1、2.1數(shù)學(xué)、方程與比例詞組翻譯1.數(shù)學(xué)分支branches of mathematics，算數(shù)arithmetics，幾何學(xué)geometry，代數(shù)學(xué)algebra，三角學(xué)trigonometry，高等數(shù)學(xué)higher mathematics，初等數(shù)學(xué)elementary mathematics，高等代數(shù)higher algebra，數(shù)學(xué)分析mathematical analysis，函數(shù)論function theory，微分方程differential equation2.命題proposition，公理axiom，公設(shè)postulate，定義definition，定理theorem，引理le

2、mma，推論deduction3.形form，數(shù)number，數(shù)字numeral，數(shù)值numerical value，圖形figure，公式formula，符號(hào)notation(symbol)，記法/記號(hào)sign，圖表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，條件等式equation of condition，項(xiàng)/術(shù)語(yǔ)term，集set，函數(shù)function，常數(shù)constant，方程equation，線性方程linear equation，二次方程quadratic equation

3、5.運(yùn)算operation，加法addition，減法subtraction，乘法multiplication，除法division，證明proof，推理deduction，邏輯推理logical deduction6.測(cè)量土地to measure land，推導(dǎo)定理to deduce theorems，指定的運(yùn)算indicated operation，獲得結(jié)論to obtain the conclusions，占據(jù)中心地位to occupy the centric place漢譯英（1）數(shù)學(xué)來(lái)源于人類(lèi)的社會(huì)實(shí)踐，包括工農(nóng)業(yè)的勞動(dòng)，商業(yè)、軍事和科學(xué)技術(shù)研究等活動(dòng)。 Mathematics co

4、mes from mans social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果沒(méi)有運(yùn)用數(shù)學(xué)，任何一個(gè)科學(xué)技術(shù)分支都不可能正常地發(fā)展。 No modern scientific and technological branches could be regularly developed without the applic

5、ation of mathematics. （3）符號(hào)在數(shù)學(xué)中起著非常重要的作用，它常用于表示概念和命題。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世紀(jì)之前，人們局限于初等數(shù)學(xué)，即幾何、三角和代數(shù)，那時(shí)只考慮常數(shù)。 Before 17th century, man confined himself to the elementary mathematics, i. e. , geo

6、metry, trigonometry and algebra, in which only the constants were considered. （5）方程與算數(shù)的等式不同在于它含有可以參加運(yùn)算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又稱(chēng)為條件等式，因?yàn)槠渲械奈粗客ǔＶ辉试S取某些特定的值。 Equipment is called an equation of condition i

7、n that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它來(lái)解決許多實(shí)際應(yīng)用問(wèn)題。Equations are of very great use. We can use equations in many mathematical problems. （8）解方程時(shí)要進(jìn)行一系列移項(xiàng)和同解變形，最后求出它的根，即未知量的值。 To solve the equation means to move and change the terms about without making the

8、equation untrue, until the root of the equation is obtained, which is the value of unknown term. 英譯漢1.Algebra has evolved from the operations and rules of arithmetic.The study of arithmetic begins with addition,multiplication,subtraction,and division of numbers:4+7,37682,49-22,408.In algebra we intr

9、oduce symbols or letterssuch as a,b,c,d,x,y,zto denote arbitrary numbers and，instead of special cases，we often consider general statements：a+b,cd,x-y,xa.代數(shù)是從算術(shù)的運(yùn)算和規(guī)則當(dāng)中逐漸發(fā)展起來(lái)的，算術(shù)的研究是從數(shù)的加減乘除開(kāi)始的。例如4+7，37682，49-22，408。在代數(shù)學(xué)里,我們采用符號(hào)或字母。例如a,b,c,d,x,y,z來(lái)表示任意的數(shù)字，而不考慮那些特殊情況。我們經(jīng)?？紤]的是一般的表達(dá)式，例如a+b,cd,x-y,xa。2.Th

10、e language of algebra serves a twofold purpose.First,we may use it as a shorthand to abbreviate and simplify long or complicated statements.Second,it proves a convenient means of generalizing many specific statements.代數(shù)的語(yǔ)言有兩個(gè)作用。第一個(gè)是使用它作為一種速記法去縮減和減化那些又長(zhǎng)又復(fù)雜的表達(dá)。第二，它被證明是一種概括許多具體的表達(dá)方式的便捷途徑。3.Many express

11、ions involve two or more operations.Grouping symbols tell us which operation is to be done first.The common grouping symbols are parentheses,(),brackets.,and the fraction bar,.For example,in the expression 2(3+4),we do the addition first and then we do the multiplication:2(3+4)=2(7)=14.許多數(shù)學(xué)表達(dá)式包含兩個(gè)或更

12、多的運(yùn)算。分組符號(hào)告訴我們哪一個(gè)運(yùn)算先做。常見(jiàn)的分組符號(hào)是圓括號(hào)，方括號(hào)和分?jǐn)?shù)線。例如，在數(shù)學(xué)表達(dá)公式2（3+4）里。我們先做加法再做乘法2（3+4）=2（7）=142.2 幾何與三角詞組翻譯1.學(xué)會(huì)institution，建筑師 architect, 機(jī)械師 machinist, 制圖員draftsman, 測(cè)量者surveyor, 木匠carpenter2.點(diǎn)point, 端點(diǎn)endpoint, 線line, 直線straight line, 線段 line segment, 曲線curved line, 折線 broken line, 射線ray , 平面 plane,曲面 curved

13、 surface3.立體solid, 柱體cylinder, 立方體cube,球 sphere, 棱錐pyramid,圓錐 cone ,4.圓circle,圓心 center, 直徑diameter, 半徑radius, 半圓semicircle, 弦chord, 弧arc, 優(yōu)弧major arc, 劣弧minor arc5.角angle, 邊side, 三角形triangle, 直角三角形right triangle,斜邊 hypotenuse, 直角邊right-angle side6.長(zhǎng)度length,寬度 breadth/width,厚度 thickness, 位置position7

14、.幾何的geometrical,立體的 three-dimensional , 彎曲的curved,等距離的 equidistant ,無(wú)限的 infinite8.培養(yǎng)創(chuàng)造力train originality,必須的毅力 necessary perseverance , 提高鑒賞力raise/improve the appreciation ability9.消失了的邊界vanishing boundaries/landmarks,有序性和優(yōu)美感 orderliness and sense of beauty, 幾何圖形大量存在geometric forms abound in , 定理成立的

15、先決條件a prerequisite to a theorem 漢譯英（1）許多專(zhuān)家都認(rèn)為數(shù)學(xué)是學(xué)習(xí)其他科學(xué)技術(shù)的必備基礎(chǔ)和先決條件。 Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology. （2）西方國(guó)家的專(zhuān)家認(rèn)為幾何起源于巴比倫和埃及人的土地測(cè)量技術(shù)，其實(shí)中國(guó)古代的數(shù)學(xué) 家對(duì)幾何做了許多出色的研究。 The western experts think that geometry had its orig

16、in in the measurements by the Babylonians and Egyptians of their lands. Infect, the ancient Chinese mathematicians made much remarkable study for geometry. （3）幾何的學(xué)習(xí)使學(xué)生在思考問(wèn)題時(shí)更周密和審慎，他們將不會(huì)盲目接受任何結(jié)論。 In studying geometry, the student is taught to think clearly and critically and he is led away from the p

17、ractice of blind acceptance of any conclusions. （4）數(shù)學(xué)培養(yǎng)學(xué)生的分析問(wèn)題的能力，使他們能應(yīng)用毅力、創(chuàng)造性和邏輯推理來(lái)解決問(wèn)題。 Studying mathematics can develop the students ability to analyze problems and utilizing perseverance, originality, and logical reasoning in solving the problem. （5）幾何主要不是研究數(shù)，而是形，例如三角形，平行四邊形和圓，雖然它也與數(shù)有關(guān)。 Geometry

18、 mainly studies hot numbers but figures such as triangles, parallelograms and circles, though it is related with numbers. （6）一個(gè)立體（圖形）有長(zhǎng)、寬和高；面（曲面或平面）有長(zhǎng)和寬，但沒(méi)有厚度；線（直線 或曲線）有長(zhǎng)度，但既沒(méi)有寬度，也沒(méi)有厚度；點(diǎn)只有位置，卻沒(méi)有大小。 A solid (figure) has length, width and height. A surface (curved surface or plane surface) has length

19、and width, but no thickness. A line (straight line or curved line) has length, but no width and thickness. A point has position, but no dimension. （7）射線從某個(gè)點(diǎn)出發(fā)無(wú)限延伸；兩條從同一點(diǎn)出發(fā)的射線構(gòu)成了角。這兩條射線稱(chēng)為這個(gè) 角的兩邊，當(dāng)這兩邊位于同一直線上且方向相反時(shí)，所得的角是平角。 A ray starts from a point and extends infinitely far. Two rays starting from on

20、e point form an angle, which are called two edges of the angle. When two edges lie in the same line and have opposite direction named plane angle. （8）平面上的閉曲線當(dāng)其中每一點(diǎn)到一個(gè)固定點(diǎn)的距離均相等時(shí)叫做圓。這個(gè)固定點(diǎn)稱(chēng)為圓 心，經(jīng)過(guò)圓心且其兩個(gè)端點(diǎn)在圓周上的線段稱(chēng)為這個(gè)圓的直徑，直徑的一半叫做半徑，這條 曲線的長(zhǎng)度叫做周長(zhǎng)。 A circle is a closed curve lying in one plane, all points o

21、f which are equidistant from a fixed point. The fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. Half of the diameter is called radius. The length of the circle is called circumference. 英譯漢 1.In geometry an angle i

22、s defined as the set of points determined by two rays land lhaving the same endpoint O. 在幾何學(xué)里從同一點(diǎn)O出發(fā)引出的兩條射線l和l所組成的點(diǎn)的集合叫做角。 2.In trigonometry we often interpret angles as rotations of rays.To obtain an angle we may start with a fixed ray lhaving endpoint O,and rotate it about O,in a plane,to a positi

23、on specified by ray l.We call l the initial side, lthe terminal side,and O the vertex of angle. 在三角學(xué)里，我們經(jīng)常解釋角就是射線的旋轉(zhuǎn)。在平面上，我們?cè)S會(huì)從端點(diǎn)是O的射線l開(kāi)始讓它繞著端點(diǎn)O旋轉(zhuǎn)，轉(zhuǎn)到一個(gè)位置，由射線l標(biāo)注。我們把l叫做角的始邊，l叫做角的終邊，O叫做角的頂點(diǎn)。 3.A right angle is a 90angle . An angle is acute if 090or obtuse if 90180.A straight angle is a 180angle .Two a

24、cute angles are complementary if their sum is 90.Two positive angles are supplementary if their sum is 180. 直角就是一個(gè)90的角。如果090把它叫做銳角，如果900，函數(shù) g(x)表示不超過(guò) x 的素?cái)?shù)的個(gè)數(shù)。 For a given real number x0, the function g(x) is defined by the number of primes less than or equal to x. （7）函數(shù)是一種對(duì)應(yīng)，它未必可以表示成一個(gè)簡(jiǎn)單的代數(shù)公式。 A fu

25、nction is a correspondence. It is not necessary to be expressed by a simple algebraic formula. （8）在函數(shù)的定義中，關(guān)于定義域和值域中的對(duì)象，沒(méi)對(duì)其性質(zhì)做出任何限制。 The function idea places no restriction on the nature of the objects in the domain X and in the range Y. 2.7 序列及其極限 序列及其極限 （1）序列各項(xiàng)對(duì) n 的相關(guān)性常利用下標(biāo)來(lái)表示，寫(xiě)成如下形式： a n , x n 等。

26、The dependence of every team of sequence on n is denoted by using subscript, and we write a n , x n and so on. （2）以正整數(shù)集為定義域的函數(shù)稱(chēng)為序列。 A function whose domain is the set of all positive integers is called an infinite sequence. （3）一個(gè)復(fù)值序列收斂當(dāng)且僅當(dāng)它的實(shí)部和虛部分別收斂。 A complex-valued sequence converges if and only

27、if both the real part and the imaginary part converge separately. （4） 一個(gè)序列 a n 若滿(mǎn)足： 對(duì)任意正數(shù) ， 存在另一個(gè)正數(shù) N （N可能與 有關(guān)） 使得 a n - L 對(duì)所有 n N 成立，就稱(chēng) a n 收斂于 L。 A sequence a n is said to have a limit L if, for every positive number , there is another positive number N (which may depend on ) such that In this cas

28、e, we say the sequence a n converges to L. an ? L for all n N. （5） 重要的是， 該集的每一個(gè)成員都用一個(gè)正整數(shù)標(biāo)上記號(hào)。 這樣一來(lái)， 就可以談?wù)摰谝豁?xiàng)、 第二項(xiàng)和一般項(xiàng)，即第 n 項(xiàng)。 The important thing is that each member of the set has been labeled with an integer so that we may speak of the first term, the second term and in general, the nth term. （6）若

29、無(wú)另加申明，本章研究的序列都假定具有實(shí)的項(xiàng)或復(fù)的項(xiàng)。 Unless otherwise specified, all sequences in this chapter are assumed to have real or complex terms. （7）作為日常用語(yǔ)，sequence 和 series 是同義詞；但作為數(shù)學(xué)術(shù)語(yǔ)，它們表示不同的概念。 In everyday usage of the English language, the words “sequence” and “series” are synonyms, but in mathematics these word

30、s have special technical meanings. （8）術(shù)語(yǔ)“收斂序列”指的是具有有限極限的序列，因此，極限為無(wú)限的序列不是收斂的， 而是發(fā)散的。 The phrase “convergent sequence” is used only for a sequence whose limit is finite. A sequence with an infinite limit is said to diverge not convergence. 2.8 函數(shù)的導(dǎo)數(shù)和它的幾何意義 （1）差商表示函數(shù) f 在連接 x 與 x+h 的區(qū)間上的平均變化率。 The diffe

31、rent quotient is referred to as the average rate of the change of f in the interval joining x to x+h. （2）速度等于位置函數(shù)的導(dǎo)數(shù)。 Velocity is equal to the derivative of positing. （3）由定義導(dǎo)數(shù)的過(guò)程所提供的幾何解釋以一種自然的方式導(dǎo)出了關(guān)于曲線的切線思想。 The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve. （4）差商表示直線 PQ 與水平線的夾角的正切。 The difference quotient represents the trigonometric tangent of the angle that PQ makes with the horizontal. （5）在直線運(yùn)動(dòng)中，速度的一階導(dǎo)數(shù)稱(chēng)為加速度。 For rectilinear motion, the first derivative of vel