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.
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