几何学的

It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

这基于在赖斯大学在计算的代数学的几何学方面在过去5 年中在一个大的跨学科的计划里给的课程，包括数学，计算机科学，biomathematics和生物信息科学。

According to one of his biographers al-Wahrani Saladin was able to answer questions on Euclid the Almagest arithmetic and law but this was an academic ideal and it was study of the Qur'an and the "sciences of religion" that linked him to his contemporaries.

据他的一位传记作者al-Wahrani记载，萨拉丁能回答有关欧几里得几何学、《天文学大成》、算术和法律的问题，但这只是一种不切实际的想法，而对于《古兰经》和"宗教科学"的学习使他和同时代的人相联系。

According to one of his biographers, al-Wahrani, Saladin was able to answer questions on Euclid, the Almagest, arithmetic, and law, but this was an academic ideal and it was study of the Qur'an and the "sciences of religion" that linked him to his contemporaries.

据他的一位传记作者 al-Wahrani 记载，萨拉丁能回答有关欧几里得几何学、《天文学大成》、算术和法律的问题，但这只是一种不切实际的想法，而对于《古兰Jīng》和"宗教科学"的学习使他和同时代的人相联系。

Comprehensively making use of the basic theory, such as Space Analytic Geometry, Gear Meshing Engagement Theory, Method of Mathematical Calculation, Theory for Error Analyzing and Data Processing, the author has established the mathematical models of the new method, which has included the analytic mathematical model for precision orientation, the mathematical model for the ball's diameter and the measuring diameter, the mathematical model about the ball's centre, the calculation model for tooth alignment diviations and the model for tooth alignment error evaluation.

本文综合应用空间解析几何学、啮合原理、计算方法、误差理论与数据处理等有关基础理论，推导建立了新方法的数学模型，包括：确定定位关系的解析法数学模型，测球直径与测量半径的数学模型，测球球心的数学模型，齿向偏差的计算模型以及齿向误差的评定数学模型等。

This thesis is aimed to study the two boundary ductile shear zones of the Qilianmicrocontinent, both of them are large ductile strike-slip shear zones, and to understand thecharacteristics and nature of shearing, original mechanism, and their contribution to the orogen,through the investigation of their spatial distribution, geometry, structural analysis, chemicalcomposition of mylonite and syntectonic anatexis, and geochronology.

祁连微地体的南北边界均为大型韧性走滑剪切带。本论文旨在通过调查这两条韧性剪切带的空间分布、几何学和运动学特征，形成的温压条件、时代，探讨这些大型韧性走滑剪切作用的特征、性质，形成机制，以及它们对造山作用的贡献。

In this paper,singularity is used to study the classification of singularities of the binormal curves and focal surfaces of a spacelike in Minkowski 3-space,and also establish the relationships between singularities of these and geometric invariants of curves under the action of Lorentzian group.

应用奇点理论方法对三维Minkowski空间内由空间型曲线生成的副法线标型和可展焦曲面的奇点进行了分类，并且研究了在Lorenzian群作用下的空间型曲线的几何学不变量同这些奇点之间的关系。

Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

为eigenvalues和30个开放式问题也提供古典isoperimetric 不平等的拘谨的赠送，这本书将是对纯并且被使用数学家有用的，特别是对偏微分方程，变分法，不同几何学或者光谱的理论感兴趣的那些。

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

His against the mathematicians and against the dogmatists contain detailed arguments against each area of knowledge: the liberal arts (grammar, rhetoric, geometry, arithmetic, astronomy, and music) and what then were the three branches of philosophy—logic, physics, and ethics.

在他的《反数学学者》和《反教条论者》中，涵盖了对各个领域知识的详尽驳斥：文科的如语法学，修辞学，几何学，算学，天文学和音乐学；然后是哲学的三个分支，逻辑学，物理学和伦理学。

Although he felt the college lacked intellectual stimulation. He missed the research atCambridge, but in his first year he wrote a number of short papers about optics, color, the eye, and a method of constructing Faradays's lines of force by geometric methods.

虽然他觉得在Marischal大学过的非常自在，但在Marischal大学缺少智力的刺激，导致他错过在剑桥的研究，但他第一年还是写许多关於光学、颜色、眼睛和建造法拉第几何学方法的论文。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。