部分翻译
选两条互相垂直的参考线（称为坐标轴）一条水平（称为x轴）另一条竖直（称为y轴?）。他们的交点记为O,称为原点。在x轴上，原点的右侧选择一个合适的点?该点与原点之间的距离称为单位长度，沿着y轴的垂直距离通常用同样的单位长度来测量?虽然有时候采用不同的尺度比较方便。现在平面上的每一个点都分配了一对数，称为坐标。这些数告诉我们如何定义一个点。
5-B
A geometric figure, such as a curve in the plane , is a collection ofpoints satisfying one or more special conditions. By translating these conditions into expressions,, involving the coordinates x and y, we obtain one or more equations which characterize the figure inquestion , for example, consider a circle of radius r with its center atthe origin, as show in figure 2-5-2. let P be an arbitrary point on this circle, and suppose Phas coordinates (x, y).
一个几何图形是满足一个或多个特殊条件的点集，比如平面上的曲线。通过把这些条件转化成含有坐标x和y的表达式，我们就得到了一个或多个能刻画该图形特征的方程。例如如图2-5-2所示的中心在原点，半径为r的圆，令P是原上任意一点，假设P的坐标为(x, y).
2.6 function concept and function idea
6-C The concept of function
Seldom has a single concept played so important a role inmathematics as has the concept of function. It is desirable toknow how the concept has developed.
在数学中，很少有个概念象函数的概念那样，起那么重要的作用的。因此?需要知道这个概念是如何发展起来的。
This concept, like many others ,originates in physics. The physical quantities were the forerunners of mathematical variables. And relation among them was called a functionrelation in the later 16th century.
这个概念像许多其他概念一样?起源于物理学。物理的量是数学的变量的先驱?他们之间的关系在16世纪后期称为函数关系。
For example , the formula s=16t2for the number of feet s a body falls in any number of seconds t is a function relation between s and t. it describes the way s varies with t. the studyof such relations led people in the 18th century to think of afunction relation as nothing but a formula.
例如?代表一物体在若干秒t中下落若干英尺s的公式s=16t2就是s和t之间的函数关系。它描述了s随t变化的公式?对这种关系的研究导致了18世纪的人们认为函数关系只不过是一个公 式罢了。
Only after the rise of modern analysis in the early 19th centurycould the concept of function be extended. In the extendedsense , a function may be defined as follows: if a variable y depends on another variable x in such a way that to each value of x corresponds a definite value of y, then y is a function of x.this definition serves many a practical purpose even today.