An excerpt from H. Petard, "A contribution to the mathematical
theory of big game hunting," The American Mathematical Monthly,
vol. 45, no. 7, pp. 446-447, 1938: The Hilbert, or axiomatic,
method. We place a locked cage at a given point of the desert.
We then introduce the following logical system. - Axiom I. The
class of lions in the Sahara Desert is non-void. - Axiom II. If
there is a lion in the Sahara Desert, there is a lion in the
cage. - Rule of Procedure. If p is a theorem, and "p implies q"
is a theorem, then q is a theorem. - Theorem I. There is a lion
in the cage. The method of inversive geometry. We place a
spherical cage in the desert, enter it, and lock it. We perform
an inversion with respect to the cage. The lion is then in the
interior of the cage, and we are outside. The method of
projective geometry. Without loss of generality, we may regard
the Sahara Desert as a plane. Project the plane into a line, and
then project the line into an interior point of the cage. The
lion is projected into th