Page:Popular Science Monthly Volume 67.djvu/645

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LEMENTARY geometry has been the most stable part of all science. This was due to one book, of which Philip Kelland says:

In all lands and languages, in all the world, there was but one geometry. For the abstractest philosophy, for the most utilitarian technology, geometry is of fundamental importance. For education it is the before and after, the oldest medium and the newest; older, more classic than the classics, as new as the automobile. The first of the sciences, it is ever the newest requisite for their ongo. Says H. J. S. Smith:

Of what startling interest then must it be that at length this century-plant has flowered, a new epoch has unfolded. How did this happen? Euclid deduced his geometry from just five axioms and five postulates. These were all very, very short and simple, except the last postulate, which was in such striking contrast to the others that not its truth, but the necessity of assuming or postulating it, was doubted from remotest antiquity. The great astronomer Ptolemæos (Ptolemy) wrote a treatise purporting to prove it, and hundreds after him spent their brains in like attempts. What vast effort has been wasted in this chimeric hope, says Poincaré, is truly unimaginable!