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从公设的基础上严谨地推演几何学。Geometry is developed rigorously from a postulational base.

文中提出了电路理论的两个基本公设和一个假设。Two basic postulates and a hypothesis in circuit theory are provided.

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作为导言，有必要陈述该理论的一些公设。As a preamble , it is necessary to state some assumptions of the theory.

表述语言系统就是表述其公设性基本特征。To account for the linguistic system is to account for its postulated basic features.

给定任何有限个公设，在该系统内都会有无穷多个无法证明的事实。Given any finite set of axioms, we have an infinite number of truths that are unprovable in that system.

在历史的层面展现为人类的信仰从盲目崇拜，到理性公设，再到人生信念的逻辑演变。On the side of history, they opened up as a logic evolvement from eyeless worship to rational assumer, till the faith of life.

凯西的联邦公设辩护律师大卫-贝纳曼在法庭上没有发言，今天早些时候也拒绝对记者发表评论。Fury's federal public defender, David Beneman, did not speak in court and earlier in the day declined to comment to the reporters.

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公设义向专化义的转化，凭借不同的方式，经由不同的途径。The transformation of the postulated meaning to the specialized meaning relies on the different ways via the different approaches.

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.

根据广义塑性公设，证明了塑性余位势函数在应变空间塑性区的存在性。The plastic complementary potential function was proved to exist in the plastic region of strain space by virtue of the new plastic postulation.

文章认为，公设义和专化义是语义的一对重要范畴，它廓清了语言义和言语义的纷乱和纠葛。The main problem of automatic semantic analysis is to realize modeling of the lexical, sentential and textual meaning on the grounds of semantic language.

让学生们记录录像中的公设，定理及其证明。下面是数学家塞乐斯的发现的定理。Have students keep a notebook to record the postulates, theorems, and proofs of selected theorems shown in the video. The following are postulates of Thales.

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从能量公设的角度论述了自由能及其判据的普遍化形式，并对其本质内涵进行了讨论。The general form of the free energy and its criterion is educed from the energy postulate, and the essential connotation of the free energy and its criterion is discussed.

据此，我们就能够以同样的权利把模态的各原理作为公设，因为它们并不扩大自己关于一般事物的概念，而是仅仅展示概念一般而言与知识能力相联结的方式。We may postulate the Principles of Modality since they do not increase our concept of things, but only show the manner in which it is connected to the faculty of knowledge.

这倒并非是就Facebook自身进行首次公开募股的前景而言，而是Facebook已成为其他公司拓展业务的正规平台，公设市场到底如何看待这件事。Not for the social network's own IPO prospects, but for how the public markets will view Facebook as a legitimate platform for other companies to build businesses on top of.

康德主张理性宗教的三个道德公设并不正确，其中自由意志的选择与上帝的存在，是彼此矛盾的公设。The three moral postulates of rational religions claimed by Kant are not correct. Among them, the postulates about the choice by free will and the existence of God contradict each other.

目前对狭义相对论的质疑集中在“光速不变公设”和“光速不能超过推论”这两方面。After the theoretical and experimental examination, the problems of SR are concentrated on two fields—the light speed constancy postulate, and the inference of light speed cant superluminal.

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随着时代的进步，学术期刊编辑诚信的价值必然由个人美德范畴超越到社会运行规则，从个性理念的追求走向制度公设范畴。With the social development, credibility of academic journal editors has moved beyond the category of ethics and personal pursuit into a requirement of social operation and system postulation.

本文概述了如何利用应变空间表述的伊留辛公设在理论上导出奇异点上的完整的本构关系，并且还给出应用于岩石帽盖模型的一个例子。This paper derives the integrated constitutive relation at the singular point theoretically by using Hyushin's postulate in the the strain space, and gives an example applicable to the rock cap model.