| 仿射几何的公理体系 |
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| 引用本文： | 侯忠义,王智秋.仿射几何的公理体系[J].首都师范大学学报(自然科学版),1992(3). |
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| 作者姓名： | 侯忠义 王智秋 |
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| 作者单位： | 北京师范学院数学系
(侯忠义)，北京师范学院数学系(王智秋) |
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| 摘 要： | 本文证明了,在欧氏几何Hilbert公理体系中,如果删去合同关系和合同公理,同时把平行公理强化成V’:“在同一平面上已知直线a和线外一点A。则过A点有且仅有一条直线b与a平行。”则得到三维仿射几何的公理体系。
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| 关 键 词： | 仿射几何 欧氏几何 公理体系 |
The Axiom System of Affine Geometry |
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| Hou Zhongyi,Wang Zhiqiu.The Axiom System of Affine Geometry[J].Journal of Capital Normal University(Natural Science Edition),1992(3). |
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| Authors: | Hou Zhongyi Wang Zhiqiu |
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| Institution: | Hou Zhongyi,Wang Zhiqiu Department of Mamthmetics,Beijing Teachers' College |
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| Abstract: | The paper provs: if the congruence relation and congruence axiom areremoved from the H-1bert axiom systems of Euclidean geometry and theparallel axioms sterengthened as follows: V': On the same plane give a linea and a point A outside a, there exists one and only one line b passing thro-ugh A and parallels to a, the axiom system of the 3-dimensional affine ge-ometry canbe gottened. |
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| Keywords: | affine geometry Euclidean geometry axion system |
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