The Complete Aristotle (eng.)

contact are not all
naturally joined, while there is no contact clearly there is no
natural junction either. Hence, if as some say ‘point’ and ‘unit’
have an independent existence of their own, it is impossible for
the two to be identical: for points can touch while units can only
be in succession. Moreover, there can always be something between
points (for all lines are intermediate between points), whereas it
is not necessary that there should possibly be anything between
units: for there can be nothing between the numbers one and
two.
    We have now defined what is meant by ‘together’ and ‘apart’,
‘contact’, ‘between’ and ‘in succession’, ‘contiguous’ and
‘continuous’: and we have shown in what circumstances each of these
terms is applicable.
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4
    There are many senses in which motion is said to be ‘one’: for
we use the term ‘one’ in many senses.
    Motion is one generically according to the different categories
to which it may be assigned: thus any locomotion is one generically
with any other locomotion, whereas alteration is different
generically from locomotion.
    Motion is one specifically when besides being one generically it
also takes place in a species incapable of subdivision: e.g. colour
has specific differences: therefore blackening and whitening differ
specifically; but at all events every whitening will be
specifically the same with every other whitening and every
blackening with every other blackening. But white is not further
subdivided by specific differences: hence any whitening is
specifically one with any other whitening. Where it happens that
the genus is at the same time a species, it is clear that the
motion will then in a sense be one specifically though not in an
unqualified sense: learning is an example of this, knowledge being
on the one hand a species of apprehension and on the other hand a
genus including the various knowledges. A difficulty, however, may
be raised as to whether a motion is specifically one when the same
thing changes from the same to the same, e.g. when one point
changes again and again from a particular place to a particular
place: if this motion is specifically one, circular motion will be
the same as rectilinear motion, and rolling the same as walking.
But is not this difficulty removed by the principle already laid
down that if that in which the motion takes place is specifically
different (as in the present instance the circular path is
specifically different from the straight) the motion itself is also
different? We have explained, then, what is meant by saying that
motion is one generically or one specifically.
    Motion is one in an unqualified sense when it is one essentially
or numerically: and the following distinctions will make clear what
this kind of motion is. There are three classes of things in
connexion with which we speak of motion, the ‘that which’, the
‘that in which’, and the ‘that during which’. I mean that there
must he something that is in motion, e.g. a man or gold, and it
must be in motion in something, e.g. a place or an affection, and
during something, for all motion takes place during a time. Of
these three it is the thing in which the motion takes place that
makes it one generically or specifically, it is the thing moved
that makes the motion one in subject, and it is the time that makes
it consecutive: but it is the three together that make it one
without qualification: to effect this, that in which the motion
takes place (the species) must be one and incapable of subdivision,
that during which it takes place (the time) must be one and
unintermittent, and that which is in motion must be one-not in an
accidental sense (i.e. it must be one as the white that blackens is
one or Coriscus who walks is one, not in the accidental sense in
which Coriscus and white may be one), nor merely in virtue of
community of nature (for there might be a case of two men being
restored to health at the same time in the same way, e.g. from
inflammation of the eye, yet this motion is not really one, but
only specifically one).
    Suppose, however, that Socrates undergoes an alteration
specifically the same but at one time and again at another: in this
case if it is possible for that which ceased to be again to come
into being and remain numerically the same, then this motion too
will be one: otherwise it will be the same but not one. And akin to
this difficulty there is