demonstration for every particular triangle, which is impossible, or once
for all demonstrate it of the ABSTRACT IDEA OF A TRIANGLE, in which all
the particulars do indifferently partake and by which they are all
equally represented. To which I answer, that, though the idea I have in
view whilst I make the demonstration be, for instance, that of an
isosceles rectangular triangle whose sides are of a determinate length, I
may nevertheless be certain it extends to all other rectilinear
triangles, of what sort or bigness soever. And that because neither the
right angle, nor the equality, nor determinate length of the sides are at
all concerned in the demonstration. It is true the diagram I have in view
includes all these particulars, but then there is not the least mention
made of them in the proof of the proposition. It is not said the three
angles are equal to two right ones, because one of them is a right angle,
or because the sides comprehending it are of the same length. Which
sufficiently shows that the right angle might have been oblique, and the
sides unequal, and for all that the demonstration have held good. And for
this reason it is that I conclude that to be true of any obliquangular or
scalenon which I had demonstrated of a particular right--angled
equicrural triangle, and not because I demonstrated the proposition of
the abstract idea of a triangle And here it must be acknowledged that a
man may consider a figure merely as triangular, without attending to the
particular qualities of the angles, or relations of the sides. So far he
may abstract; but this will never prove that he can frame an abstract,
general, inconsistent idea of a triangle. In like manner we may consider
Peter so far forth as man, or so far forth as animal without framing the
fore-mentioned abstract idea, either of man or of animal, inasmuch as all
that is perceived is not considered.

17. ADVANTAGE OF INVESTIGATING THE DOCTRINE OF ABSTRACT GENERAL IDEAS.--
It were an endless as well as an useless thing to trace the