sort it matters not, doth equally stand for and represent all rectilinear
triangles whatsoever, and is in that sense UNIVERSAL. All which seems
very plain and not to include any difficulty in it.

16. OBJECTION.--ANSWER.--But here it will be demanded, HOW WE CAN KNOW ANY
PROPOSITION TO BE TRUE OF ALL PARTICULAR TRIANGLES, EXCEPT we have first
seen it DEMONSTRATED OF THE ABSTRACT IDEA OF A TRIANGLE which equally
agrees to all? For, because a property may be demonstrated to agree to
some one particular triangle, it will not thence follow that it equally
belongs to any other triangle, which in all respects is not the same with
it. For example, having demonstrated that the three angles of an isosceles
rectangular triangle are equal to two right ones, I cannot therefore
conclude this affection agrees to all other triangles which have neither
a right angle nor two equal sides. It seems therefore that, to be certain
this proposition is universally true, we must either make a particular
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, w