数学专业英语(吴炯圻)(2)

curve 曲线，弯曲 straight line 直线 broken line 折线 equidistant 等距离的

2.2 几何与三角

Geometry and Trigonology

1

New Words & Expressions:

side 边

angle 角

diameter 直径 circle 圆周，圆 arc 弧 major arc 优弧 right angle 直角 adjacent side 邻边 radius（radii）半径 endpoint 端点 semicircle 半圆 minor arc 劣弧 acute angle 锐角 hypotenuse 斜边

chord 弦 circumference 周长

2

Many leading institutions of higher learning have recognized that positive benefits can be gained

by all who study this branch of mathematics.

2－A Why study geometry?

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。

This is evident from the fact that they require study of geometry as a prerequisite to

matriculation in those schools.

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。

3

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.

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。

The greek word geometry is derived from geo, meaning “earth” and metron, meaning

“measure” .

希腊语几何来源于geo ，意思是”土地“，和metron意思是”测量“。

4

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 .

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。

One of the most important objectives derived from a study of geometry is making the student be

more critical in his listening, reading and thinking. In studying geometry he is led away from the

practice of blind acceptance of statements and ideas and is taught to think clearly and critically

before forming conclusions.

几何的学习使学生在思考问题时更周密、审慎，他们将不会盲目接受任何结论.

5

第二版 课文翻译及课后习题

A solid is a three-dimensional figure. Common examples of solids are cube, sphere, cylinder, cone

and pyramid.

2－B Some geometrical terms

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。

A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply

planes.

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。

6

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.

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。

A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed

point called the center.

平面上的闭曲线当其中每点到一个固定点的距离均相当时叫做圆。固定点称为圆心。

7

A line segment drawn from the center of the circle to a point on the circle is a radius of the circle.

The circumference is the length of a circle.

经过圆心且其两个端点在圆周上的线段称为这个园的直径，这条曲线的长度叫做周长。

One of the most important applications of trigonometry is the solution of triangles. Let us now

take up the solution to right triangles.

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。

8

A triangle is composed of six parts three sides and three angles. To solve a triangle is to find the

parts not given.

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。

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.

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。

New Words & Expressions:

brace 大括号 roster 名册

consequence 结论，推论 roster notation 枚举法

designate 标记，指定 rule out 排除，否决

diagram 图形，图解 subset 子集

distinct 互不相同的 the underlying set 基础集

distinguish 区别，辨别 universal set 全集

divisible 可被除尽的 validity 有效性

dummy 哑的，哑变量 visual 可视的

even integer 偶数 visualize 可视化

irrelevant 无关紧要的 void set(empty set) 空集

第二版 课文翻译及课后习题

2.3 集合论的基本概念

Basic Concepts of the Theory of Sets

1

The concept of a set has been utilized so extensively throughout modern mathematics that an

understanding of it is necessary for all college students. Sets are a means by which

mathematicians talk of collections of things in an abstract way.

3－A Notations for denoting sets

集合论的概念已经被广泛使用，遍及现代数学，因此对大学生来说，理解它的概念是必要的。

集合是数学家们用抽象的方式来表述一些事物的集体的工具。

Sets usually are denoted by capital letters; elements are designated by lower-case letters.

集合通常用大写字母表示，元素用小写字母表示。

2

We use the special notation to mean that “x is an element of S” or “x belongs to S”.

If x does not belong to S, we write .

我们用专用记号来表示x是S的元素或者x属于S。如果x不属于S，我们记为。

When convenient, we shall designate sets by displaying the elements in braces; for example, the

set of positive even integers less than 10 is displayed as {2,4,6,8} whereas the set of all positive

even integers is displayed as {2,4,6,…}, the three dots taking the place of “and so on.”

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