2-A Why study geometry?
Why do we study geometry? The student beginning the study of this text may well ask, "What is geometry? What can I expect to gain from this study?
2-A为什么研究几何学？
为什么我们研究几何学？刚开始学习这篇文章的学生会疑问，“几何是什么？研究几何我们能学到什么呢？
Many 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很好的收益。事实是，他们需要学习几何作为学校入学考试的先决条件。
Geometry had its origin long ago in the measurements 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 reestablishing vanishing landmarks and boundaries by utilizing the truths of geometry.
很早以前，几何学源于测量被尼罗河的洪水淹没了的巴比伦人和埃及人的土地。希腊语的几何学源于geo,意思是土地；metron意思是测量。早在公元前2000年，我们发现土地测量者利用几何知识重新建立消失了的地标和边界。
Geometry is a science that deals with forms made by lines. A study of geometry is an essential part of the training of the successful engineer, scientist, architect, and draftsman. The carpenter, machinist, stonecutter, artist, and designer all apply the facts of geometry in their trades. In this course the student will learn a great deal about geometric figures such as lines, angles, triangles, circles, and designs and patterns of many kinds.
几何学是解决线性形式的一门学科。几何的学习对于培养成功的工程师，科学家，建筑师和制图员是非常重要的。木匠、机械师、石匠、画家和设计师在他们领域中都应用了几何学的知识。在课堂上学生将学习很多几何的特征，如线、角、三角形、圆、各种设计和图案。
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.
一个很重要的客观原因是几何的学习能使学生在倾听、阅读和思考方面更加带有批评的观点。几何学的研究能让人不盲目地接受别人的陈述和观点，它能教人在形式结论之前要仔细地批判地思考。
There are many other less direct benefits the student of geometry may gain. mong these one must include training in the exact use of the English language and in the ability to analyze a new situation or problem into its basic parts", and utilizing perseverance, originality, and logical
reasoning in solving the problem. An apprecia- tion for the orderliness and beauty of geometric forms that abound in man's works and the creations of nature will be a byproduct of the study of geometry. The student should also develop an awareness of the contributions of mathematics and mathematicians to our culture and civilization.
学习几何的学生可能很少得到的直接好处。总之，一个人应具有训练英语的准确使用及在分析新情况与新问题时直达基本要素，和解决问题时要有毅力、创造性和逻辑推理能力。赞扬大量的人类作品和大自然创造的井然有序和美丽的几何图形，它们会成为几何研究的产物。学生也应该培养数学的贡献意识以及数学家们应对文化和文明作贡献。
2-B Some geometrical terms
1. Solids and planes. A solid is a three-dimensional figure. Common examples of solids are cube, sphere, cylinder, cone and pyramid.
2-B一些几何的术语．
1.立体和平面立体是三维的特征。常见立体图形的例子有立方体、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. 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.
一个立方体有六个光滑的平面，这些面被叫做平面或者简单平面。一个平面是两维的，包括长度和宽度。黑板面和桌面是平面的例子。
2. Lines and line segments.
We are all familiar with lines, but it is difficult to define the term. A line may be represented by the mark made by moving a pencil or pen across a piece of paper. A line may be considered as having only one dimension, length. Although when we draw a line we give it breadth and thickness, we think only of the length of the trace when considering the line. A point has no length, no width, and no thickness, but marks a position. We are familiar with such expressions as pencil point and needle point. We represent a point by a small dot and name it by a capital letter printed beside it, as "point A" in Fig. 2-2-1.
2.线和直线段我们都很熟悉直线，但却但很难定义直线。一个直线可能由铅笔或钢笔在纸上移动留下的痕迹表示。一条直线被认为仅有一维的长度。尽管我们画一条直线会给定宽度和厚度，但我们只考虑线直线痕迹的长度。一个点没有长度，宽度和厚度，但是能标记一个位置。我们熟悉这样的表示像铅笔点和指针点。我们用一个小圆点表示一个点并用大写字母在旁边写上“点A”命名该点。如图2-2-1.
The line is named by labeling two points on it with capital letters or one small letter near it. The straight line in Fig. 2-2-2 is read "line AB" or "line I". A straight line extends infinitely far in two directions and has no ends. The part of the line between two points on the line is termed a line segment. A line segment is named by the two end points., Thus, in Fig. 2-2-2, we refer to AB as a line segment of line. . When no confusion may result, the expression "line segment AB" is
often replaced by segment AB or, simply, line AB.
一条直线是用大写字母或小写字母在旁边标记两个点而命名直线”。如图2-2-2的直线读作线AB或线l.一条直线表示两个方向无限远并且无端点。直线上两点之间的直线被称为直线段。一条直线段是有两个端点命名。因此，在图2-2-2中，我们将直线l的直线段称为AB.当没有矛盾产生时，直线段AB的表达也经常用线段AB取代或简化为线AB.
There are three kinds of lines: the straight line, the broken line, and the curved line. A curved line or, simply, curve is a line no part of which is straight. A broken line is composed of joined, straight line segments, as ABCDE of Fig. 2-2-3.
这里有三种线：直线，折线和曲线。简单地，一条曲线或者弯曲的线是一条没有笔直部分的线。折线是由节点，笔直的直线段混合组成的，如图2-2-3的ABCDE.
3. Parts of a circle. A cirele is a closed curve lying in one plane, all points of which are equidistant from a fixed point called the center (Fig. 2-2-4). The symbol for a circle is O. In Fig. 2-2-4, 0 is the center of OABC, or simply of O0. A line segment drawn from the center of the circle to a point on the circle is a radius (plural, radii) of the circle. OA, OB, and OC are radii of OO. A diameter of a cir- cle is a line segment through the center of the circle with endpoints on the circle. A diameter is equal to two radii. A chord is any line segment joining two points on the cirele. ED is a chord of the circle in Fig. 2-2-4;
3.圆的部分一个圆是平面上封闭的曲线形成，圆上所有的点到圆心都是等距离的（如图2-2-4).圆的符号是⊙:在图2-2-4中，点0是⊙ABC的中心，或简记为⊙0. 从圆中心到圆上的一个点的直线段是圆的半径。OA.OB和0C是⊙0的半径，圆的直径是通过圆心在圆上有端点的直线段。直径等于两个半径。弦是连接圆上两个点的任意直线段。ED是图2-2-4上图上的弦。
From this definition it should be apparent that a diameter is a chord. Any part of a circle is an are, such as arc AE, which is denoted by AE. Points A and E divide the circle into minor arc AE and major arc ABE. A diameter divides a circle into two arcs termed semicircles, such as AB and
BCA. The circumference is the length of a circle.
根据定义显然有直径是一个弦。圆周的任何部分是一个弧，例如弧AE,它是由弧AE表示。点A和E将圆周划分为劣弧AE和优弧ABE,一个直径将圆划分为两个半圆，例如弧AB 和弧BCA.周长就是圆周的长度。