15. NOR FOR THE ENLARGEMENT OF KNOWLEDGE.--Nor do I think them
a whit more needful for the ENLARGEMENT OF KNOWLEDGE than for
COMMUNICATION. It is, I know, a point much insisted on, that
all knowledge and demonstration are about universal notions, to
which I fully agree: but then it doth not appear to me that those notions
are formed by ABSTRACTION in the manner PREMISED--UNIVERSALITY, so far as
I can comprehend, not consisting in the absolute, POSITIVE nature or
conception of anything, but in the RELATION it bears to the particulars
signified or represented by it; by virtue whereof it is that things,
names, or notions, being in their own nature PARTICULAR, are rendered
UNIVERSAL. Thus, when I demonstrate any proposition concerning triangles,
it is to be supposed that I have in view the universal idea of a
triangle; which ought not to be understood as if I could frame an idea of
a triangle which was neither equilateral, nor scalenon, nor equicrural;
but only that the particular triangle I consider, whether of this or that
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