The Complete Aristotle (eng.)

motions of the parts, OI will be equal to DZ: if
on the other hand there is any remainder, say KI, this will be a
motion of nothing: for it can be the motion neither of the whole
nor of the parts (as the motion of that which is one must be one)
nor of anything else: for a motion that is continuous must be the
motion of things that are continuous. And the same result follows
if the division of OI reveals a surplus on the side of the motions
of the parts. Consequently, if this is impossible, the whole motion
must be the same as and equal to DZ.
    This then is what is meant by the division of motion according
to the motions of the parts: and it must be applicable to
everything that is divisible into parts.
    Motion is also susceptible of another kind of division, that
according to time. For since all motion is in time and all time is
divisible, and in less time the motion is less, it follows that
every motion must be divisible according to time. And since
everything that is in motion is in motion in a certain sphere and
for a certain time and has a motion belonging to it, it follows
that the time, the motion, the being-in-motion, the thing that is
in motion, and the sphere of the motion must all be susceptible of
the same divisions (though spheres of motion are not all divisible
in a like manner: thus quantity is essentially, quality
accidentally divisible). For suppose that A is the time occupied by
the motion B. Then if all the time has been occupied by the whole
motion, it will take less of the motion to occupy half the time,
less again to occupy a further subdivision of the time, and so on
to infinity. Again, the time will be divisible similarly to the
motion: for if the whole motion occupies all the time half the
motion will occupy half the time, and less of the motion again will
occupy less of the time.
    In the same way the being-in-motion will also be divisible. For
let G be the whole being-in-motion. Then the being-in-motion that
corresponds to half the motion will be less than the whole
being-in-motion, that which corresponds to a quarter of the motion
will be less again, and so on to infinity. Moreover by setting out
successively the being-in-motion corresponding to each of the two
motions DG (say) and GE, we may argue that the whole
being-in-motion will correspond to the whole motion (for if it were
some other being-in-motion that corresponded to the whole motion,
there would be more than one being-in motion corresponding to the
same motion), the argument being the same as that whereby we showed
that the motion of a thing is divisible into the motions of the
parts of the thing: for if we take separately the being-in motion
corresponding to each of the two motions, we shall see that the
whole being-in motion is continuous.
    The same reasoning will show the divisibility of the length, and
in fact of everything that forms a sphere of change (though some of
these are only accidentally divisible because that which changes is
so): for the division of one term will involve the division of all.
So, too, in the matter of their being finite or infinite, they will
all alike be either the one or the other. And we now see that in
most cases the fact that all the terms are divisible or infinite is
a direct consequence of the fact that the thing that changes is
divisible or infinite: for the attributes ‘divisible’ and
‘infinite’ belong in the first instance to the thing that changes.
That divisibility does so we have already shown: that infinity does
so will be made clear in what follows?
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    div id="section51" class="section" title="5">
5
    Since everything that changes changes from something to
something, that which has changed must at the moment when it has
first changed be in that to which it has changed. For that which
changes retires from or leaves that from which it changes: and
leaving, if not identical with changing, is at any rate a
consequence of it. And if leaving is a consequence of changing,
having left is a consequence of having changed: for there is a like
relation between the two in each case.
    One kind of change, then, being change in a relation of
contradiction, where a thing has changed from not-being to being it
has left not-being. Therefore it will be in being: for everything
must either be or not be. It is evident, then, that in
contradictory change that which has changed must be in that to
which it has changed. And if this is true in this kind of change,
it will be true in all other kinds as