基本解释：非德萨格几何
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, his students and cooperators construct geometric lattice by means of linear spaces,and discuss the geometric lattice that generated by various orbits or subspaces with the same dimension or rank under the action of classical groups over finite field.在国内，万哲先与他的学生和合作者们利用线性空间的办法，讨论了在有限域上的典型群作用下，由各个轨道或相同维数和秩的子空间生成的几何格。
The relation of inclusion between sets generated by different orbits,the condition that a subspace is an elment of set generated by the given orbit,and when sets generated by orbits form geometric lattices are discussed.讨论了在辛群作用下,各个轨道生成的集合L(m,s;2ν)之间的包含关系;一个子空间是由给定的M(m,s;2ν)生成的集合L(m,s;2ν)中的一个元素的条件;以及L(m,s;2ν)何时作成几何格。
It was this concept that Riemann generalized, thereby opening up new vistas in non-Euclidean geometry.这个概念嗣后为Riemann所推广，从而在非欧几里德几何学中开辟了新前景。
noneuclidean geometry非欧几里得几何(学)
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
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。
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。
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。
plane Euclidean geometry平面欧几里得几何学
n-dimensional Euclidean geometryｎ维欧几里得几何学
the postulates of Euclideangeometry欧几里得几何学的公设.
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。
hyperbolic (non-Euclidean) geometry双曲型(非欧)几何学
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。
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。
pioneer of non-Euclidean geometry (1826-1866).（1826－1866）非欧几里得几何的创立者。
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。
Euclid requires no prior study of mathematics.阅读欧几里得几何学无须先学习数学，
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。
