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160 THE FOURFOLD BOOT. [CHAP. VI.
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 geo
metrical 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 demon
stration. 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.)
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.
"
For, if side a b be not equal to side a c, one of them is
greater than the other. Let a b be greater than a c ; and
from b a cut off b d equal to c a, and draw d c. Then, in the
triangles d b c, a b c, because d b is equal to a c, and b c is
common to both triangles, the two sides d b and b c are
equal to the two sides a c, a b, each to each ; and the angle
d b c is equal to the angle a c b, therefore the base d c is
equal to the base a b, and the triangle d b c is equal to the