The Complete Aristotle (eng.)

infinite.
    So, too, of that which has changed there is no primary part that
has changed. For suppose that of AE the primary part that has
changed is AZ (everything that changes having been shown to be
divisible): and let OI be the time in which DZ has changed. If,
then, in the whole time DZ has changed, in half the time there will
be a part that has changed, less than and therefore prior to DZ:
and again there will be another part prior to this, and yet
another, and so on to infinity. Thus of that which changes there
cannot be any primary part that has changed. It is evident, then,
from what has been said, that neither of that which changes nor of
the time in which it changes is there any primary part.
    With regard, however, to the actual subject of change-that is to
say that in respect of which a thing changes-there is a difference
to be observed. For in a process of change we may distinguish three
terms-that which changes, that in which it changes, and the actual
subject of change, e.g. the man, the time, and the fair complexion.
Of these the man and the time are divisible: but with the fair
complexion it is otherwise (though they are all divisible
accidentally, for that in which the fair complexion or any other
quality is an accident is divisible). For of actual subjects of
change it will be seen that those which are classed as essentially,
not accidentally, divisible have no primary part. Take the case of
magnitudes: let AB be a magnitude, and suppose that it has moved
from B to a primary ‘where’ G. Then if BG is taken to be
indivisible, two things without parts will have to be contiguous
(which is impossible): if on the other hand it is taken to be
divisible, there will be something prior to G to which the
magnitude has changed, and something else again prior to that, and
so on to infinity, because the process of division may be continued
without end. Thus there can be no primary ‘where’ to which a thing
has changed. And if we take the case of quantitative change, we
shall get a like result, for here too the change is in something
continuous. It is evident, then, that only in qualitative motion
can there be anything essentially indivisible.
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6
    Now everything that changes changes time, and that in two
senses: for the time in which a thing is said to change may be the
primary time, or on the other hand it may have an extended
reference, as e.g. when we say that a thing changes in a particular
year because it changes in a particular day. That being so, that
which changes must be changing in any part of the primary time in
which it changes. This is clear from our definition of ‘primary’,
in which the word is said to express just this: it may also,
however, be made evident by the following argument. Let ChRh be the
primary time in which that which is in motion is in motion: and (as
all time is divisible) let it be divided at K. Now in the time ChK
it either is in motion or is not in motion, and the same is
likewise true of the time KRh. Then if it is in motion in neither
of the two parts, it will be at rest in the whole: for it is
impossible that it should be in motion in a time in no part of
which it is in motion. If on the other hand it is in motion in only
one of the two parts of the time, ChRh cannot be the primary time
in which it is in motion: for its motion will have reference to a
time other than ChRh. It must, then, have been in motion in any
part of ChRh.
    And now that this has been proved, it is evident that everything
that is in motion must have been in motion before. For if that
which is in motion has traversed the distance KL in the primary
time ChRh, in half the time a thing that is in motion with equal
velocity and began its motion at the same time will have traversed
half the distance. But if this second thing whose velocity is equal
has traversed a certain distance in a certain time, the original
thing that is in motion must have traversed the same distance in
the same time. Hence that which is in motion must have been in
motion before.
    Again, if by taking the extreme moment of the time-for it is the
moment that defines the time, and time is that which is
intermediate between moments-we are enabled to say that motion has
taken place in the whole time ChRh or in fact in any period of it,
motion may likewise be said to have taken place in every other such
period. But half the time finds an extreme in the point of
division. Therefore motion