(22) I shall call both these ways of regarding
things knowledge of the first kind, opinion,
or imagination.
(3.) (40:23) From the fact that we have notions common to
all men, and adequate ideas of the properties of things
([xxxviii] Coroll., [xxxix] and Coroll. and [xl] );
this I call reason and knowledge of the second kind.
(24) Besides these two kinds of knowledge, there is,
as I will hereafter show, a third kind of knowledge,
which we will call intuition. (25) This kind of
knowledge proceeds from an adequate idea of the
absolute essence of certain attributes of God to the
adequate knowledge of the essence of things.
(40:26) I will illustrate all three kinds of knowledge by a single
example. (27) Three numbers are given for finding a fourth, which
shall be to the third as the second is to the first. (28) Tradesmen
without hesitation multiply the second by the third, and divide the
product by the first; either because they have not forgotten the
rule which they received from a master without any proof, or because
they have often made trial of it with simple numbers, or by virtue
of the proof of the nineteenth proposition of the seventh book of
Euclid, namely, in virtue of the general property of proportionals.
(40:29) But with very simple numbers there is no need of this.
(30) For instance, one, two, three, being given, everyone can see
that the fourth proportional is six; and this is much clearer,
because we infer the fourth number from an intuitive grasping of
the ratio, which the first bears to the second.
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