a new method of mathematical demonstration, nor the substitution of my own proof for that of Euclid, for which its whole nature unfits it, as well as the fact that it presupposes the conception of parallel lines, which in Euclid comes much later. I merely wished to show what the reason of being is, and wherein lies the difference between it and the reason of knowing, which latter only effects convictio, a thing that differs entirely from insight into the reason of being. The fact that Geometry only aims at effecting convictio, and that this, as I have said, leaves behind it a disagreeable impression, but gives no insight into the reason of being—which insight, like all knowledge, is satisfactory and pleasing—may perhaps be one of the reasons for the great dislike which many otherwise eminent heads have for mathematics.
I cannot resist again giving fig. 6, although it has already been presented elsewhere; because the mere sight of it without words conveys ten times more persuasion of the truth of the Pythagorean theorem than Euclid's mouse trap demonstration.
Those readers for whom this chapter may have a special interest will find the subject of it more fully treated in my chief work, "Die Welt als Wille und Vorstellung," vol. i. § 15 ; vol. ii. chap. 13.
