Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

it is also surpassed by the last number by 3. But it contains the
geometrical analogy in the four numbers 6, 8, 9, and 12. For
as 8 is to 6, so is 12 to 9; the ratio being sesquitertian. And it
contains the harmonic analogy in the three numbers 6, 8, and
12. There is however a twofold criterion of harmonic analogy;
one indeed, when as is the last term to the first, so is the difference
between the last and middle, to the difference between
the middle and first term. Of this, the most evident credibility
may be derived from the proposed numbers 6, 8, and 12. For
the last is double of the first term; and 12 exceeds 8 by 4, and
8 exceeds 6 by 2. But 12 : 6 :: 4 : 2. The other criterion however
of harmonic analogy is, when the middle term by an
equal part surpasses and is surpassed by the extremes. For 8
being the middle term, surpasses the first by a third part of the
first term; for 8-6=2 the third part of 6; but it is surpassed
by the last term by an equal part of the last; for 12-8=4,
which is the third of 12. These things indeed necessarily thus
subsist with respect to the venerable nature of this diagram,
whether it may be proper to call it plinthion, or to give it some
other appellation. So many ideas, and still more than these,
does the hebdomad exhibit in things incorporeal and intelligible.
But the nature of it likewise extends to every visible essence,
pervading through heaven and earth, which are the boundaries
of the universe. For what part of the world is there, which is
not enamoured of the hebdomad, being tamed by the love and
desire of it? They say therefore, in the first place, that heaven
is begirt with seven circles, the names of which are, the arctic,
antarctic, the summer tropic, the winter tropic, the equinoctial,
the zodiac, and besides these, the galaxy. For the horizon belongs
to us; according to the acuteness of our vision, or the
contrary, our sensible perception being circumscribed by it in a
greater or less degree. The planets indeed, an army proceeding
in a course contrary to that of the fixed stars, being ar-