E5: PROP. 25. The highest endeavour of the mind, and the highest virtue is to understand things by the third kind of knowledge.

가장 높은 시도, 그리고 가장 높은 힘은 직관으로 사물을 아는 것이다.

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E2: PROP. 40, Note 2. --From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:--
(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (E2P29C); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience.
(2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (E2P18N). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination.
(3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (E2P38C, E2P39, E2P39C, and E2P40); this I call reason and knowledge of the second kind.
[(4.)] Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition. 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.
I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. 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 b0ok of Euclid, namely, in virtue of the general property of proportionals.
But with very simple numbers there is no need of this. 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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