第二章精读课文-- 入门必修2.1 数学方程与比例（Mathematics，Equation and Ratio）一、词汇及短语：1. Cha nge the terms about变形2. full of ：有许多的充满的例The StreetS are full of people as on a holiday像假日一样，街上行人川流不息）3. in groups of ten∙∙4. match SOmething against sb. “匹配”例Long ago ,when people had to Count many things ,they matChed them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。
5. grow out of 源于由…引起例Many close friendships grew out of common acquaintance6. arrive at 得出（到达抵达达到达成）例We both arrived at the Same COnclusion我们俩个得出了相同的结论）7. stand for “表示，代表”8. in turn “反过来，依次”9. bring about 发生导致造成10. arise out of 引起起源于11. express by “用…表示”12. occur 发生，产生13. come from 来源于，起源于14. resulting method 推论法15. be equal to 等于的相等的例TWiCe two is equal to four（2 乘以 2 等于4）16. no matter 无论不管17. mathematical analysis 数学分析18. differential equation 微分方程19. higher mathematics 高等数学higher algebra 高等代数20. equation of condition 条件等式二句型及典型翻译1. For a long period of the history of mathematics, the centric place of mathematicalmethods was occupied by the logical deductions “在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or numbersymbols.equation ：“方程”“等式” 等式是关于两个数或数的符号相等的一种陈述3. In such an equation either the two members are alike, or become alike onperformance of the indicated operation. 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。
注“ two memberS'表等号的两端alike 相同的一样的On the PerfOrmance of∙∙∙中的“ on”引导一个介词短语做状语Either ∙∙∙or∙∙∙4. is true “成立”5. to more and Change the term移次和变形without making the equation untrue 保持方程同解2.2几何与三角Geometry and Trigondogy )1. Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. 其中“ higher Ieaming ”表示“高学识” “博学”Positive “确实的”“肯定的”全句 许多居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 实的收获。
2∙∙∙ .we find the Iand SurVeyOrS Of these people re-establishi ng VaniShing Ian dmarks and boundaries by utiIizing the truths of geometry我们发现这些民族的土地测量者利用几何只是重新确定消失了的土地标志和边 界。
3. A circle is a clOsed curVe lying in One plane, all pOint Of which are equidistant frOm a fined pOint called the center.平面上到定点的距离等于定长的所有点组成的图形叫做圆。
2.3 BaSiC Con CePtS Of the Theory Of SetSSeCtiOn A1. SetS are a means by WhiCh mathematicia ns talk of collect ions of things in anabstract Way词汇 cube 立方体、plane 平面、 abound 大量存在、 cone 圆锥、 straight line 直线、 broken line 折线、 prerequisite 先决条件、 典型句子翻译cylinder 柱体、 breadth surface 曲面、 弓形（面积）、 sphere 球solid 立体的 立体、 infinitely 无限地、 angle 角、 blind acceptance of 盲目接受geometrical 几何的、 宽度、 segment 线段 prerequisite 先决条件、 triangle 三角形、 line segment 直线段、 diameter 直径、 chord 弦、注by WhiCh引起一个定语从句talk of表达译为集合是数学家们用抽象的方式来表达一些事物的集体的工具2. belOng to …“属于”3. even integers 偶数less tha n 小于more tha n 大于4. be denoted by 被记作…5. be referred to as 被称为…6. exactly the Same 完全相同7. there fore , the definition requires that We call these SetS equal .因此，根据定义我们认为这两个集合相等8. divisible by… 被…整除SeCtiOn B1. For example, the Set conSiSting of those POSitiVe integers less than 10. WhiChare divisible by 4 is a SUbSet of the Set of all eve n in tegers less tha n.由小于10且能被4整除的正整数组成的集合是所有小于10的偶数集的子集2. A-B”读作A is con ta in ed in B or B con tai ns A3. A=B =A B and B AA is equal toB if and onIy if A is COntained in B, and B is also COntained in A4. reference to 提至卩涉及关于5. 真子集PrOPer SUbSet6. “ ” empty Set 或void Set7. 单元集one -element Set2.4 整数有理数与实数(Integers, Rational Numbers and Real Numbers)一、专业词语1 rational number 有理数irrational number 无理数2. difference 差quotient 商3 real axis 实轴4. fraction 分数denominator 分母numerator 分子5. 数学归纳法：proof by induction二、Section-A Integers and rational numbers1. 1+1=2The number 1 plus 1 is denoted by 22. Strictly speaking 严格地说3. repeated addition of 1 “反复加1”4. Convenient method 简便方法5. ordered field 有序域6. The sum, difference , or product of two integers is an integer ,but the quotient oftwo integers need not be an integer.(两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数)思考What is an inductive set?A set of real numbers is called an inductive set if it has the following two properties: (a) The number 1 is in the set(b)For every x in the set , the number x+1 is also in the set.三、Section-B Geometric interpretation of real number as points on a line1. be familiar With 熟悉…be familiar to 被某人熟悉2. If x<y, the point x lies to the left of the point y“lies to ”位于如果x<y, by x 点位于y 点的左侧3. This device for representing real numbers geometrically is a very worthwhile aidthat helps us to discover and understand better certain properties of real numbers 这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。