The Complete Aristotle (eng.)

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 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.)
    Knowledge, also, and perception, we call the measure of things
for the same reason, because we come to know something by
them-while as a matter of fact they are measured rather than
measure other things. But it is with us as if some one else
measured us and we came to know how big we are by seeing that he
applied the cubit-measure to such and such a fraction of us. But
Protagoras says ‘man is the measure of all things’, as if he had
said ‘the man who knows’ or ‘the man who perceives’; and these
because they have respectively knowledge and perception, which we
say are the measures of objects. Such thinkers are saying nothing,
then, while they appear to be saying something remarkable.
    Evidently, then, unity in the strictest sense, if we define it
according to the meaning of the word, is a measure, and most
properly of quantity, and secondly of quality. And some things will
be one if they are indivisible in quantity, and others if they are
indivisible in quality; and so that which is one is indivisible,
either absolutely or qua one.
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2
    With regard to the substance and nature of the one we must ask
in which of two ways it exists. This is the very question that we
reviewed in our discussion of problems, viz. what the one is and
how we must conceive of it, whether we must take the one itself as
being a substance (as both the Pythagoreans say in earlier and
Plato in later times), or there is, rather, an underlying nature
and the one should be described more intelligibly and more in the
manner of the physical philosophers, of whom one says the one is
love, another says it is air, and another the indefinite.
    If, then, no universal can be a substance, as has been said our
discussion of substance and being, and if being itself cannot be a
substance in the sense of a one apart from the many (for it is
common to the many), but is only a predicate, clearly unity also
cannot be a substance; for being and unity are the most universal
of all predicates. Therefore, on the one hand, genera are not
certain entities and substances separable from other things; and on
the other hand the one cannot be a genus, for