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Nineteenth Century Geometry (Stanford Encyclopedia of Philosophy) |
 | | During this period, the content of geometry and its internal diversity increased almost beyond recognition; the axiomatic method, vaunted since antiquity by the admirers of geometry, finally attained true logical sufficiency, and the ground was laid for replacing, in the description of physical phenomena, the standard geometry of Euclid by Riemann's wonderfully pliable system. |
 | | The present article reviews the aspects of nineteenth century geometry that are of major interest for philosophy and hints in passing, at their philosophical significance. |
 | | However, it had been practised in arithmetic for centuries, as the initial stock of natural numbers 1, 2, 3, …, was supplemented with zero, the negative integers, the non-integral rationals, the irrationals, and the so-called imaginary numbers. |
| plato.stanford.edu /entries/geometry-19th (5103 words) |
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