In Geometry, it is therefore only in dealing with axioms that we appeal to intuition. All the other theorems are demonstrated: that is to say, a reason of knowing is given, the truth of which everyone is bound to acknowledge. The logical truth of the theorem is thus shown, but not its transcendental truth (v. §§ 30 and 32), which, as it lies in the reason of _being_ and not in the reason of _knowing_, never can become evident excepting by means of intuition. This explains _why_ this sort of geometrical demonstration, while it no doubt conveys the conviction that the theorem which has been demonstrated is true, nevertheless gives no insight as to why that which it asserts is what it is. In other words, we have not found its Reason of Being; but the desire to find it is usually then thoroughly roused. For proof by indicating the reason of knowledge only effects conviction (_convictio_), not knowledge (_cognitio_): therefore it might perhaps be more correctly called _elenchus_ than _demonstratio_. This is why, in most cases, therefore, it leaves behind it that disagreeable feeling which is given by all want of insight, when perceived; and here, the want of knowledge _why_ a thing is as it is, makes itself all the more keenly felt, because of the certainty just attained, _that_ it is as it is. This impression is very much like the feeling we have, when something has been conjured into or out of our pocket, and we cannot conceive how. The reason of knowing which, in such demonstrations as these, is given without the reason of being, resembles certain physical theories, which present the phenomenon without being able to indicate its cause: for instance, Leidenfrost's experiment, inasmuch as it succeeds also in a platina crucible; whereas the reason of being of a geometrical proposition which is discovered by intuition, like every knowledge we acquire, produces satisfaction. When once the reason of being is found, we base our conviction of the truth of the theorem upon that reason alone, and no longer upon the reason of knowing given us by the demonstration. Let us, for instance, take the sixth proposition of the first Book of Euclid:-- "If two angles of a triangle are equal, the sides also which subtend, or are opposite to, the equal angles shall be equal to one another." (See fig. 3.) [Illustration: _Fig. 3._] Which Euclid demonstrates as follows:-- "Let _a b c_ be a triangle having the angle _a b c_ equal to the angle _a c b_, then the side _a c_ must be equal to the side _a b_ also.