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读欧几里德不需要先研究数学。Euclid requires no prior study of mathematics.

问题是一位瞎子如何能够，即使他能够使用点字法，他如何能够阅读欧几里得的几何学？How can a blind man, even if he is able to use Braille, how can he read Euclid?

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他沉迷于自我完善，整日整夜地研究欧几里德和语法学。He engaged in feverish bouts of self-improvement, studying Euclid and grammar at all hours.

欧几里德、欧拉，以及其他数学家们，只不过是发现了这些规律，加以文字表述而已。Euclid , Euler and all the others discovered and put into words things that were already there.

当考虑到古代的数学时，我们往往首先想到的是毕达哥拉斯和欧几里德。When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid.

他说，那种喜悦远远超过了去逛欧几里德大街那边的当地奇幻超市的快乐。A joy that cannot ever be matched, he says, by a sort hop to the local Miracle Mart just beyond Euclid Ave.

其重要性不在结果，而在欧几里德用来发展及呈现的系统性方法。Its importance lies less in its results than in the systematic method Euclid used to develop and present them.

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然后，作者又使用了一种基于边缘检测的蓝箱抠像算法，综合利用经典的图像分割算法提取前景目标。The author uses improved Euclid Distance as measurement to extract the object and tests the method in several color spaces.

像许多其他的南方人一样，我也来到这儿，沿着尤克利德大道的那些根本不可能给我们提供工作的工厂找工作，做发财梦。Like many other Southerners, I came to seek my fortune in one of those pot-at-the-end-of-the-rainbow factories along Euclid Avenue.

在此基础上，组合欧氏距离和马氏距离实现字符分类。Character classification is realized by combining the Euclid distance and the Mahalanobis distance based on the projection coefficients.

欧几里德仅仅依靠形式思维，通过图形佐证形成体系，在第29个命题中首先运用第五公设。Depending only on formal thinking, Euclid formed system through figure proof, firstly applied the fifth postulate in the 29th proposition.

研究解决了基于工作空间焊接机器人无碰撞轨迹规划问题的有效途径几何图形法。In this paper, an effective geometry-graphics method based on Euclid space for welding robot collision-free trajectory planning is studied.

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传统TOPSIS方法采用固定的欧氏距离作为距离度量，各属性间的补偿关系固定。Euclid distance metric was adopted in the Traditional TOPSIS, it leads to the problem that the compensatory relationships between each properties are fixed.

在我自学的过程中，我已经学过一些简单的算法比如，欧几里德法则并且这个法则帮助了我写了第一个程序，小数计算器。During the course of self-studying, I have learnt some simple algorithms such as Euclid algorithm which helped me create my first program, fractional calculator.

欧几里德几何是对自然的高度抽象，分形几何则更为真实地反映了自然的形式结构。Euclid geometry can be regarded as an abstraction of nature. Comparing to Euclid geometry's simpleness, Fractal geometry reflects natural contexture more veritably.

你给它渲染了一层浪漫主义色彩，简直就像是给欧几里得第五定理掺进了恋爱故事或私奔情节。You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.

将待检索图像所有值域块的欧氏距离求平均，此平均欧氏距离较小的几幅图像即为检索出的图像。Average the Euclid distances of all the range blocks in the retrieval image, then the images whose average Euclid distances are smaller are selected as the retrieval images.

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网络流量数据表现出一定的混沌特性，而在传统的混沌预测算法中，使用欧氏距离衡量相空间中相点间的相关性。The network traffic data is chaotic, and in traditional chaotic forecasting algorism, the Euclid distance is used to measure correlation between phase points in phase space.

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.

基于生态环境质量概念的模糊性和评价指标的不相容性，在模糊物元分析的基础上，结合模糊集理论和欧氏贴近度概念，建立了区域生态环境评价的模糊物元模型。On the basis of the fuzzy set theory and the concept of Euclid approach degree, a fuzzy matter-element model for assessment of regional eco-environmental quality is established.