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.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
divisible.
The measure is always homogeneous with the thing measured; the
measure of spatial magnitudes is a spatial magnitude, and in
particular that of length is a length, that of breadth a breadth, that
of articulate sound an articulate sound, that of weight a weight, that
of units a unit. (For we must state the matter so, and not say that
the measure of numbers is a number; we ought indeed to say this if
we were to use the corresponding form of words, but the claim does not
really correspond-it is as if one claimed that the measure of units is
units and not a unit; number is a plurality of units
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