[1016a]
[1]
and a continuous
line, even if it is bent, is said to be one, just like each of the
limbs; e.g. the leg or arm. And of these things themselves those which
are naturally continuous are one in a truer sense than those which are
artificially continuous."Continuous" means that whose motion is essentially one, and cannot
be otherwise; and motion is one when it is indivisible, i.e.
indivisible in time . Things are essentially continuous
which are one not by contact only; for if you put pieces of wood
touching one another you will not say that they are one
piece of wood, or body, or any other continuous thing.And things which are completely
continuous are said to be "one" even if they contain a joint, and
still more those things which contain no joint; e.g., the shin or the
thigh is more truly one than the leg, because the motion of the leg
may not be one.And the
straight line is more truly one than the bent. We call the line which
is bent and contains an angle both one and not one, because it may or
may not move all at once; but the straight line always moves all at
once, and no part of it which has magnitude is at rest while another
moves, as in the bent line.(b) Another
sense of "one" is that the substrate is uniform in kind.Things are uniform whose form
is indistinguishable to sensation;
[20]
and the substrate is either that which is primary,
or that which is final in relation to the end. For wine is said to be
one, and water one, as being something formally indistinguishable. And
all liquids are said to be one (e.g. oil and wine), and melted things;
because the ultimate substrate of all of them is the same, for all
these things are water or vapor.(c) Things are
said to be "one" whose genus is one and differs in its opposite
differentiae. All these things too are said to be "one" because the
genus, which is the substrate of the differentiae, is one (e.g.,
"horse," "man" and "dog" are in a sense one, because they are all
animals); and that in a way very similar to that in which the matter
is one.Sometimes these
things are said to be "one" in this sense, and sometimes their higher
genus is said to be one and the same (if they are final species of
their genus)—the genus, that is, which is above the genera
of which their proximate genus is one; e.g., the isosceles and
equilateral triangles are one and the same figure (because they are
both triangles), but not the same triangles.(d)
Again, things are said to be "one" when the definition stating the
essence of one is indistinguishable from a definition explaining the
other; for in itself every definition is distinguishable <into
genus and differentiae>. In this way that which increases and
decreases is one, because its definition is one; just as in the case
of planes the definition of the form is one.
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