Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

ives something from both through its alliance to each; which
is of itself indeed second and composite, but with reference to
others is found to be first and incomposite.
CHAPTER IX.
On the first and incomporite number.
AND the first and incomposite number indeed, is that which
has no other part except that which is denominated from the
whole quantity of the number; so that the part itself is no
other than unity. And such are the numbers 3.5.7.11.13.17.
19.23.29.31. In each of these numbers therefore, no other
part can be found except that which is denominated from
them, and this, as we have before observed, is unity alone. For
in 3 there is only one part, i.e. a third, which is denominated
from 3, and this third part is unity. After the same manner in
5 there is only one part which is a fifth, and this is unity. And
the same consequence will be found to take place in the rest.
This number however, is called first and incomposite, because
no other number measures it than unity, which is the mother
of all number. And this is owing to its not being composed
from any other numbers, and to its being generated from unities
alone multiplied into themselves.* For thrice one is three,
five times one is five, seven times one is seven, and so of the
rest. But these being multiplied into themselves produce other
numbers like themselves. Being allotted also a primary essence,
they wilI be found to be as it were certain elements of
a11 the numbers generated from them; because they are incomposite,
and formed by a simple generation; and all the
viz. From unities when added tog&
king multiplied by unity
forming a number, and this numb