Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK Two
CHAPTER IV.
On the qztantity subsisting by itself, which is considered in
geometrical f igurcs, etc.
AND thus much may suffice at present, respecting relative
quantity. In what follows, we shall discuss certain particulars
pertaining to that quantity which subsists by itself, and is not
referred to any thing else, which may be profitable to what we
shall afterwards again unfold about relative quantity. For the
speculation of mathesis loves in a certain respect to be conversant
with alternate demonstration. Our business however, at
present, is with the numbers which subsist in geometrical figures,
and their spaces and dimensions, viz. with linear, triangular,
or square numbers, and with others which superficies
alone unfolds, as also with those that are formed by an unequal
composition of sides. We have likewise to discuss solid numbers,
viz. such as are cubical, spherical, and pyramidal, and
such as have the form of tiles or beams, or wedges; all which
indeed, properly pertain to the geometric speculation. But as
the science of geometry is produced from arithmetic, as from
a certain root and mother, so likewise we find the seeds of its
figures in the first numbers.
Unity therefore, or the monad, which is in arithmetic what
a point is in geometry, is the principle of interval and length;
but itself is neither capacious of interval nor of length; just as
a point is the principle of a line and of interval, but is itself
neither interval nor line. For a point placed on a point, does
not produce any interval. Between things also that are equal
there is no interval. Thus, if three sixes are placed after this
manner, 6. 6. 6. as is the first to the second, so is the second
to the third; but between the first and second, or the second