课文1—AB数学专业英语翻译(第二版)吴炯圻

1-A What is mathematics

1-A 数学是什么？

Mathematics comes from man' s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.

数学来源于人类的社会实践，例如，工农业生产，商业活动，军事行动和科学技术研究。总之，数学服务于实践且在众多领域扮演重要角色。没有数学的应用，现代科学技术分支也不会得到广泛地发展。

From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land, and trigonometry came from problems of surveying. To deal with some more complex practical problems, man established and then solved equation with unknown numbers, thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i. e. geometry, trigonometry and algebra, in which only the constants were considered.

早期数字的概念和形成源于人类的需要。之后，几何学发展源于测量土地的问题，三角学源于调查问题。为了解决某些较复杂的实际问题，人们用未知数建立方程并解决方程，因此学产生了代数。17世纪以前，人们专注研究初等数学，如几何学、三角学和代数学，其中初等数学只需考虑常数。

The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics —analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on.

17世纪，工业的快速发展推动了经济和科技的进步，同时要求解决变量。从常数到变量的跳跃带来了两个新的数学分支：解析几何和微积分，它们都属于高等数学。现在高等数学有许多分支，众多分支中有数学分析，高等代数，微分方程和函数理论等。

Mathematicians study conceptions and propositions. Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas, figures and charts are full of different symbols. Some of the best known symbols of mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0, and the signs of ad- dition "+" , subtraction "-" , multiplication "x" , division "" and equality “="

数学研究概念和命题。公理、公设、定义和定理都是命题。符号是一个特殊的，强大的数学工具，它经常被用来表达概念和命题。公式，图形和图表是不同的符号。一些显著周知的数学象征符号，如阿伯数字1.2、3、4、5、6、7.8.9.0和符号加“＋”，减“一”，乘“x”，除“÷”和相等“二”。

The conclusions in mathematics are obtained mainly by logical deductions and computation. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions. Now, since electron-ic computers are developed promptly and used widely, the role of computation be-comes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work that merely could be sdone earlier by logical deductions, for example, the proof of most of geometrical theorems

数学的结论主要由逻辑推导和计算得到。在数学历史的很长一段时期，逻辑推理占据了数学方法的中心位置。现在，自从电子计算机的迅速发展和广泛使用，计算的角色变得越来越重要。现在，计算不仅被用来解决大量的信息和数据，而且被用来解决一些在以前由逻辑推理几乎不能完成的工作，例如，大多数的几何学定理的证明。

1-B Equation

An equation is a statement of the equality between two equal numbers or number symbols. Thus a(a-5)= a2-5a and x-3-5 are equations.

Equations are of two kinds - identities and equations of condition.

1-B 等式

等式是相等的一种陈述，体现在相等的教或相等符号上。

因此a(a-5)=a2-5a和x-3=5都是等式．

等式有两种-恒等式和条件等式。

An arithmetic or an algebraic identity is an equation. In such an equation either the two members are alike, or become alike on the performance of the indicated operation.

Thus 12-2=2+8, (m+n) (m-n)= m2-n2 are identities.

An identity involving letters is true for any set of numerical values of the letters in it.

Thus the identity x(a+2)= ax+2x becomes 3(7+2)= 21+6 or 27=27, when, for example, x=3, and a=7.

一个算术的或代数的恒等式是一个等式。在这样的等式中要么两个数字相等，要么在指定的运算形式上相同。

因此12-2=2+8.(m+n)(m-n)=m2-n2都是恒等式．

含有字母的恒等式对其中字母取的任何一组数值都成立。

因此恒等式x(a+2)=ax+2x，当x=3,a=7时·即变成3(7+2)=21+6或27=27.

An equation which is true only for certain values of a letter in it, or for certain sets of related values of two or more of its letters, is an equation of condition, or simply an equation. Thus 3x-5 -7 is true for x=4 only; and 2x-y=10 is true for x=6 and y=2 and for many other pairs of values for x and y.

只有当字母赋予特定数值，或字母赋予两个或更多相关的数值之后，条件等式或简单的等式