In the Hilbert axiom system it is just an axiom (contract Axiom),whereas in Euclidean geometry systems it is proved by sports intuitive,which was later proved to be a lot of criticism for being not strict.
本文讨论“边、角、边”定理,在希尔伯特公理体系中这是作为一条公理的(即合同公理),而在欧几里德几何体系中是用运动的直观来证明的,这样的证明后来受到很多非议,主要是说它不严格。
Examination of the possible world in Europead s geometrical system based on pure deduction;
对欧几里德几何体系之可能世界的考察——以纯粹演绎的观点为基础
Euclid geometry is the first system of Axiomatizing and non-Euclid geometry causes the strict examination to Euclid geometry.
欧几里得几何是第一个公理化体系,非欧几何的出现促使人们对它的基础作了严格审视,其中希尔伯特公理化方法最为成功;但它的相容性问题一直没有解决,集合论悖论使得这个问题更加尖锐。
The non-Euclidena geometries were in effect subordinated to Euclidean geometry.
非欧几里德几何实际上是从属于欧几里德几何的。
Movement Axiom of Euclid Geometric System and High School Maths Education
欧几里德几何体系中运动与中学教学
He did not grant independent existence to the non-Euclidean geometries.
他不承认非欧几里德几何的独立存在性。
The common conclusion was the uniqueness and necessity of Euclidean geometry.
欧几里德几何的唯一性与必要性已被公认。
Science should always try to use Euclidean geometry and vary the laws of physics where necessary.
科学应该永远试用欧几里德几何学，并在必要处改变物理定律。
But none of the mathematicians believed that these basic non-Euclidean geometries would be physically significant.
但数学家们无人相信这些基本的非欧几里德几何必然有物理意义。
Each innovation destined to dwarf the one extensive accomplishment of the Greeks-Euclidean geometry.
每一个创新都注定希腊人的巨大成就--欧几里德几何相形见绌。
The advent of the theory of relativity forced a drastic change in the attitude toward non-Euclidean geometry.
相对论的发现迫使对待非欧几里德几何的态度有激烈的变化。
Economics is not a straightforward discipline like Newtonian mechanics or Euclidean geometry.
经济学不像牛顿力学或者欧几里德几何，它不是门直观的学科。
In the case of non-Euclidean geometry he published no definitive work.
至于非欧几里德几何，他没有发表过权威性的著作。
Examination of the possible world in Europead s geometrical system based on pure deduction;
对欧几里德几何体系之可能世界的考察——以纯粹演绎的观点为基础
Historical Materialism and Euclidean Geometry in History: A Critical Reading of Baudrillard s The Mirror of Production;
历史唯物主义与历史中的欧几里德几何学——鲍德里亚《生产之镜》的批判性解读
plane Euclidean geometry
平面欧几里得几何学
n-dimensional Euclidean geometry
ｎ维欧几里得几何学
noneuclidean geometry
非欧几里得几何(学)
the postulates of Euclideangeometry
欧几里得几何学的公设.
Euclid was not always right.
欧几里德不一定全对。
of or relating to Riemann's non-Euclidean geometry.
属于或关于黎曼几何学而非欧几里得几何学的。