(that can distinctly see white and black),
Whether this ink and this paper be all of a colour. If there be sight in
the eyes, it will, at first glimpse, without hesitation, perceive the
words printed on this paper different from the colour of the paper: and
so if the mind have the faculty of distinct perception, it will perceive
the agreement or disagreement of those ideas that produce intuitive
knowledge. If the eyes have lost the faculty of seeing, or the mind of
perceiving, we in vain inquire after the quickness of sight in one, or
clearness of perception in the other.

6. Not so clear as Intuitive Knowledge.

It is true, the perception produced by demonstration is also very clear;
yet it is often with a great abatement of that evident lustre and full
assurance that always accompany that which I call intuitive: like a
face reflected by several mirrors one to another, where, as long as it
retains the similitude and agreement with the object, it produces a
knowledge; but it is still, in every successive reflection, with a
lessening of that perfect clearness and distinctness which is in the
first; till at last, after many removes, it has a great mixture of
dimness, and is not at first sight so knowable, especially to weak eyes.
Thus it is with knowledge made out by a long train of proof.

7. Each Step in Demonstrated Knowledge must have Intuitive Evidence.

Now, in every step reason makes in demonstrative knowledge, there is an
intuitive knowledge of that agreement or disagreement it seeks with the
next intermediate idea which it uses as a proof: for if it were not
so, that yet would need a proof; since without the perception of such
agreement or disagreement, there is no knowledge produced: if it
be perceived by itself, it is intuitive knowledge: if it cannot be
perceived by itself, there is need of some intervening idea, as a common
measure, to show their agreement or disagreement. By which it is plain,
that every step in reasoning that produces knowledge, has intuitive
certainty; which when the mind perceives, there is no more required
but to remember it, to make the agreement or disagreement of the ideas
concerning which we inquire visible and certain. So that to make
anything a demonstration, it is necessary to perceive the immediate
agreement of the intervening ideas, whereby the agreement or
disagreement of the two ideas under examination (whereof the one is
always the first, and the other the last in the