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something else of the sort is by its own nature the element), but in a
sense it is not; for it is not the same thing to be fire and to be
an element, but while as a particular thing with a nature of its own
fire is an element, the name 'element' means that it has this
attribute, that there is something which is made of it as a primary
constituent. And so with 'cause' and 'one' and all such terms. For
this reason, too, 'to be one' means 'to be indivisible, being
essentially one means a "this" and capable of being isolated either in
place, or in form or thought'; or perhaps 'to be whole and
indivisible'; but it means especially 'to be the first measure of a
kind', and most strictly of quantity; for it is from this that it
has been extended to the other categories. For measure is that by
which quantity is known; and quantity qua quantity is known either
by a 'one' or by a number, and all number is known by a 'one'.
Therefore all quantity qua quantity is known by the one, and that by
which quantities are primarily known is the one itself; and so the one
is the starting-point of number qua number. And hence in the other
classes too 'measure' means that by which each is first known, and the
measure of each is a unit-in length, in breadth, in depth, in
weight, in speed. (The words 'weight' and 'speed' are common to both
contraries; for each of them has two meanings-'weight' means both that
which has any amount of gravity and that which has an excess of
gravity, and 'speed' both that which has any amount of movement and
that which has an excess of movement; for even the slow has a
certain speed and the comparatively light a certain weight.)
In all these, then, the measure and starting-point is something
one and indivisible, since even in lines we treat as indivisible the
line a foot long. For everywhere we seek as the measure something
one and indivisible; and this is that which is simple either in
quality or in quantity. Now where it is thought impossible to take
away or to add, there the measure is exact (hence that of number is
most exact; for we posit the unit as indivisible in every respect);
but in all other cases we imitate this sort of measure. For in the
case of a furlong or a talent or of anything comparatively large any
addition or subtraction might more easily escape our notice than in
the case of something smaller; so that the first thing from which,
as far as our perception goes, nothing can be subtracted, all men make
the measure, whether of liquids or of solids, whether of weight or
of size; and they think they know the quantity when they know it by
means of this measure. And indeed they know movement too by the simple
movement and the quickest; for this occupies least time. And so in
astronomy a 'one' of this sort is the starting-point and measure
(for they assume the movement of the heavens to be uniform and the
quickest, and judge the others by reference to it), and in music the
quarter-tone (because it is the least interval), and in speech the
letter. And all these are ones in this sense--not that 'one' is
something predicable in the same sense of all of these, but in the
sense we have mentioned.
But the measure is not always one in number--sometimes there are
several; e.g. the quarter-tones (not to the ear, but as determined
by the ratios) are two, and the articulate sounds by which we
measure are more than one, and the diagonal of the square and its side
are measured by two quantities, and all spatial magnitudes reveal
similar varieties of unit. Thus, then, the one is the measure of all
things, because we come to know the elements in the substance by
dividing the things either in respect of quantity or in respect of
kind. And the one is indivisible just because the first of each
class of things is indivisible. But it is not in the same way that
every 'one' is indivisible e.g. a foot and a unit; the latter is
indivisible in every respect, while the former must be placed among
things which are undivided to perception, as has been said
already-only to perception, for doubtless every continuous thing is
The measure is always homogeneous with the thing measured; the

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