Just as Euclid illuminates Newton and Galileo, so they in turn help to make Einstein intelligible.

1、

Some of these are mistakes made by Euclid that can be remedied.

有些错误是欧几里德搞错的,可以纠正.

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2、

Where Euclid unconsciously assumed the infinitude of straight lines.

欧几里得不自觉地假定了直线的无限性.

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3、

Cauchy-Buniakowski inequality is one of the important bases of the theories of Euclid ( or unitary ) spaces .

Cauchy -Buniakowski 不等式是Euclid空间理论的重要基石之一,文献[1,2]都给出了该不等式的向量内积形式.

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4、

His style shows how deeply he was influenced by Euclid's treatment of ration and proportions.

牛顿书中的写法表明,他深受欧几里得对量和比例分析的影响.

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5、

The concept of the cross product of vectors in Euclid space is introduced.

在欧式空间中引进了向量叉积的概念.

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6、

Archimedes and Euclid writings are still relevant today.

阿基米德和欧几里得的著作今天仍有意义.

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7、

Euclid requires no prior study of mathematics.

读欧几里德不需要先研究数学.

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8、

Euclid, Euler and all the others discovered and put into words things that were already there.

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.

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9、

Lastly, we extend Erd s-Mordell inequality to n dimensional Euclidean space E ~ n ( n 3 ).

并将Erds-Mordell不等式推广到n维欧氏空间E ( n3 ).

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10、

These are Regular Triangles in Non-Euclidean plane.

这些都是非欧平面上的正三角形,像不像扇子?

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11、

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.

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12、

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.

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13、

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.

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14、

There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes.

有二种主要类型的虫孔: 洛伦兹虫孔和欧几里得虫孔.

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15、

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.

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16、

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.

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17、

The common conclusion was the uniqueness and necessity of Euclidean geometry.

欧几里德几何的唯一性与必要性已被公认.

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18、

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.

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19、

The euclidean norm of an n-vector x with real or complex components is defined as following.

凡具实数分量或复数分量的n - 维向量x的欧氏范数被定义如下.

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20、

All the process of clustering based on the Euclidean distance among data vectors.

聚类过程都是根据数据之间的Euclidean(欧几里得)距离.

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