Since of
these principles numbers are by nature the first, and in numbers
they seemed to see many resemblances to the things that exist and come
into being-more than in fire and earth and water (such and such a
modification of numbers being justice, another being soul and
reason, another being opportunity-and similarly almost all other
things being numerically expressible); since, again, they saw that the
modifications and the ratios of the musical scales were expressible in
numbers;-since, then, all other things seemed in their whole nature to
be modelled on numbers, and numbers seemed to be the first things in
the whole of nature, they supposed the elements of numbers to be the
elements of all things, and the whole heaven to be a musical scale and
a number. And all the properties of numbers and scales which they
could show to agree with the attributes and parts and the whole
arrangement of the heavens, they collected and fitted into their
scheme; and if there was a gap anywhere, they readily made additions
so as to make their whole theory coherent. E.g. as the number 10 is
thought to be perfect and to comprise the whole nature of numbers,
they say that the bodies which move through the heavens are ten, but
as the visible bodies are only nine, to meet this they invent a
tenth--the 'counter-earth'. We have discussed these matters more
exactly elsewhere.
But the object of our review is that we may learn from these
philosophers also what they suppose to be the principles and how these
fall under the causes we have named.
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