account) is found.
This intuitive perception of the agreement or disagreement of the
intermediate ideas, in each step and progression of the demonstration,
must also be carried exactly in the mind, and a man must be sure that no
part is left out: which, because in long deductions, and the use of
many proofs, the memory does not always so readily and exactly retain;
therefore it comes to pass, that this is more imperfect than intuitive
knowledge, and men embrace often falsehood for demonstrations.

8. Hence the Mistake, ex praecognitis, et praeconcessis.

The necessity of this intuitive knowledge, in each step of scientifical
or demonstrative reasoning, gave occasion, I imagine, to that mistaken
axiom, That all reasoning was EX PRAECOGNITIS ET PRAECONCESSIS: which,
how far it is a mistake, I shall have occasion to show more at
large, when I come to consider propositions, and particularly those
propositions which are called maxims, and to show that it is by a
mistake that they are supposed to be the foundations of all our
knowledge and reasonings.

9. Demonstration not limited to ideas of mathematical Quantity.

[It has been generally taken for granted, that mathematics alone are
capable of demonstrative certainty: but to have such an agreement or
disagreement as may intuitively be perceived, being, as I imagine, not
the privilege of the ideas of number, extension, and figure alone, it
may possibly be the want of due method and application in us, and not of
sufficient evidence in things, that demonstration has been thought to
have so little to do in other parts of knowledge, and been scarce so
much as aimed at by any but mathematicians.] For whatever ideas we have
wherein the mind can perceive the immediate agreement or disagreement
that is between them, there the mind is capable of intuitive knowledge;
and where it can perceive the agreement or disagreement of any two
ideas, by an intuitive perception of the agreement or disagreement
they have with any intermediate ideas, there the mind is capable of
demonstration: which is not limited to ideas of extension, figure,
number, and their modes.

10. Why it has been thought to be so limited.

The reason why it has been generally sought for, and supposed to be only
in those, I imagine has been, not only the general usefulness of those
sciences; but because, in comparing their equality or excess, the modes
of numbers have every the least difference very clear and pe