Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

BOOK Two 65
distended by a triple dimension, nor consolidated by any crassitude.
Thus also in numbers, unity indeed is not itself a linear number,
yet it is the principle of number extended into length.
And linear number being itself void of all breadth, is the origin
of number distended into breadth. Superficial number
likewise, is itself deprived of all solidity, yet being added to
depth is the summit of a numerical solid. This however we
shall render more manifest by examples. But linear number
begins from 2; and the series of such numbers is formed by
the continual addition of unity; as in the following example:
CHAPTER V.
On plane rectilinear figures.-That the triangle is the principle
of them. And on the distribution of triangles, their sides, and
generation.
A PLANE superficies however, is found in numbers to have
its beginning from 3, and with the addition of breadth the angles
are dilated in the multitude of numbers that follow each
other in a natural order. Hence the first plane superficies in
numbers is a triangle; the second is a square; the third, a pentagon;
the fourth, a hexagon; the fifth, a heptagon; the sixth,
an octagon; and the rest after the same manner increase their
angles, in the plane description of figures, according to the
order of the natural numbers.
But these begin from the number 3, because the ternary alone
is the principle of breadth and superficies. The same thing
also, is more evidently found to take place in geometry. For
two right lines do not contain space. And in every multangu-