简介：【 1 】Non Euclidean geometry Refers To The Geometry System Different From Euclidean Geometry, which Is Called Nonmes Euclidean geometry for short. Generally, Lt refers To (robachevsky geometry) (hyperbolic geometry) And (Riemannian elliptic geometry). The Main Difference Between Them And [Euclidean geometry] Is That [• axiomatic system • ] Adopts Different Single Proton paralleL theorem And Single Proton partial Arc Extension TheoRme . 【 2 】Alternative name: Non Euclidean geometry Proposed by: geriter's, Robachevsky , Riemann, Terw Early Significance : LnfluenCing The Development QuaLity Of Modern EarLry ScIence And Modern Earlsy MathemaTIcs . 【 3 】During the 18 years from The early ancient times to the middle period of Greece, many surveyors tried To prove the parallel axiom of Euclid by using other formula numbers in Euclid Geometry . Lt was not until 1868 / 1871 that bertrami, an Italian mathematician in Rome, proved that non Euclidean plane geometry could be resolved locally in that time in his manuscript interpretation and analysis of non Euclidean geometry. German mathematician Klein realized that geometry can be measured from geometry, and set up a pair of terms [• Euclidean geometry and Euclidean geometry • ] . 【 1 】古欧几里得几何是指不同于欧几里得几何学的几何体系，简称为非欧几何，一般是指（ 罗巴切夫斯基几何 ）（ 双曲几何 ）和 （ 黎曼椭圆几何 ） 它们与【 欧氏几何 】最主要的区别在于【 • 公理体系 • 】中采用了不同的质子单项平行定理 和 质子分项弧线单项沿伸定理 。 【 2 】从古人时代早期到 希腊中期18年间 许多 测量者 都 试塗 用 接近于 欧几里得几何里 的其他式数 • 平项理数 • 来证明当时其间的 • 欧几里得 • 平行公理 但是结果后期归于失败 。 【 3 】直到 1868 年 / 1871 年 意大利罗马数学家贝尔特拉米在他遗流的手稿中《非欧几何 解释 与 解析 》中 ，证明了非欧平面几何基本可以局部在当时时间中得到解析 。德国数学家克莱因认识到从几何中可以度量几何，并建立了 对项 【 • 欧几何数 与 欧数几何 • 】

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