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08424_Field_TCGG T189.txt
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of anharmonic ratios but Euclid’s “porism”, the latter of
which was as close a miss as possible for Desargues’
Theorem. But they regarded these things as isolated
propositions having no relation to each other. Had the
late Greeks only added to them the one further idea that
parallel lines meet at infinity, they would have had in their
hands at least logical equivalents of the basic ideas for
geometrical continuity and for perspective and
perspective geometry. That is to say that again and
again during a period of six or seven centuries they went
right up to the door of modern geometry, but that,
inhibited by their tactile-muscular, metrical ideas, they
were never able to open that door and pass out into the
great open spaces of modern thought.
The story of uniformity, continuity, and homogeneity was