| 1. | It arises in synthetic geometry and has an associated transformation group.
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| 2. | Edwin Bidwell Wilson and Gilbert N . Lewis developed the concept within synthetic geometry in 1912.
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| 3. | In the 1890s logicians were reducing the primitive notions of synthetic geometry to an absolute minimum.
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| 4. | It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on geometric constructions.
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| 5. | This result is much more difficult in synthetic geometry ( where projective spaces are defined through axioms ).
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| 6. | It was also a subject with a large number of practitioners for its own sake, as synthetic geometry.
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| 7. | They revamped the analytic geometry implicit in the split-complex number algebra into synthetic geometry of premises and deductions.
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| 8. | If projective spaces are defined by means of axioms ( synthetic geometry ), the third part is simply a definition.
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| 9. | Note that the proof of the Pythagorean theorem in synthetic geometry is considerably more elaborate because of the paucity of underlying structure.
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| 10. | In his " Systematische Entwickelung der Abh�ngigkeit geometrischer Gestalten von einander " he laid the foundation of modern synthetic geometry.
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