Study on Complex Model of Euclid Approach Degree-Grey Relational Analysis: Its Application in Environmental Quality Assessment

Euclid贴近度-灰色关联模型在环境评价中的应用

A low-latency Recursive Cell Architecture of Modified Euclid ’s Algorithm for Decoding Reed-Solomon Codes

RS译码修正Euclid算法的一种高效低延迟的实现结构

The same cannot be said for Newton, because Newton uses mathematics in the solution of physical problems. His style shows how deeply he was influenced by Euclid ’s treatment of ration and proportions.

而牛顿的书则不同，因为他使用数学解释物理问题。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。

The Functions of the External Causes in Development of Non-Euclid Geometry

非逻辑性因素在非欧几何创立中的作用

On the Estimates of Euclid Distance of the Spectrum for Arbitrary Matrices

关于任意矩阵谱的Euclid距离的估计

Scheme Evaluating Method of Highway Passenger Transportation Hub Based on Euclid Norm

基于欧氏范数的公路客运枢纽规划方案评价

Several Important Concepts and Theorems for the n Dimension Euclid Space

几个n维Euclid空间概念与定理

It began with Euclid ’s Elements as an inquiry into the logical and philosophical basis of mathematics-in essence, whether the axioms of any system (be it Euclidean geometry or calculus)can ensure its completeness and consistency.

开始于欧几里德的《几何原本》，对数学的逻辑和哲学基础提出质问。其基本点是，任何系统的公理(例如欧几里德几何或微积分)是否可以保证它的完整性和一致性。

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。

Where euclid unconsciously assumed the infinitude of straight lines

欧几里德不自觉地假定了直线的无限性。

The logical basis for the theory of the integers that euclid presented in books VII to IX of the “Elements” was woefully deficient

欧几里德在《原本》的第七到第九册中提出的整数理论的逻辑基础是十分令人遗憾地有缺陷的。

Let me illustrate this point by taking Euclid ’s elements of Geometry and Newton’s Mathematical Principles of Natural Philosophy.

让我以欧几里得的《几何学大纲》和牛顿的《自然哲学的数学原理》二书为例，来证明这一点。

The Estimates of Euclid Distance of the Spectrum for Arbitrary Matrices

任意矩阵的谱的Euclid距离的估计

Euclid and Shelley, Edmund Spenser and Herbert Spencer, King David Hume, are all followers of the art of letters.

事实上，不论欧几里德与雪莱，魂德蒙·斯宾塞与赫伯特·斯宾塞，大卫王与大卫·休漠，他们都是语言文字这门艺术的追逐者。

Discussion on the Contrast between Vector Space and Euclid Space

向量空间与欧氏空间的对比讨论

Study of points, lines, angles, surfaces, and solids based on Euclid ’s axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them.

以欧几里德的公理为基础对点、线、角、面和立体的研究。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。

His book is, therefore, not readily intelligible, even to scientists, unless euclid has been read before

因此，如果事先没读过欧几里得几何学，牛顿的书是不易理解的，即使科学家也是如此。

Euclid Algorithm for Computing the Inverse and Generalized Inverse of the Companion Circulant Matrix

友循环矩阵求逆和广义逆的Euclid算法

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。

Euclid requires no prior study of mathematics. His book is generally an introduction to geometry, and to basic arithmetic as well.

阅读欧几里得几何学无须先学习数学，他的书，概括地讲，是几何学入门，也是基础数学入门。

euclid requires no prior study of mathematics

阅读欧几里得几何学无须先学习数学。

This work was long held to constitute an accurate description of the physical world and to provide a sufficient basis for understanding it. During the 19th century, rejection of some of Euclid ’s postulates resulted in two non-Euclidean geometries that proved just as valid and consistent

这项研究工作曾长期进行，以精确地描述实体世界，并为了解几何提供了充足条件的基础。19世纪期间，一些欧几里德假设受到摈弃，因而产生了两个非欧几里德几何，并证实同样有效而连贯。

This axiomatic method has been the model for many systems of rational thought, even outside mathematics, for over 2,000 years. From 10 axioms and postulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures.

这种公理方法是2,000多年来许多理性思想体系(甚至体系外之数学)的模范。欧几里德从10个公理和假设中演绎出465个公理或命题，涉及了平面与立体几何图形各方面。

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

正如欧几里得的几何学帮助人们理解牛顿和伽利略的著作一样，它们又可帮助人们读懂爱因斯坦的书。

Just as Euclid illuminates Newton and Galileo, so they in turn help to make Einstein intelligible. The point applies to philosophical books as well.

正如欧几里得的几何学帮助人们理解牛顿和伽利略的著作一样，它们又可帮助人们读懂爱因斯坦的书。这一点也适用于哲学名著。

When Euclid originally laid down the axioms of his geometric system 23 centuries ago, one of them seemed less than obvious.

2300年前，当欧几里得（Euclidian）最初提出构成他几何体系的那些公理时，其中一个公理似乎一点也不显眼。

Research and Application of Euclid Algorithm and Extended Euclid Algorithm

Euclid算法及扩展在密码学中的研究和应用

The Effect of Mathematics Having on the Human Culture from the Foundationof Non-Euclid Geometry

从非欧几何的产生看数学对人类文化的影响

When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid .

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。

Thanks to the ancient Greek mathematician Euclid , we know that there are prime numbers out there with as many digits as we want.

跟据古希腊数学家欧几里德的理论，我们知道，我们可以找到拥有任意多位数的素数。

Euclid norm

欧几里德范数

algorithm of euclid

欧几里得算法

euclid parallel postulate

欧几里得平行公设

euclid factorization theorem for rational integers

因子分解定理