The Complete Aristotle (eng.)

else which does
persist. Since, then, one thinker places the 1 as contrary to
plurality, and another places it as contrary to the unequal,
treating the 1 as equal, number must be being treated as coming
from contraries. There is, then, something else that persists, from
which and from one contrary the compound is or has come to be.
Again, why in the world do the other things that come from
contraries, or that have contraries, perish (even when all of the
contrary is used to produce them), while number does not? Nothing
is said about this. Yet whether present or not present in the
compound the contrary destroys it, e.g. ‘strife’ destroys the
‘mixture’ (yet it should not; for it is not to that that is
contrary).
    Once more, it has not been determined at all in which way
numbers are the causes of substances and of being-whether (1) as
boundaries (as points are of spatial magnitudes). This is how
Eurytus decided what was the number of what (e.g. one of man and
another of horse), viz. by imitating the figures of living things
with pebbles, as some people bring numbers into the forms of
triangle and square. Or (2) is it because harmony is a ratio of
numbers, and so is man and everything else? But how are the
attributes-white and sweet and hot-numbers? Evidently it is not the
numbers that are the essence or the causes of the form; for the
ratio is the essence, while the number the causes of the form; for
the ratio is the essence, while the number is the matter. E.g. the
essence of flesh or bone is number only in this way, ‘three parts
of fire and two of earth’. And a number, whatever number it is, is
always a number of certain things, either of parts of fire or earth
or of units; but the essence is that there is so much of one thing
to so much of another in the mixture; and this is no longer a
number but a ratio of mixture of numbers, whether these are
corporeal or of any other kind.
    Number, then, whether it be number in general or the number
which consists of abstract units, is neither the cause as agent,
nor the matter, nor the ratio and form of things. Nor, of course,
is it the final cause.
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6
    One might also raise the question what the good is that things
get from numbers because their composition is expressible by a
number, either by one which is easily calculable or by an odd
number. For in fact honey-water is no more wholesome if it is mixed
in the proportion of three times three, but it would do more good
if it were in no particular ratio but well diluted than if it were
numerically expressible but strong. Again, the ratios of mixtures
are expressed by the adding of numbers, not by mere numbers; e.g.
it is ‘three parts to two’, not ‘three times two’. For in any
multiplication the genus of the things multiplied must be the same;
therefore the product 1X2X3 must be measurable by 1, and 4X5X6 by 4
and therefore all products into which the same factor enters must
be measurable by that factor. The number of fire, then, cannot be
2X5X3X6 and at the same time that of water 2X3.
    If all things must share in number, it must follow that many
things are the same, and the same number must belong to one thing
and to another. Is number the cause, then, and does the thing exist
because of its number, or is this not certain? E.g. the motions of
the sun have a number, and again those of the moon,-yes, and the
life and prime of each animal. Why, then, should not some of these
numbers be squares, some cubes, and some equal, others double?
There is no reason why they should not, and indeed they must move
within these limits, since all things were assumed to share in
number. And it was assumed that things that differed might fall
under the same number. Therefore if the same number had belonged to
certain things, these would have been the same as one another,
since they would have had the same form of number; e.g. sun and
moon would have been the same. But why need these numbers be
causes? There are seven vowels, the scale consists of seven
strings, the Pleiades are seven, at seven animals lose their teeth
(at least some do, though some do not), and the champions who
fought against Thebes were seven. Is it then because the number is
the kind of number it is, that the champions were seven or the
Pleiad consists of seven stars? Surely the champions were seven
because there were seven gates or for some other reason, and the
Pleiad we count as seven, as we count the Bear