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 another; viz. is health one? and generally are the states and
affections in bodies severally one in essence although (as is clear)
the things that contain them are obviously in motion and in flux? Thus
if a person's health at daybreak and at the present moment is one
and the same, why should not this health be numerically one with
that which he recovers after an interval? The same argument applies in
each case. There is, however, we may answer, this difference: that
if the states are two then it follows simply from this fact that the
activities must also in point of number be two (for only that which is
numerically one can give rise to an activity that is numerically one),
but if the state is one, this is not in itself enough to make us
regard the activity also as one: for when a man ceases walking, the
walking no longer is, but it will again be if he begins to walk again.
But, be this as it may, if in the above instance the health is one and
the same, then it must be possible for that which is one and the
same to come to be and to cease to be many times. However, these
difficulties lie outside our present inquiry.

    Since every motion is continuous, a motion that is one in an
unqualified sense must (since every motion is divisible) be
continuous, and a continuous motion must be one. There will not be
continuity between any motion and any other indiscriminately any
more than there is between any two things chosen at random in any
other sphere: there can be continuity only when the extremities of the
two things are one. Now some things have no extremities at all: and
the extremities of others differ specifically although we give them
the same name of "end": how should e.g. the "end" of a line and the
"end" of walking touch or come to be one? Motions that are not the
same either specifically or generically may, it is true, be
consecutive (e.g. a man may run and then at once fall ill of a fever),
and again, in the torch-race we have consecutive but not continuous
locomotion: for according to our definition there can be continuity
only when the ends of the two things are one. Hence motions may be
consecutive or successive in virtue of the time being continuous,
but there can be continuity only in virtue of the motions themselves
being continuous, that is when the end of each is one with the end
of the other. Motion, therefore, that is in an unqualified sense
continuous and one must be specifically the same, of one thing, and in
one time. Unity is required in respect of time in order that there may
be no interval of immobility, for where there is intermission of
motion there must be rest, and a motion that includes intervals of
rest will be not one but many, so that a motion that is interrupted by
stationariness is not one or continuous, and it is so interrupted if
there is an interval of time. And though of a motion that is not
specifically one (even if the time is unintermittent) the time is one,
the motion is specifically different, and so cannot really be one, for
motion that is one must be specifically one, though motion that is
specifically one is not necessarily one in an unqualified sense. We
have now explained what we mean when we call a motion one without
qualification.

    Further, a motion is also said to be one generically,
specifically, or essentially when it is complete, just as in other
cases completeness and wholeness are characteristics of what is one:
and sometimes a motion even if incomplete is said to be one,
provided only that it is continuous.

    And besides the cases already mentioned there is another in which
a motion is said to be one, viz. when it is regular: for in a sense
a motion that is irregular is not regarded as one, that title
belonging rather to that which is regular, as a straight line is
regular, the irregular being as such divisible. But the difference
would seem to be one of degree. In every kind of motion we may have
regularity or irregularity: thus there may be regular alteration,
and locomotion in a regular path, e.g. in a circle or on a straight
line, and it is the same with regard to increase and decrease. The
difference that makes a motion irregular is sometimes to be found in
its path: thus a motion cannot be regular if its path is an
irregular magnitude, e.g. a broken line, a spiral, or any other
magnitude that is not such that any part of it taken at random fits on
to any other that may be chosen. Sometimes it is found neither in
the place nor in the time nor in the goal but in the manner of the
motion: for in some cases the motion is differentiated by quickness
and slowness: thus if its velocity is uniform a motion is regular,
if not it is irregular. So quickness and slowness are not species of
motion nor do they constitute specific differences of motion,
because this distinction occurs in connexion with all the distinct
species of motion. The same is true of heaviness and lightness when
they refer to the same thing: e.g. they do not specifically
distinguish earth from itself or fire from itself. Irregular motion,
therefore, while in virtue of being continuous it is one, is so in a
lesser degree, as is the case with locomotion in a broken line: and
a lesser degree of something always means an admixture of its
contrary. And since every motion that is one can be both regular and
irregular, motions that are consecutive but not specifically the
same cannot be one and continuous: for how should a motion composed of
alteration and locomotion be regular? If a motion is to be regular its
parts ought to fit one another.