Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

great power of difference. For every finite and definite
power, when it departs from the nature of equality, and from
an essence which contains itself within its own bounds, either
becomes exuberant or deficient, verges to the greater, or declines
to the less. And, on the contrary, by taking the side of
the square from the greater, or adding it to the less number
longer in the other part, the intermediate square will be produced.
Thus 6-2, or 2+2 is equal to 4.
Hence it appears in the first place, that the monad is the
principle of an essence which is properly immutable and the
same; but that the duad is the principle of difference and mutation.
In the second place it appears that all odd numbers on
account of their alliance to the monad, participate of the essence
which is invariably the same; but that even numbers
on account of their alliance to the duad, are mingled with
difference. Thus too, squares, because their composition and
conjunction is from odd numbers, participate of an immutable
essence; but numbers longer in the other part, because they
are generated from the conjunction of even numbers, are never
separated from the variety of difference.
CHAPTER XXI.
What agreement there i~ in difference and in ratio, between
squares and nsrmbets LONGER IN THE OTHER PART, when they
me alternately arranged.
IF, therefore, squares and numbers longer in $he other part,
are arranged in an alternate order, there is so great a conjunction
between these, that at one time they accord in the same
ratios, but are discordant in their differences; and at another
time they are equal in their differences, but discordant in their