Download (PDF, 23.58MB) - Plurality Press

164 THE FOURFOLD BOOT. [CHAP. vi.
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 pre
supposes 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 con-
victio, 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,
Fig. 6.
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,
15 ; vol. ii. chap. 13.
"
Die Welt als Wille und Vorstellung," vol. i.