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Part I The Mathematical Sciences Chapter 1 Intuition and Logic in Mathematics
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Part I
The Mathematical Sciences
Chapter 1
1
It is impossible to study the works of the great mathematicians3, or even those of the lesser4, without noticing and distinguishing two opposite tendencies, or rather two entirely5 different kinds of minds. The one sort are above all preoccupied6 with logic; to read their works, one is tempted7 to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches8 against the place besieged9, leaving nothing to chance. The other sort are guided by intuition and at the first stroke make quick but sometimes precarious10 conquests, like bold cavalrymen of the advance guard.
The method is not imposed by the matter treated. Though one often says of the first that they are analysts12 and calls the others geometers, that does not prevent the one sort from remaining analysts even when they work at geometry, while the others are still geometers even when they occupy themselves with pure analysis. It is the very nature of their mind which makes them logicians or intuitionalists, and they can not lay it aside when they approach a new subject.
Nor is it education which has developed in them one of the two tendencies and stifled14 the other. The
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logic
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| n.逻辑(学);逻辑性 | |
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mathematician
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| n.数学家 | |
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mathematicians
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| 数学家( mathematician的名词复数 ) | |
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lesser
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| adj.次要的,较小的;adv.较小地,较少地 | |
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entirely
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| ad.全部地,完整地;完全地,彻底地 | |
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preoccupied
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| adj.全神贯注的,入神的;被抢先占有的;心事重重的v.占据(某人)思想,使对…全神贯注,使专心于( preoccupy的过去式) | |
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tempted
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| v.怂恿(某人)干不正当的事;冒…的险(tempt的过去分词) | |
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trenches
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| 深沟,地沟( trench的名词复数 ); 战壕 | |
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besieged
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| 包围,围困,围攻( besiege的过去式和过去分词 ) | |
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precarious
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| adj.不安定的,靠不住的;根据不足的 | |
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analyst
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| n.分析家,化验员;心理分析学家 | |
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analysts
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| 分析家,化验员( analyst的名词复数 ) | |
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logician
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| n.逻辑学家 | |
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stifled
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| (使)窒息, (使)窒闷( stifle的过去式和过去分词 ); 镇压,遏制; 堵 | |
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accentuate
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| v.着重,强调 | |
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subdivided
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| 再分,细分( subdivide的过去式和过去分词 ) | |
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celebrated
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| adj.有名的,声誉卓著的 | |
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metallic
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| adj.金属的;金属制的;含金属的;产金属的;像金属的 | |
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precisely
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| adv.恰好,正好,精确地,细致地 | |
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enunciation
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| n.清晰的发音;表明,宣言;口齿 | |
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sketch
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| n.草图;梗概;素描;v.素描;概述 | |
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rigor
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| n.严酷,严格,严厉 | |
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demonstration
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| n.表明,示范,论证,示威 | |
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immortality
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| n.不死,不朽 | |
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forth
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| adv.向前;向外,往外 | |
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evoke
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| vt.唤起,引起,使人想起 | |
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shun
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| vt.避开,回避,避免 | |
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analytic
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| adj.分析的,用分析方法的 | |
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transformations
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| n.变化( transformation的名词复数 );转换;转换;变换 | |
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incapable
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| adj.无能力的,不能做某事的 | |
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perplexed
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| adj.不知所措的 | |
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legitimate
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| adj.合法的,合理的,合乎逻辑的;v.使合法 | |
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devoted
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| adj.忠诚的,忠实的,热心的,献身于...的 | |
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reigned
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| vi.当政,统治(reign的过去式形式) | |
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ERECTED
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| adj. 直立的,竖立的,笔直的 vt. 使 ... 直立,建立 | |
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concessions
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| n.(尤指由政府或雇主给予的)特许权( concession的名词复数 );承认;减价;(在某地的)特许经营权 | |
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derivative
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| n.派(衍)生物;adj.非独创性的,模仿他人的 | |
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derivatives
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| n.衍生性金融商品;派生物,引出物( derivative的名词复数 );导数 | |
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attain
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| vt.达到,获得,完成 | |
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equilibrium
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| n.平衡,均衡,相称,均势,平静 | |
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attained
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| (通常经过努力)实现( attain的过去式和过去分词 ); 达到; 获得; 达到(某年龄、水平、状况) | |
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awakened
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| v.(使)醒( awaken的过去式和过去分词 );(使)觉醒;弄醒;(使)意识到 | |
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tautologies
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| n.同义反复,赘述( tautology的名词复数 );恒真命题 | |
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synthetic
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| adj.合成的,人工的;综合的;n.人工制品 | |
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judgment
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| n.审判;判断力,识别力,看法,意见 | |
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induction
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| n.感应,感应现象 | |
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passionately
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| ad.热烈地,激烈地 | |
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precocious
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| adj.早熟的;较早显出的 | |
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instinctive
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| adj.(出于)本能的;直觉的;(出于)天性的 | |
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generalization
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| n.普遍性,一般性,概括 | |
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enunciated
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| v.(清晰地)发音( enunciate的过去式和过去分词 );确切地说明 | |
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enunciate
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| v.发音;(清楚地)表达 | |
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syllogism
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| n.演绎法,三段论法 | |
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imprisoning
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| v.下狱,监禁( imprison的现在分词 ) | |
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renouncing
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| v.声明放弃( renounce的现在分词 );宣布放弃;宣布与…决裂;宣布摒弃 | |
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seclusion
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| n.隐遁,隔离 | |
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pertains
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| 关于( pertain的第三人称单数 ); 有关; 存在; 适用 | |
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irreproachable
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| adj.不可指责的,无过失的 | |
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remains
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| n.剩余物,残留物;遗体,遗迹 | |
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conformity
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| n.一致,遵从,顺从 | |
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distinguished
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| adj.卓越的,杰出的,著名的 | |
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verity
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| n.真实性 | |
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unreasonable
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| adj.不讲道理的,不合情理的,过度的 | |
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complement
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| n.补足物,船上的定员;补语;vt.补充,补足 | |
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antidote
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| n.解毒药,解毒剂 | |
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physiologists
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| n.生理学者( physiologist的名词复数 );生理学( physiology的名词复数 );生理机能 | |
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unity
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| n.团结,联合,统一;和睦,协调 | |
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isolated
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| adj.与世隔绝的 | |
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naturalist
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| n.博物学家(尤指直接观察动植物者) | |
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sufficiently
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| adv.足够地,充分地 | |
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analogous
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| adj.相似的;类似的 | |
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ascertained
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| v.弄清,确定,查明( ascertain的过去式和过去分词 ) | |
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elude
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| v.躲避,困惑 | |
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embark
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| vi.乘船,着手,从事,上飞机 | |
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promptly
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| adv.及时地,敏捷地 | |
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faculty
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| n.才能;学院,系;(学院或系的)全体教学人员 | |
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afterward
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| adv.后来;以后 | |
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primitive
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| adj.原始的;简单的;n.原(始)人,原始事物 | |
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frail
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| adj.身体虚弱的;易损坏的 | |
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imprint
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| n.印痕,痕迹;深刻的印象;vt.压印,牢记 | |
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aggregate
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| adj.总计的,集合的;n.总数;v.合计;集合 | |
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dissection
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| n.分析;解剖 | |
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formulating
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| v.构想出( formulate的现在分词 );规划;确切地阐述;用公式表示 | |
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scruples
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| n.良心上的不安( scruple的名词复数 );顾虑,顾忌v.感到于心不安,有顾忌( scruple的第三人称单数 ) | |
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insistence
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| n.坚持;强调;坚决主张 | |
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apparently
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| adv.显然地;表面上,似乎 | |
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demonstrations
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| 证明( demonstration的名词复数 ); 表明; 表达; 游行示威 | |
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makers
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| n.制造者,制造商(maker的复数形式) | |
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thither
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| adv.向那里;adj.在那边的,对岸的 | |
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dominant
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| adj.支配的,统治的;占优势的;显性的;n.主因,要素,主要的人(或物);显性基因 | |
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modifications
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| n.缓和( modification的名词复数 );限制;更改;改变 | |
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uncommon
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| adj.罕见的,非凡的,不平常的 | |
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penetration
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| n.穿透,穿人,渗透 | |
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evoked
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| [医]诱发的 | |
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sensuous
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| adj.激发美感的;感官的,感觉上的 | |
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entities
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| 实体对像; 实体,独立存在体,实际存在物( entity的名词复数 ) | |
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justify
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| vt.证明…正当(或有理),为…辩护 | |
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faculties
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| n.能力( faculty的名词复数 );全体教职员;技巧;院 | |
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edifice
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| n.宏伟的建筑物(如宫殿,教室) | |
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vertigo
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| n.眩晕 | |
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apropos
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| adv.恰好地;adj.恰当的;关于 | |
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conceal
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| v.隐藏,隐瞒,隐蔽 | |
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purely
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| adv.纯粹地,完全地 | |
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