《几何原本》（欧几里得几何）在中国传播了平面几何的知识。
The "Elements" (of Euclides Geometry) spreads the knowledge of plane geometry in China.
Geometry描述扁平(比如欧几里得)平面上的位置，并可用来判定诸如多边形形状和面积之类的信息。
Geometry describes locations on a flat (i.e. Euclidean) plane, and can be used to determine information such as the shape and area of a polygon.
它演奏的调子是那么悲哀，似乎老欧几里得用后腿站着吞下了氢氰酸。
The melancholy of it! As if old Euclid had stood up on his hind legs and swallowed prussic acid.
76岁的陶乐希·理查德森(Dorothy Richardson)家住俄亥俄州克利夫兰城郊的欧几里得镇。
In JUNE 76-year-old Dorothy Richardson of Euclid, Ohio, a suburb of Cleveland, discovered a fawn nestled in her garden.
在本文中，我们讨论了欧几里得和丢番图著作中与数论有关的某些问题。
In this article we discuss some questions with respect to number theory in the works of Euclid and diophantus.
有二种主要类型的虫孔：洛伦兹虫孔和欧几里得虫孔。
There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes.
基于平面欧几里得图和抽象胞腔复形理论，提出了街道网矢量数据的渐进式表达模型。
A progressive representation model for street networks of vector data was presented based on the theory of plane Euclidean graph and abstract complex cell.
根据监护的科斯马斯，约翰取得如此迅速的进展，在热烈的语言，他的传记作家，他很快等于丢番图代数和欧几里得几何。
Under the tutelage of Cosmas, John made such rapid progress that, in the enthusiastic language of his biographer, he soon equalled Diophantus in algebra and Euclid in geometry.
介绍了基于内容图像检索中多种颜色的特征提取和匹配算法，以及加权欧几里得距离、中心距的加权距离、直方图交集算法等。
Introduces color feature extraction and matching algorithms in content-based image retrieval, such as weighted Euclidean-distance, weighted centre distance, histogram intersection algorithm, etc.
本文的工作表明，欧几里得空间下的佯谬解就是辛空间下的约当型解，而且通过标准的数学方法可以直接获得所有佯谬问题的解析解。
It is revealed that the paradox solution in Euclidean space is just a solution in symplectic space in the Jordan form which can easily be obtained by conventional mathematical means.
我们都学习过，欧几里得几何中对勾股定理的证明方法，从繁杂的欧氏几何的公理开始，邦，邦邦，邦邦，邦邦。
And we learned how to prove the Pythagorean Theorem in Euclidean geometry, starting with the various axioms in Euclidean geometry, ba, ba-ba, ba-ba, ba-ba, ba bum.
本文证明了：群、欧几里得空间、距离空间和拓扑空间的公理系统的独立性。
It has been proved that the nature of independence exists in the axiomatic system of Group, Euclidean space, distance space and topological space.
由于基因表达谱非线性的特点，普通的欧几里得距离无法很好地表示基因之间的相似性度量。
As the gene expression data owns the characteristics of nonlinear and high noise, normal Euclidean distance can not represent the similarity measurement between genes.
上下文：欧几里得关于毕德哥拉斯定理的证明利用了前已证明的命题41。
Context: Euclid's proof of the Pythagorean theorem made use of the previous proven theorem known as Proposition 41.
此外，他为欧几里得系统论述几何的十二卷专著写了精彩的概要。
In addition, he wrote a brilliant synopsis of Euclid's twelve-volume systematic treatment of geometry.
理解欧几里得对毕德哥拉斯定理的证明。
本文用欧几里得算法，给出求解基矢变换对应矩阵的解析表达式。
An analytical method to find correspondence matrix for basic vector transformation is given by using elementary theory of numbers.
基于不同于欧几里得公理的几何学。
本文首先简单介绍了目前常用的两类分子空间结构相似性比较方法，一类是基于欧几里得几何距离的，另一类是基于特征相关性的。
This paper briefly introduces two classes of methods for molecular 3D structure comparison, one is based on Euclidean distances, and another is based on relativity of properties.
面积贴合法是欧几里得《几何原本》中的重要方法，它甚至涉及希腊数学的起源问题。
The application of areas, which is an important method in Euclid's Elements, involves the origin of Greek mathematics.
生活在公元前540年左右的毕达哥拉斯，便提出了闻名于世的关于直角三角形各边的 勾股定理 。古代最知名的几何学家欧几里得生活在公元前300年左右。
Pythagoras, who is remembered for his theorem about the sides of a right-angled triangle, lived around 540 BC, while Euclid, the best known geometer of the ancient world, lived around 300 BC.
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 algorithm is based on a modification of Euclids 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 algorithm is based on a modification of Euclids algorithm.
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