Now let us consider the triangle, which is formed of three lines. Why
should it not belong to quantity? Would it be so, because it is not
constituted by three lines merely, but by three lines arranged in some
particular manner? But a quadrilateral would also be constituted by
four lines arranged in some particular manner. (But being arranged in
some particular manner does not hinder a figure from being a quantity).
The straight line, indeed, is arranged in some particular manner, and
is none the less a quantity. Now if the straight line be not simply a
quantity, why could this not also be said of a limited line? For the
limit of the line is a point, and the point does not belong to any
genus other than the line. Consequently, a limited surface is also
a quantity, because it is limited by lines, which even more belong
to quantity. If then the limited surface be contained in the genus
of quantity, whether the surface be a triangle, a quadrilateral, a
hexagon, or any other polygon, all figures whatever will belong to the
genus of quantity. But if we assigned the triangle or quadrilateral
to the genus of quality merely because we are speaking of some one
definite triangle or quadrilateral, nothing would hinder one and the
same thing from being subsumed under several categories. A triangle
would then be a quantity so far as it was both a general and particular
magnitude, and would be a quality by virtue of its possessing a
particular form. The same might be predicated of the Triangle in
itself because of its possessing a particular form; and so also with
the sphere. By following this line of argument, geometry would be
turned into a study of qualities, instead of that of quantities,
which of course it is. The existing differences between magnitudes
do not deprive them of their property of being magnitudes, just as
the difference between essences does not affect their essentiality.
Besides, every surface is limited, because an infinite surface is
impossible. Further, when I consider a difference that pertains to
essence, I call it an essential difference. So much the more, on
considering figures, I am considering differences of magnitude. For
if the differences were not of magnitude, of what would they be
differences? If then they be differences of magnitude, the different
magnitudes which are derived from differences of magnitude should
be classified according to the species constituted by them (when
considered in the light of being magnitudes).