arches; and this is that which we call
REASONING. Thus, the mind being willing to know the agreement or
disagreement in bigness between the three angles of a triangle and
two right ones, cannot by an immediate view and comparing them do it:
because the three angles of a triangle cannot be brought at once, and be
compared with any other one, or two, angles; and so of this the mind has
no immediate, no intuitive knowledge. In this case the mind is fain to
find out some other angles, to which the three angles of a triangle have
an equality; and, finding those equal to two right ones, comes to know
their equality to two right ones.

3. Demonstration depends on clearly perceived proofs.

Those intervening ideas, which serve to show the agreement of any two
others, are called PROOFS; and where the agreement and disagreement is
by this means plainly and clearly perceived, it is called DEMONSTRATION;
it being SHOWN to the understanding, and the mind made to see that it is
so. A quickness in the mind to find out these intermediate ideas, (that
shall discover the agreement or disagreement of any other,) and to apply
them right, is, I suppose, that which is called SAGACITY.

4. As certain, but not so easy and ready as Intuitive Knowledge.

This knowledge, by intervening proofs, though it be certain, yet the
evidence of it is not altogether so clear and bright, nor the assent so
ready, as in intuitive knowledge. For, though in demonstration the mind
does at last perceive the agreement or disagreement of the ideas it
considers; yet it is not without pains and attention: there must be more
than one transient view to find it. A steady application and pursuit are
required to this discovery: and there must be a progression by steps and
degrees, before the mind can in this way arrive at certainty, and come
to perceive the agreement or repugnancy between two ideas that need
proofs and the use of reason to show it.

5. The demonstrated conclusion not without Doubt, precedent to the
demonstration.

Another difference between intuitive and demonstrative knowledge
is, that, though in the latter all doubt be removed when, by the
intervention of the intermediate ideas, the agreement or disagreement
is perceived, yet before the demonstration there was a doubt; which in
intuitive knowledge cannot happen to the mind that has its faculty of
perception left to a degree capable of distinct ideas; no more than it
can be a doubt to the eye