基本解释：欧几里得几何
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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 algorithm is based on a modification of Euclid s algorithm.在扩展欧几里得算法的基础上提出了有限域乘法逆元的计算方法。
The development of calculus was based on not very strict but practical thought instead of Euclid s strict thought.微积分是在不很严格、讲究实用的基础上 ,而不是在欧几里得严密思想的基础上发展起来的 。
plane Euclidean geometry平面欧几里得几何学
n-dimensional Euclidean geometryｎ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.
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。
n-dimensional Euclidean geometry in the wide sense广义ｎ维欧几里得几何学
pioneer of non-Euclidean geometry (1826-1866).（1826－1866）非欧几里得几何的创立者。
Euclid requires no prior study of mathematics.阅读欧几里得几何学无须先学习数学，
a non-Euclidean geometry that regards space is like a sphere and a line is a great circle.视空间为球而线为圆圈的非欧几里得几何学。
Euclid requires no prior study of mathematics. His book is generally an introduction to geometry, and to basic arithmetic as well.阅读欧几里得几何学无须先学习数学，他的书，概括地讲，是几何学入门，也是基础数学入门。
What we do know about Gauss's work in non-Euchidean geometry is gleaned from his letters to friends.我们所知道的高斯在非欧几里得几何上的工作是从他给朋友们的信中透露出来的。
His book is, therefore, not readily intelligible, even to scientists, unless Euclid has been read before.因此，如果事先没读过欧几里得几何学，牛顿的书是不易理解的，即使科学家也是如此。
The Elements of Euclid and the Classical Axiom Method of Geometry欧几里得的《几何原本》及几何学古典公理法
relating to geometry as developed by Euclid.关于欧几里得发展的几何学的。
geometry based on axioms different from Euclid's.基于不同于欧几里得公理的几何学。
Elements of Geometry in Chinese View;中国人眼中的欧几里得《几何原本》
Of, relating to, or being any of several modern geometries that are not based on the postulates of Euclid.非欧几里得的属于、关于或是一种不是建立在欧几里得的基本原理基础之上的现代几何的
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。
