| 41. | This discovery forced the abandonment of the pretensions to the absolute truth of Euclidean geometry.
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| 42. | Non-Euclidean geometry considers spaces where Euclid's parallel postulate fails.
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| 43. | Euclid of Alexandria authored the earliest extant axiomatic presentation of Euclidean geometry and number theory.
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| 44. | Euclidean geometry can be axiomatically described in several ways.
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| 45. | The book also includes proofs in Euclidean geometry.
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| 46. | Points are considered fundamental objects in Euclidean geometry.
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| 47. | Articles on noneuclidean geometry compare to Euclidean geometry.
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| 48. | But Euclidean geometry distinguish " regular polytopes ".
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| 49. | Walter ( 1999 ) re-examined Minkowski's non-Euclidean geometry.
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| 50. | Both Non-Euclidean geometry and four-dimensional space are discussed.
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