基本解释：欧几里得平行公设
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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 。
Indeed, the reader who is slightly familiar with tessellations of the sphere, the Eaclidean plane and the hyperbolic plane, can easily prove the following result.事实上，稍微熟悉球面、欧几里得平面和双曲平面的分格的读者，都能容易地证明出下面的结果。
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.
Euclidean body (=rigid solid)欧几里得体,刚性体
a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane.假设在平面中同一点上可以有两个或两个以上的平行线不交叉于一个给定直线的非欧几里得几何学。
n-dimensional Euclidean geometry in the wide sense广义ｎ维欧几里得几何学
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。
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，
Elements of Geometry in Chinese View;中国人眼中的欧几里得《几何原本》
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。
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
geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line.基于欧几里得公理的几何学:例如从一点只可以劃一直线平行与另一直线。
The Comparison between Euclid s Mathematics Thoughts and Archimedes s;欧几里得与阿基米德数学思想之比较
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。
