第21数学方程与比例.pptx

Key points:useful terms and definitions of Mathematics,equation and geometryDifficult points:Some geometrical termsRequirements:1.掌握所讲课文的生词和词组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理解所讲段落的翻译技巧与方法 New Words&Expressions:geometry n.几何学几何学function theory 函数论函数论 trigonometry n.三角学三角学 conception n.概念概念algebra n.代数学代数学 proposition 命题命题equation 方程方程,等式等式 definition 定义定义mathematical analysis 数学分析数学分析 logical deduction 逻辑推理逻辑推理,推论推论Roman-number n.罗马数字罗马数字notation 符号符号,记号记号higher mathematics 高等数学高等数学constant n.常量常量differential equation 微分方程微分方程 variable adj.变化的变化的,n.变量变量formula 公式公式 even number 偶数偶数equation of condition 条件等式条件等式 linear equation 线性等式线性等式arithmetic 算术算术,算术的算术的 identity 恒等式恒等式algebraic 代数的代数的 numerical 数值的数值的,数字的数字的term 项项,术语术语,命名为命名为 operation 运算运算fraction 分数分数 dimension 大小大小,维数维数,尺寸尺寸2.1 Mathematics,Equation and RatioMathematics comes from mans 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.数数学学来来源源于于人人类类的的社社会会实实践践，比比如如工工农农业业生生产产，商商业业活活动动，军军事事行行动动和和科科学学技技术术研研究究。反反过过来来，数数学学服服务务于于实实践践，并并在在各各个个领领域域中中起起着着非非常常重重要要的的作作用用。没没有有应应用用数数学学，任任何何一一个个现现在的科技的分支都不能正常发展。在的科技的分支都不能正常发展。1A What is mathematicsFrom 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.很很早早的的时时候候，人人类类的的需需要要产产生生了了数数和和形形式式的的概概念念，接接着着，测测量量土土地地的的需需要要形形成成了了几几何何，出出于于测测量量的的需需要要产产生生了了三三角角几几何何，为为了了处处理理更更复复杂杂的的实实际际问问题题，人人类类建建立立和和解解决决了了带带未未知知参参数数的的方方程程，从从而而产产生生了了代代数数学学，17世世纪纪前前，人人类类局局限限于于只只考考虑虑常常数数的的初等数学，即几何，三角几何和代数。初等数学，即几何，三角几何和代数。1A What is mathematicsThe 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世世纪纪工工业业的的快快速速发发展展推推动动了了经经济济技技术术的的进进步步，从从而而遇遇到到需需要要处处理理变变量量的的问问题题，从从常常数数带带变变量量的的跳跳跃跃产产生生了了两两个个新新的的数数学学分分支支-解解析析几几何何和和微微积积分分，他他们们都都属属于于高高等等数数学学，现现在在高高等等数数学学里里面面有有很很多多分分支支，其其中中有有数数学学分分析析，高高等等代代数数，微微分分方方程程，函数论等。函数论等。1A What is mathematicsMathematicians 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.数数学学家家研研究究的的是是概概念念和和命命题题，公公理理，公公设设，定定义义和和定定理理都都是是命命题题。符符号号是是数数学学中中一一个个特特殊殊而而有有用用的的工工具具，常常用用于于表表达达概概念念和和命题。公式，图表都是不同的符号命题。公式，图表都是不同的符号.1A What is mathematicsThe 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.数数学学结结论论主主要要由由逻逻辑辑推推理理和和计计算算得得到到，在在数数学学发发展展历历史史的的很很长长时时间间内内，逻逻辑辑推推理理一一直直占占据据着着数数学学方方法法的的中中心心地地位位，现现在在，由由于于电电子子计计算算机机的的迅迅速速发发展展和和广广泛泛使使用用，计计算算机机的的地地位位越越来来越越重重要要，现现在在计计算算机机不不仅仅用用于于处处理理大大量量的的信信息息和和数数据据，还还可可以以完完成成一一些些之之前前只只能能由由逻逻辑辑推推理理来来做做的的工工作作，例例如如，大大多多数数几几何何定定理理的证明。的证明。1A What is mathematics回顾：回顾：1如如果果没没有有运运用用数数学学，任任何何一一个个科科学学技技术术分分支支都都不不可可能能正正常常的发展的发展。2符符号号在在数数学学中中起起着着非非常常重重要要的的作作用用，它它常常用用于于表表示示概概念念和和命题。命题。1A What is mathematics 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.等等式式是是关关于于两两个个数数或或者者数数的的符符号号相相等等的的一一种种描描述述。等等式式有有两两种种恒恒等等式式和和条条件件等等式式。算算术术或或者者代代数数恒恒等等式式是是等等式式。这这种种等等式式的两端要么一样，要么经过执行指定的运算后变成一样。的两端要么一样，要么经过执行指定的运算后变成一样。1B EquationAn 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.含含有有字字母母的的恒恒等等式式对对其其中中字字母母的的任任一一组组数数值值都都成成立立。一一个个等等式式若若仅仅仅仅对对其其中中一一个个字字母母的的某某些些值值成成立立，或或对对其其中中两两个个或或着着多多个个字字母母的的若若干干组组相相关关的的值值成成立立，则则它它是是一一个个条条件件等等式式，简简称称方方程程。因因此此3x-5=7仅仅当当x=4 时时成成立立，而而2x-y=0，当当x=6,y=2时时成成立立，且且对对x,y的其他许多对值也成立。的其他许多对值也成立。1B EquationA 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.方方程程的的根根是是满满足足方方程程的的任任意意数数或或者者数数的的符符号号。方方程程有有很很多多种种，例如：例如：线性方程，二次方程等。线性方程，二次方程等。1B EquationTo 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.解解方方程程意意味味着着求求未未知知项项的的值值，为为了了求求未未知知项项的的值值，当当然然必必须须移移项项，直直到到未未知知项项单单独独在在方方程程的的一一边边，令令其其等等于于方方程程的的另另一一边边，从从而而求求得得未未知知项项的的值值，解解决决了了问问题题。因因此此解解方方程程意意味味着着进进行行一一系系列列的的移移项项和和同同解解变变形形，直直到到未未知知量量被被单单独独留留在在方方程程的的一一边边，无论那一边。无论那一边。1B EquationEquation 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.方方程程作作用用很很大大，可可以以用用方方程程解解决决很很多多数数学学问问题题。注注意意到到几几乎乎每每一一个个问问题题都都给给出出一一个个或或多多个个关关于于一一个个事事情情与与另另一一个个事事情情相相等等的的陈陈述述，这这就就给给出出了了方方程程，利利用用该该方方程程，如如果果我我们们需需要要的的话话，可可以解方程。以解方程。1B Equation回顾：回顾：1方方程程不不同同于于恒恒等等式式，它它含含有有未未知知量量，方方程程又又称称为为条条件件等等式式，因为其中的未知量通常只允许取某些特定的值因为其中的未知量通常只允许取某些特定的值。2解解方方程程时时要要进进行行一一系系列列移移项项和和同同解解变变形形，最最后后求求出出它它的的根根，即未知量的值。即未知量的值。1B EquationNew Words&Expressions:numerical 数值的，数的数值的，数的position 位置，状态位置，状态 cube n.立方体立方体 sphere n.球球cylinder n.柱体柱体 cone 圆锥圆锥geometrical 几何的几何的 triangle 三角形三角形surface 面，面，曲面曲面 pyramid 菱形菱形plane 平面平面 solid 立体，立体的立体，立体的straight line 直线直线 line segment 直线段直线段broken line 折线折线 ray 射线射线equidistant 等距离的等距离的 curve 曲线，弯曲曲线，弯曲side 边边 angle 角角radius（radii）半径半径 diameter 直径直径endpoint 端点端点 circle 圆周，圆圆周，圆semicircle 半圆半圆 arc 弧弧minor arc 劣弧劣弧 major arc 优弧优弧acute angle 锐角锐角 right angle 直角直角hypotenuse 斜边斜边 adjacent side 斜边斜边2.2 Geometry and TrigonologyMany 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.许许多多居居于于领领导导地地位位的的学学术术机机构构承承认认，所所有有学学习习这这个个数数学学分分支支的的人人都都将将得得到到确确实实的的受受益益，许许多多学学校校把把几几何何的的学学习习作作为为入入学学考考试试的先决条件，从这一点上可以证明。的先决条件，从这一点上可以证明。2A Why study geometry?Geometry 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.几几何何学学起起源源于于很很久久以以前前巴巴比比伦伦人人和和埃埃及及人人测测量量他他们们被被尼尼罗罗河河洪洪水水淹淹没没的的土土地地，希希腊腊语语几几何何来来源源于于geo，意意思思是是”土土地地“，和和metron 意意思思是是”测测量量“。公公元元前前2000年年之之前前，我我们们发发现现这这些些民民族族的的土土地地测测量量者者利利用用几几何何知知识识重重新新确确定定消消失失了了的的土土地地标标志志和和边界。边界。2A Why study geometry?A 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.立立体体是是一一个个三三维维图图形形，立立体体常常见见的的例例子子是是立立方方体体，球球体体，柱柱体体，圆圆锥锥和和棱棱锥锥。立立方方体体有有6个个面面，都都是是光光滑滑的的和和平平的的，这这些些面面被被称称为为平平面面曲曲面面或或者者简简称称为为平平面面。平平面面曲曲面面是是二二维维的的，有有长长度度和和宽度，黑板和桌子上面的面都是平面曲面的例子。宽度，黑板和桌子上面的面都是平面曲面的例子。2B Some geometrical termsOne 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.三三角角形形最最重重要要的的应应用用之之一一是是解解三三角角形形，现现在在我我们们来来解解直直角角三三角角形形。一一个个三三角角形形由由6个个部部分分组组成成，三三条条边边和和三三只只角角。解解一一个个三三角角形形就就是是要要求求出出未未知知的的部部分分。如如果果三三角角形形的的三三个个部部分分（其其中中至至少少有有一一个个为为边边）为为已已知知，则则此此三三角角形形就就可可以以解解出出。直直角角三三角角形形的的一一只只角角，即即直直角角，总总是是已已知知的的。因因此此，如如果果它它的的两两边边，或或一一边和一锐角为已知，则此直角三角形可解。边和一锐角为已知，则此直角三角形可解。2C 三角函数于直角三角形的解三角函数于直角三角形的解回顾：回顾：1许许多多专专家家都都认认为为数数学学是是学学习习其其它它科科学学技技术术的的必必备备基基础础和和先先决条件决条件。2 几几何何的的学学习习使使学学生生在在思思考考问问题题时时更更周周密密和和审审慎慎，他他们们将将不不在盲目接受任何结论。在盲目接受任何结论。3几几何何主主要要不不是是研研究究数数，而而是是形形，例例如如三三角角形形，平平行行四四边边形形和圆，虽然它也与数有关。和圆，虽然它也与数有关。22 Geometry and trigonology被动语态的译法被动语态的译法一、一、翻译成汉语的主动句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、英语原文中的主语在译文中仍做主语在在采采用用此此方方法法时时,我我们们往往往往在在译译文文中中使使用用“加加以以”,“经经过过”,“用用来来”等词来体现原文中的被动含义。等词来体现原文中的被动含义。例例1.Other questions will be discussed briefly.其他问题将简单地加以讨论其他问题将简单地加以讨论。例例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.换换言言之之,矿矿物物就就是是存存在在于于地地球球上上,但但须须经经过过挖挖掘掘、钻钻孔孔、人人工工爆爆破破或类似作业才能获得的物质。或类似作业才能获得的物质。一、一、翻译成汉语的主动句翻译成汉语的主动句2、将将英英语语原原文文中中的的主主语语翻翻译译为为宾宾语语,同同时时增增补补泛泛指指性性的的词词语语(人们，大家等人们，大家等)做主语。做主语。例例1.It could be argued that the radio performs this service as well,but on television everything is much more living,much more real.可可能能有有人人会会指指出出,无无线线电电广广播播同同样样也也能能做做到到这这一一点点,但但还还是是电电视视屏幕上的节目要生动、真实得多。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下列的结构也可以通过这一手段翻译:It is asserted that 有人主张有人主张 It is believed that 有人认为有人认为 It is generally considered that 大家大家(一般人一般人)认为认为 It is well known that 大家知道大家知道(众所周知众所周知)It will be said 有人会说有人会说 It was told that 有人曾经说有人曾经说 被动语态的译法被动语态的译法一、一、翻译成汉语的主动句翻译成汉语的主动句3、将将英英语语原原文文中中的的by,in,for等等做做状状语语的的介介词词短短语语翻翻译译成成译译文文的主语的主语,而英语原文中的主语一般被翻译成宾语。而英语原文中的主语一般被翻译成宾语。例如，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.许许多多人人认认为为,普普通通人人的的思思维维活活动动根根本本无无法法与与科科学学家家的的思思维维过过程程相相比比,而而且且认认为为这这些些思思维维过过程程必必须须经经过过某某种种专专门门的的训训练练才才能能掌掌握。握。被动语态的译法被动语态的译法一、一、翻译成汉语的主动句翻译成汉语的主动句4、翻译成汉语的无主句翻译成汉语的无主句 例如：例如：Many strange new means of transport have been developed in our century,the strangest of them being perhaps the hovercraft.在在我我们们这这个个世世纪纪内内研研制制了了许许多多新新奇奇的的交交通通工工具具,其其中中最最奇奇特特的的也许就是气垫船了。也许就是气垫船了。It is hoped that 希望希望 It is reported that 据报道据报道 It is said that 据说据说 It is supposed that 据推测据推测 It may be said without fear of exaggeration that 可以毫不夸张地说可以毫不夸张地说It must be admitted that 必须承认必须承认 It must be pointed out that 必须指出必须指出 It will be seen from this that 由此可见由此可见 被动语态的译法被动语态的译法一一、翻译成汉语的主动句、翻译成汉语的主动句5、翻译成带表语的主动句翻译成带表语的主动句例例1.The decision to attack was not taken lightly.进攻的决定不是轻易做出的。进攻的决定不是轻易做出的。例例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.总总的的来来说说,得得出出这这种种结结论论是是有有一一定定程程度度把把握握的的,但但必必须须具具备备两两个个条条件件：能能够够假假定定这这个个孩孩子子对对测测试试的的态态度度和和与与他他比比较较的的另另一一个个孩孩子子的的态态度度相相同同;他他也也没没有有因因为为缺缺乏乏别别的的孩孩子子已已掌掌握握的的有有关关知知识识而而被扣分。被扣分。被动语态的译法被动语态的译法二、二、译成汉语的被动语态译成汉语的被动语态 英英语语中中的的许许多多被被动动句句可可以以翻翻译译成成汉汉语语的的被被动动句句。常常用用“被被”,“给给”,“遭遭”,“挨挨”,“为为所所”,“使使”,“由由”,“受受到到”等等表示。表示。例例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。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.工工具具和和技技术术本本身身作作为为根根本本性性创创新新的的源源泉泉多多年年来来在在很很大大程程度度上上被被科学史学家和科学思想家们忽视了。科学史学家和科学思想家们忽视了。被动语态的译法被动语态的译法