第2-1数学方程与比例

nullMathematical English Mathematical English Chapter 2 精读课文---入门必读nullKey points: useful terms and definitions of Mathematics, equation and geometry Difficult points: Some geometrical termsnullRequirements:掌握所讲课文的生词和词组 2. 理解并掌握课外作业里面的汉译英 3. 理解所讲段落的翻译技巧与方法 nullNew Words & Expressions: geometry n. 几何学 function theory 函数论 trigonometry n. 三角学 conception n. 概念 algebra n. 代数学 proposition 命 equation 方程,等式 definition 定义 mathematical analysis 数学 logical deduction 逻辑推理,推论Roman-number n. 罗马数字 notation 符号, 记号 higher mathematics 高等数学 constant n. 常量 differential equation 微分方程 variable adj. 变化的, n.变量 formula 公式 even number 偶数 equation of condition 条件等式 linear equation 线性等式 arithmetic 算术, 算术的 identity 恒等式 algebraic 代数的 numerical 数值的, 数字的 term 项, 术语, 命名为 operation 运算 fraction 分数 dimension 大小,维数,尺寸2.1 Mathematics, Equation and RationullMathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics. 数学来源于人类的社会实践，比如工农业生产，商业活动， 军事行动和科学技术研究。反过来，数学服务于实践，并在各个领域中起着非常重要的作用。 没有应用数学，任何一个现在的科技的分支都不能正常发展。1－A What is mathematicsnullFrom the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。1－A What is mathematicsnullThe rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速发展推动了经济技术的进步， 从而遇到需要处理变量的问题，从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分，他们都属于高等数学，现在高等数学里面有很多分支，其中有数学分析，高等代数，微分方程，函数论等。1－A What is mathematicsnullMathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas ,figures and charts are full of different symbols. Some of the best known symbols of mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition, subtraction , multiplication, division and equality. 数学家研究的是概念和命题，公理，公设，定义和定理都是命题。符号是数学中一个特殊而有用的工具，常用于达概念和命题。公式，图表都是不同的符号……..1－A What is mathematicsnullThe conclusions in mathematics are obtained mainly by logical deductions and computation. For a long period of the history of mathematics, the centric place of mathematics methods was occupied by the logical deductions. Now , since electronic computers are developed promptly and used widely, the role of computation becomes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work that merely could be done earlier by logical deductions, for example, the proof of most of geometrical theorems. 数学结论主要由逻辑推理和计算得到，在数学发展历史的很长时间内，逻辑推理一直占据着数学方法的中心地位，现在，由于电子计算机的迅速发展和广泛使用，计算机的地位越来越重要，现在计算机不仅用于处理大量的信息和数据，还可以完成一些之前只能由逻辑推理来做的工作，例如，大多数几何定理的证明。1－A What is mathematicsnull回顾： 如果没有运用数学， 任何一个科学技术分支都不可能正常的发展 。 符号在数学中起着非常重要的作用，它常用于表示概念和命题。1－A What is mathematicsnull An equation is a statement of the equality between two equal numbers or number symbols. Equation are of two kinds---- identities and equations of condition. An arithmetic or an algebraic identity is an equation. In such an equation either the two members are alike. Or become alike on the performance of the indicated operation. 等式是关于两个数或者数的符号相等的一种描述。等式有两种－恒等式和条件等式。算术或者代数恒等式是等式。这种等式的两端要么一样，要么经过执行指定的运算后变成一样。1－B EquationnullAn identity involving letters is true for any set of numerical values of the letters in it. An equation which is true only for certain values of a letter in it, or for certain sets of related values of two or more of its letters, is an equation of condition, or simply an equation. Thus 3x-5=7 is true for x=4 only; and 2x-y=0 is true for x=6 and y=2 and for many other pairs of values for x and y. 含有字母的恒等式对其中字母的任一组数值都成立。一个等式若仅仅对其中一个字母的某些值成立，或对其中两个或着多个字母的若干组相关的值成立，则它是一个条件等式，简称方程。因此3x-5=7仅当x=4 时成立，而2x-y=0，当x=6,y=2时成立，且对x, y的其他许多对值也成立。1－B EquationnullA root of an equation is any number or number symbol which satisfies the equation. There are various kinds of equation. They are linear equation, quadratic equation, etc. 方程的根是满足方程的任意数或者数的符号。方程有很多种，例如： 线性方程，二次方程等。1－B EquationnullTo solve an equation means to find the value of the unknown term. To do this , we must, of course, change the terms about until the unknown term stands alone on one side of the equation, thus making it equal to something on the other side. We then obtain the value of the unknown and the answer to the question. To solve the equation, therefore, means to move and change the terms about without making the equation untrue, until only the unknown quantity is left on one side ,no matter which side. 解方程意味着求未知项的值，为了求未知项的值，当然必须移项，直到未知项单独在方程的一边，令其等于方程的另一边，从而求得未知项的值，解决了问题。因此解方程意味着进行一系列的移项和同解变形，直到未知量被单独留在方程的一边，无论那一边。1－B EquationnullEquation are of very great use. We can use equation in many mathematical problems. We may notice that almost every problem gives us one or more statements that something is equal to something, this gives us equations, with which we may work if we need it. 方程作用很大，可以用方程解决很多数学问题。注意到几乎每一个问题都给出一个或多个关于一个事情与另一个事情相等的陈述，这就给出了方程，利用该方程，如果我们需要的话，可以解方程。1－B Equationnull回顾： 方程不同于恒等式，它含有未知量，方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值 。 解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。1－B EquationnullNew Words & Expressions: numerical 数值的，数的 position 位置，状态 cube n. 立方体 sphere n. 球 cylinder n. 柱体 cone 圆锥 geometrical 几何的 triangle 三角形 surface 面， 曲面 pyramid 菱形 plane 平面 solid 立体，立体的 straight line 直线 line segment 直线段 broken line 折线 ray 射线 equidistant 等距离的 curve 曲线，弯曲 side 边 angle 角 radius（radii） 半径 diameter 直径 endpoint 端点 circle 圆周，圆 semicircle 半圆 arc 弧 minor arc 劣弧 major arc 优弧 acute angle 锐角 right angle 直角 hypotenuse 斜边 adjacent side 斜边2.2 Geometry and TrigonologynullMany leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools. 许多居于领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的受益，许多学校把几何的学习作为入学考试的先决条件，从这一点上可以证明。2－A Why study geometry?nullGeometry had its origin long ago in the measurement by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning “earth” and metron, meaning “measure” . As early as 2000 B.C. we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry . 几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地，希腊语几何来源于geo ，意思是”土地“，和metron 意思是”测量“。公元前2000年之前，我们发现这些民族的土地测量者利用几何知识重新确定消失了的土地标志和边界。2－A Why study geometry?nullA solid is a three-dimensional figure. Common examples of solids are cube, sphere, cylinder, cone and pyramid. A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. A plane surface has two dimensions, length and width. The surface of a blackboard or of a tabletop is an example of a plane surface. 立体是一个三维图形，立体常见的例子是立方体，球体，柱体，圆锥和棱锥。立方体有6个面，都是光滑的和平的，这些面被称为平面曲面或者简称为平面。平面曲面是二维的，有长度和宽度，黑板和桌子上面的面都是平面曲面的例子。2－B Some geometrical termsnullOne of the most important applications of trigonometry is the solution of triangles. Let us now take up the solution to right triangles. A triangle is composed of six parts three sides and three angles. To solve a triangle is to find the parts not given. A triangle may be solved if three parts (at least one of these is a side ) are given. A right triangle has one angle, the right angle, always given. Thus a right triangle can be solved when two sides, or one side and an acute angle, are given. 三角形最重要的应用之一是解三角形，现在我们来解直角三角形。一个三角形由6个部分组成，三条边和三只角。解一个三角形就是要求出未知的部分。如果三角形的三个部分（其中至少有一个为边）为已知，则此三角形就可以解出。直角三角形的一只角，即直角，总是已知的。因此，如果它的两边，或一边和一锐角为已知，则此直角三角形可解。2－C 三角函数于直角三角形的解null回顾： 许多专家都认为数学是学习其它科学技术的必备基础和先决条件 。 几何的学习使学生在思考问题时更周密和审慎，他们将不在盲目接受任何结论。 几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关。2－2 Geometry and trigonologynull被动语态的译法一、翻译成汉语的主动句 1、英语原文中的主语在译文中仍做主语 在采用此方法时, 我们往往在译文中使用“加以”, “经过”, “用…来”等词来体现原文中的被动含义。 例1. Other questions will be discussed briefly. 其他问题将简单地加以讨论。 例2. In other words mineral substances which are found on earth must be extracted by digging, boring holes, artificial explosions, or similar operations which make them available to us. 换言之, 矿物就是存在于地球上, 但须经过挖掘、钻孔、人工爆破或类似作业才能获得的物质。 null一、翻译成汉语的主动句 2、将英语原文中的主语翻译为宾语, 同时增补泛指性的词语(人们，大家等)做主语。 例1.It could be argued that the radio performs this service as well, but on television everything is much more living, much more real. 可能有人会指出, 无线电广播同样也能做到这一点, 但还是电视屏幕上的节目要生动、真实得多。 下列的结构也可以通过这一手段翻译: It is asserted that … 有人主张 …… It is believed that … 有人认为…… It is generally considered that … 大家(一般人)认为 It is well known that … 大家知道(众所周知)…… It will be said … 有人会说…… It was told that … 有人曾经说…… 被动语态的译法null一、翻译成汉语的主动句 3、将英语原文中的by, in, for等做状语的介词短语翻译成译文的主语, 而英语原文中的主语一般被翻译成宾语。 例如， And it is imagined by many that the operations of the common mind can be by no means compared with these processes, and that they have to be acquired by a sort of special training. 许多人认为, 普通人的思维活动根本无法与科学家的思维过程相比, 而且认为这些思维过程必须经过某种专门的训练才能掌握。 被动语态的译法null一、翻译成汉语的主动句 4、翻译成汉语的无主句 例如： Many strange new means of transport have been developed in our century, the strangest of them being perhaps the hovercraft. 在我们这个世纪内研制了许多新奇的交通工具, 其中最奇特的也许就是气垫船了。 It is hoped that … 希望…… It is reported that … 据报道…… It is said that … 据说…… It is supposed that … 据推测…… It may be said without fear of exaggeration that … 可以毫不夸张地说… It must be admitted that … 必须承认…… It must be pointed out that … 必须指出…… It will be seen from this that … 由此可见…… 被动语态的译法null一、翻译成汉语的主动句 5、翻译成带表语的主动句 例1.The decision to attack was not taken lightly. 进攻的决定不是轻易做出的。 例2. On the whole such an conclusion can be drawn with a certain degree of confidence, but only if the child can be assumed to have had the same attitude towards the test as the other with whom he is being compared, and only if he was not punished by lack of relevant information which they possessed. 总的来说, 得出这种结论是有一定程度把握的, 但必须具备两个条件：能够假定这个孩子对测试的态度和与他比较的另一个孩子的态度相同; 他也没有因为缺乏别的孩子已掌握的有关知识而被扣分。 被动语态的译法null二、译成汉语的被动语态 英语中的许多被动句可以翻译成汉语的被动句。常用“被”, “给”, “遭”, “挨”, “为……所”, “使”, “由…”, “受到”等表示。 例1. These signals are produced by colliding stars or nuclear reactions in outer space. 这些讯号是由外层空间的星球碰撞或者核反应所造成的。 例2. Over the years, tools and technology themselves as a source of fundamental innovation have largely been ignored by historians and philosophers of science. 工具和技术本身作为根本性创新的源泉多年来在很大程度上被科学史学家和科学思想家们忽视了。 被动语态的译法