2.5笛卡儿几何学的基本概念

2.5 笛卡儿几何学的基本概念

1. 翻译单词、词组、短语

(1)解析几何analytic geometry, 笛卡儿几何Cartesian geometry, 三维的three-dimensional, 坐标coordinate,坐标系 coordinate system, 坐标原点 the origin, 横坐标 abscissa,坐标轴coordinate axis,纵坐标ordinate，象限quadrant,有序对ordered pair, 尺

度

scale,

单

位

长

度

the

unit

distance

(2) 向量vector, 线段line segment, 垂直的perpendicular,水平的 horizontal, 竖直的vertical,

相

交

intersect

，

交

点

a

point

(3) 三角形triangle,直角三角形 right triangle, 斜边 hypotenuse, 直角边leg,区域area/region, 多边形的polygonal, 多边形区域polygonal region,抛物线的parabolic,

抛物线弓形 parabolic segment circular, 圆的circular，圆域circular region (4)积分的计算integral calculation, 整数的性质integral quality, 微积分的基本定理 basic

theorem

an

of

appropriate

regard

calculusp for

(5)对符号做适当认定signs,

把一个问题转化为另一个问题to reduce a question to another question,

把条件翻译成表达式to translate these conditions into expressions ， 紧

密

融

合

在

一

起

inntimately

intertwined

，

刻画了该曲线的特征2.

汉

to characterize the curve in question

译

英

（1）计算图形的面积是积分的一种重要应用。

The calculation of figure area is the important application of the integral.

（2）在 x-轴上 O 点右边选定一个适当的点，并把它到 O 点的距离称为单位长度。

On the x-axis a convenient point is chosen to the right of O and its distance from O is called the unit distance.

（3）对 xy-平面上的每一个点都指定了一个数对，称为它的坐标。

Each point in the xy-plane is assigned a pair of numbers, called its coordinates.

（4）选取两条互相垂直的直线，其中一条是水平的，另一条是竖立的，把它们的交点记作 O， 称为原点。

Two perpendicular reference lines are chosen, one horizontal, the other vertical. Their point of intersection, denoted by O, is called the origin.

（5）当我们用一对数（a, b）来表示平面的点时，商定要把横坐标写在第一个位置上。

When we write a pair of numbers such as (a, b) to represent a point, we agree that the abscissa or x-coordinate, a, is written first.

（6）微积分与解析几何在它们的发展史上已经互相融合在一起了。

Throughout their historical development, calculus and analytic geometry have been intimately intertwined.

（7）如果想拓展微积分的范围与应用，需要进一步研究解析几何，而这种研究需用到向量的方法。

A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and this study will be carried out using vector methods.

（8）今后我们要对三维解析几何做详细研究，但目前只限于考虑平面解析几何。

We shall discuss three-dimensional Cartesian geometry in more detail later on; for the present we confine our attention to plane analytic geometry.