But it is not so, for the parallelism depends not on these
angles being equal to one another because each is a right angle, but
simply on their being equal to one another. An example of (1) would be
as follows: if isosceles were the only triangle, it would be thought
to have its angles equal to two right angles qua isosceles. An
instance of (2) would be the law that proportionals alternate.
Alternation used to be demonstrated separately of numbers, lines,
solids, and durations, though it could have been proved of them all by
a single demonstration. Because there was no single name to denote
that in which numbers, lengths, durations, and solids are identical,
and because they differed specifically from one another, this property
was proved of each of them separately. To-day, however, the proof is
commensurately universal, for they do not possess this attribute qua
lines or qua numbers, but qua manifesting this generic character which
they are postulated as possessing universally. Hence, even if one
prove of each kind of triangle that its angles are equal to two
right angles, whether by means of the same or different proofs; still,
as long as one treats separately equilateral, scalene, and
isosceles, one does not yet know, except sophistically, that
triangle has its angles equal to two right angles, nor does one yet
know that triangle has this property commensurately and universally,
even if there is no other species of triangle but these.
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