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and has an angle we call both one and not one, because its movement
may be either simultaneous or not simultaneous; but that of the
straight line is always simultaneous, and no part of it which has
magnitude rests while another moves, as in the bent line.
(b)(i) Things are called one in another sense because their
substratum does not differ in kind; it does not differ in the case
of things whose kind is indivisible to sense. The substratum meant
is either the nearest to, or the farthest from, the final state.
For, one the one hand, wine is said to be one and water is said to
be one, qua indivisible in kind; and, on the other hand, all juices,
e.g. oil and wine, are said to be one, and so are all things that
can be melted, because the ultimate substratum of all is the same; for
all of these are water or air.
(ii) Those things also are called one whose genus is one though
distinguished by opposite differentiae-these too are all called one
because the genus which underlies the differentiae is one (e.g. horse,
man, and dog form a unity, because all are animals), and indeed in a
way similar to that in which the matter is one. These are sometimes
called one in this way, but sometimes it is the higher genus that is
said to be the same (if they are infimae species of their genus)-the
genus above the proximate genera; e.g. the isosceles and the
equilateral are one and the same figure because both are triangles;
but they are not the same triangles.
(c) Two things are called one, when the definition which states
the essence of one is indivisible from another definition which
shows us the other (though in itself every definition is divisible).
Thus even that which has increased or is diminishing is one, because
its definition is one, as, in the case of plane figures, is the
definition of their form. In general those things the thought of whose
essence is indivisible, and cannot separate them either in time or
in place or in definition, are most of all one, and of these
especially those which are substances. For in general those things
that do not admit of division are called one in so far as they do
not admit of it; e.g. if two things are indistinguishable qua man,
they are one kind of man; if qua animal, one kind of animal; if qua
magnitude, one kind of magnitude.-Now most things are called one
because they either do or have or suffer or are related to something
else that is one, but the things that are primarily called one are
those whose substance is one,-and one either in continuity or in
form or in definition; for we count as more than one either things
that are not continuous, or those whose form is not one, or those
whose definition is not one.
While in a sense we call anything one if it is a quantity and
continuous, in a sense we do not unless it is a whole, i.e. unless
it has unity of form; e.g. if we saw the parts of a shoe put
together anyhow we should not call them one all the same (unless
because of their continuity); we do this only if they are put together
so as to be a shoe and to have already a certain single form. This
is why the circle is of all lines most truly one, because it is
whole and complete.
(3) The essence of what is one is to be some kind of beginning
of number; for the first measure is the beginning, since that by which
we first know each class is the first measure of the class; the one,
then, is the beginning of the knowable regarding each class. But the
one is not the same in all classes. For here it is a quarter-tone, and
there it is the vowel or the consonant; and there is another unit of
weight and another of movement. But everywhere the one is
indivisible either in quantity or in kind. Now that which is
indivisible in quantity is called a unit if it is not divisible in any
dimension and is without position, a point if it is not divisible in
any dimension and has position, a line if it is divisible in one
dimension, a plane if in two, a body if divisible in quantity in
all--i.e. in three--dimensions. And, reversing the order, that which
is divisible in two dimensions is a plane, that which is divisible

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