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. 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
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