2. II. Demonstrative.
The next degree of knowledge is, where the mind perceives the agreement or disagreement
of any ideas, but not immediately. Though wherever the mind perceives the agreement or disagreement of any of
its ideas, there be certain knowledge; yet it does not always happen, that the mind sees that agreement or
disagreement, which there is between them, even where it is discoverable; and in that case remains in ignorance,
and at most gets no further than a probable conjecture. The reason why the mind cannot always perceive presently
the agreement or disagreement of two ideas, is, because those ideas, concerning whose agreement or disagreement
the inquiry is made, cannot by the mind be so put together as to show it. In this case then, when the mind cannot
so bring its ideas together as by their immediate comparison, and as it were juxta-position or application one to
another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more, as
it happens) to discover the agreement or disagreement which it searches; 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.
