and that they never

  are at a starting-point and at a finishing-point (so that a

  revolving sphere, while it is in motion, is also in a sense at rest,

  for it continues to occupy the same place). The reason of this is that

  in this case all these characteristics belong to the centre: that is

  to say, the centre is alike starting-point, middle-point, and

  finishing-point of the space traversed; consequently since this

  point is not a point on the circular line, there is no point at

  which that which is in process of locomotion can be in a state of rest

  as having traversed its course, because in its locomotion it is

  proceeding always about a central point and not to an extreme point:

  therefore it remains still, and the whole is in a sense always at rest

  as well as continuously in motion. Our next point gives a

  convertible result: on the one hand, because rotation is the measure

  of motions it must be the primary motion (for all things are

  measured by what is primary): on the other hand, because rotation is

  the primary motion it is the measure of all other motions. Again,

  rotatory motion is also the only motion that admits of being

  regular. In rectilinear locomotion the motion of things in leaving the

  starting-point is not uniform with their motion in approaching the

  finishing-point, since the velocity of a thing always increases

  proportionately as it removes itself farther from its position of

  rest: on the other hand rotatory motion is the only motion whose

  course is naturally such that it has no starting-point or

  finishing-point in itself but is determined from elsewhere.

  As to locomotion being the primary motion, this is a truth that is

  attested by all who have ever made mention of motion in their

  theories: they all assign their first principles of motion to things

  that impart motion of this kind. Thus 'separation' and 'combination'

  are motions in respect of place, and the motion imparted by 'Love' and

  'Strife' takes these forms, the latter 'separating' and the former

  'combining'. Anaxagoras, too, says that 'Mind', his first movent,

  'separates'. Similarly those who assert no cause of this kind but

  say that 'void' accounts for motion-they also hold that the motion

  of natural substance is motion in respect of place: for their motion

  that is accounted for by 'void' is locomotion, and its sphere of

  operation may be said to be place. Moreover they are of opinion that

  the primary substances are not subject to any of the other motions,

  though the things that are compounds of these substances are so

  subject: the processes of increase and decrease and alteration, they

  say, are effects of the 'combination' and 'separation' of atoms. It is

  the same, too, with those who make out that the becoming or

  perishing of a thing is accounted for by 'density' or 'rarity': for it

  is by 'combination' and 'separation' that the place of these things in

  their systems is determined. Moreover to these we may add those who

  make Soul the cause of motion: for they say that things that undergo

  motion have as their first principle 'that which moves itself': and

  when animals and all living things move themselves, the motion is

  motion in respect of place. Finally it is to be noted that we say that

  a thing 'is in motion' in the strict sense of the term only when its

  motion is motion in respect of place: if a thing is in process of

  increase or decrease or is undergoing some alteration while

  remaining at rest in the same place, we say that it is in motion in

  some particular respect: we do not say that it 'is in motion'

  without qualification.

  Our present position, then, is this: We have argued that there

  always was motion and always will be motion throughout all time, and

  we have explained what is the first principle of this eternal

  motion: we have explained further which is the primary motion and

  which is the only motion that can be eternal: and we have pronounced

  the first movent to be unmoved.

  10

  We have now to assert that the first movent must be without parts

  and without magnitude, beginning with the establishment of the

  premisses on which this conclusion depends.

  One of these premisses is that nothing finite can cause motion

  during an infinite time. We have three things, the movent, the

  moved, and thirdly that in which the motion takes place, namely the

  time: and these are either all infinite or all finite or partly-that

  is to say two of them or one of them-finite and partly infinite. Let A

  be the movement, B the moved, and G the infinite time. Now let us

  s
uppose that D moves E, a part of B. Then the time occupied by this

  motion cannot be equal to G: for the greater the amount moved, the

  longer the time occupied. It follows that the time Z is not

  infinite. Now we see that by continuing to add to D, I shall use up

  A and by continuing to add to E, I shall use up B: but I shall not use

  up the time by continually subtracting a corresponding amount from it,

  because it is infinite. Consequently the duration of the part of G

  which is occupied by all A in moving the whole of B, will be finite.

  Therefore a finite thing cannot impart to anything an infinite motion.

  It is clear, then, that it is impossible for the finite to cause

  motion during an infinite time.

  It has now to be shown that in no case is it possible for an

  infinite force to reside in a finite magnitude. This can be shown as

  follows: we take it for granted that the greater force is always

  that which in less time than another does an equal amount of work when

  engaged in any activity-in heating, for example, or sweetening or

  throwing; in fact, in causing any kind of motion. Then that on which

  the forces act must be affected to some extent by our supposed

  finite magnitude possessing an infinite force as well as by anything

  else, in fact to a greater extent than by anything else, since the

  infinite force is greater than any other. But then there cannot be any

  time in which its action could take place. Suppose that A is the

  time occupied by the infinite power in the performance of an act of

  heating or pushing, and that AB is the time occupied by a finite power

  in the performance of the same act: then by adding to the latter

  another finite power and continually increasing the magnitude of the

  power so added I shall at some time or other reach a point at which

  the finite power has completed the motive act in the time A: for by

  continual addition to a finite magnitude I must arrive at a

  magnitude that exceeds any assigned limit, and in the same way by

  continual subtraction I must arrive at one that falls short of any

  assigned limit. So we get the result that the finite force will occupy

  the same amount of time in performing the motive act as the infinite

  force. But this is impossible. Therefore nothing finite can possess an

  infinite force. So it is also impossible for a finite force to

  reside in an infinite magnitude. It is true that a greater force can

  reside in a lesser magnitude: but the superiority of any such

  greater force can be still greater if the magnitude in which it

  resides is greater. Now let AB be an infinite magnitude. Then BG

  possesses a certain force that occupies a certain time, let us say the

  time Z in moving D. Now if I take a magnitude twice as great at BG,

  the time occupied by this magnitude in moving D will be half of EZ

  (assuming this to be the proportion): so we may call this time ZH.

  That being so, by continually taking a greater magnitude in this way I

  shall never arrive at the full AB, whereas I shall always be getting a

  lesser fraction of the time given. Therefore the force must be

  infinite, since it exceeds any finite force. Moreover the time

  occupied by the action of any finite force must also be finite: for if

  a given force moves something in a certain time, a greater force

  will do so in a lesser time, but still a definite time, in inverse

  proportion. But a force must always be infinite-just as a number or

  a magnitude is-if it exceeds all definite limits. This point may

  also be proved in another way-by taking a finite magnitude in which

  there resides a force the same in kind as that which resides in the

  infinite magnitude, so that this force will be a measure of the finite

  force residing in the infinite magnitude.

  It is plain, then, from the foregoing arguments that it is

  impossible for an infinite force to reside in a finite magnitude or

  for a finite force to reside in an infinite magnitude. But before

  proceeding to our conclusion it will be well to discuss a difficulty

  that arises in connexion with locomotion. If everything that is in

  motion with the exception of things that move themselves is moved by

  something else, how is it that some things, e.g. things thrown,

  continue to be in motion when their movent is no longer in contact

  with them? If we say that the movent in such cases moves something

  else at the same time, that the thrower e.g. also moves the air, and

  that this in being moved is also a movent, then it would be no more

  possible for this second thing than for the original thing to be in

  motion when the original movent is not in contact with it or moving

  it: all the things moved would have to be in motion simultaneously and

  also to have ceased simultaneously to be in motion when the original

  movent ceases to move them, even if, like the magnet, it makes that

  which it has moved capable of being a movent. Therefore, while we must

  accept this explanation to the extent of saying that the original

  movent gives the power of being a movent either to air or to water

  or to something else of the kind, naturally adapted for imparting

  and undergoing motion, we must say further that this thing does not

  cease simultaneously to impart motion and to undergo motion: it ceases

  to be in motion at the moment when its movent ceases to move it, but

  it still remains a movent, and so it causes something else consecutive

  with it to be in motion, and of this again the same may be said. The

  motion begins to cease when the motive force produced in one member of

  the consecutive series is at each stage less than that possessed by

  the preceding member, and it finally ceases when one member no

  longer causes the next member to be a movent but only causes it to

  be in motion. The motion of these last two-of the one as movent and of

  the other as moved-must cease simultaneously, and with this the

  whole motion ceases. Now the things in which this motion is produced

  are things that admit of being sometimes in motion and sometimes at

  rest, and the motion is not continuous but only appears so: for it

  is motion of things that are either successive or in contact, there

  being not one movent but a number of movents consecutive with one

  another: and so motion of this kind takes place in air and water. Some

  say that it is 'mutual replacement': but we must recognize that the

  difficulty raised cannot be solved otherwise than in the way we have

  described. So far as they are affected by 'mutual replacement', all

  the members of the series are moved and impart motion

  simultaneously, so that their motions also cease simultaneously: but

  our present problem concerns the appearance of continuous motion in

  a single thing, and therefore, since it cannot be moved throughout its

  motion by the same movent, the question is, what moves it?

  Resuming our main argument, we proceed from the positions that there

  must be continuous motion in the world of things, that this is a

  single motion, that a single motion must be a motion of a magnitude

  (for that which is without magnitude cannot be in motion), and that

&n
bsp; the magnitude must be a single magnitude moved by a single movent (for

  otherwise there will not be continuous motion but a consecutive series

  of separate motions), and that if the movement is a single thing, it

  is either itself in motion or itself unmoved: if, then, it is in

  motion, it will have to be subject to the same conditions as that

  which it moves, that is to say it will itself be in process of

  change and in being so will also have to be moved by something: so

  we have a series that must come to an end, and a point will be reached

  at which motion is imparted by something that is unmoved. Thus we have

  a movent that has no need to change along with that which it moves but

  will be able to cause motion always (for the causing of motion under

  these conditions involves no effort): and this motion alone is

  regular, or at least it is so in a higher degree than any other, since

  the movent is never subject to any change. So, too, in order that

  the motion may continue to be of the same character, the moved must

  not be subject to change in respect of its relation to the movent.

  Moreover the movent must occupy either the centre or the

  circumference, since these are the first principles from which a

  sphere is derived. But the things nearest the movent are those whose

  motion is quickest, and in this case it is the motion of the

  circumference that is the quickest: therefore the movent occupies

  the circumference.

  There is a further difficulty in supposing it to be possible for

  anything that is in motion to cause motion continuously and not merely

  in the way in which it is caused by something repeatedly pushing (in

  which case the continuity amounts to no more than successiveness).

  Such a movent must either itself continue to push or pull or perform

  both these actions, or else the action must be taken up by something

  else and be passed on from one movent to another (the process that

  we described before as occurring in the case of things thrown, since

  the air or the water, being divisible, is a movent only in virtue of

  the fact that different parts of the air are moved one after another):

  and in either case the motion cannot be a single motion, but only a