数学 mathematics, maths(BrE), math(AmE)
公理 axiom
定理 theorem
计算 calculation
运算 operation
证明 prove
假设 hypothesis, hypotheses(pl.)
命题 proposition
算术 arithmetic
加 plus(prep.), add(v.), addition(n.)
被加数 augend, summand
加数 addend
和 sum
减 minus(prep.), subtract(v.), subtraction(n.)
被减数 minuend
减数 subtrahend
差 remainder
乘 times(prep.), multiply(v.), multiplication(n.)
被乘数 multiplicand, faciend
乘数 multiplicator
积 product
除 divided by(prep.), divide(v.), division(n.)
被除数 dividend
除数 divisor
商 quotient
等于 equals, is equal to, is equivalent to
大于 is greater than
小于 is lesser than
大于等于 is equal or greater than
小于等于 is equal or lesser than
运算符 operator
数字 digit
数 number
自然数 natural number
整数 integer
小数 decimal
小数点 decimal point
分数 fraction
分子 numerator
分母 denominator
比 ratio
正 positive
负 negative
零 null, zero, nought, nil
十进制 decimal system
二进制 binary system
十六进制 hexadecimal system
权 weight, significance
进位 carry
截尾 truncation
四舍五入 round
下舍入 round down
上舍入 round up
有效数字 significant digit
无效数字 insignificant digit
代数 algebra
公式 formula, formulae(pl.)
单项式 monomial
多项式 polynomial, multinomial
系数 coefficient
未知数 unknown, x-factor, y-factor, z-factor
等式，方程式 equation
一次方程 simple equation
二次方程 quadratic equation
三次方程 cubic equation
四次方程 quartic equation
不等式 inequation
阶乘 factorial
对数 logarithm
指数，幂 exponent
乘方 power
二次方，平方 square
三次方，立方 cube
四次方 the power of four, the fourth power
n次方 the power of n, the nth power
开方 evolution, extraction
二次方根，平方根 square root
三次方根，立方根 cube root
四次方根 the root of four, the fourth root
n次方根 the root of n, the nth root
集合 aggregate
元素 element
空集 void
子集 subset
交集 intersection
并集 union
补集 complement
映射 mapping
函数 function
定义域 domain, field of definition
值域 range
常量 constant
变量 variable
单调性 monotonicity
奇偶性 parity
周期性 periodicity
图象 image
数列，级数 series
微积分 calculus
微分 differential
导数 derivative
极限 limit
无穷大 infinite(a.) infinity(n.)
无穷小 infinitesimal
积分 integral
定积分 definite integral
不定积分 indefinite integral
有理数 rational number
无理数 irrational number
实数 real number
虚数 imaginary number
复数 complex number
矩阵 matrix
行列式 determinant
几何 geometry
点 point
线 line
面 plane
体 solid
线段 segment
射线 radial
平行 parallel
相交 intersect
角 angle
角度 degree
弧度 radian
锐角 acute angle
直角 right angle
钝角 obtuse angle
平角 straight angle
周角 perigon
底 base
边 side
高 height
三角形 triangle
锐角三角形 acute triangle
直角三角形 right triangle
直角边 leg
斜边 hypotenuse
勾股定理 Pythagorean theorem
钝角三角形 obtuse triangle
不等边三角形 scalene triangle
等腰三角形 isosceles triangle
等边三角形 equilateral triangle
四边形 quadrilateral
平行四边形 parallelogram
矩形 rectangle
长 length
宽 width
菱形 rhomb, rhombus, rhombi(pl.), diamond
正方形 square
梯形 trapezoid
直角梯形 right trapezoid
等腰梯形 isosceles trapezoid
五边形 pentagon
六边形 hexagon
七边形 heptagon
八边形 octagon
九边形 enneagon
十边形 decagon
十一边形 hendecagon
十二边形 dodecagon
多边形 polygon
正多边形 equilateral polygon
圆 circle
圆心 centre(BrE), center(AmE)
半径 radius
直径 diameter
圆周率 pi
弧 arc
半圆 semicircle
扇形 sector
环 ring
椭圆 ellipse
圆周 circumference
周长 perimeter
面积 area
轨迹 locus, loca(pl.)
相似 similar
全等 congruent
四面体 tetrahedron
五面体 pentahedron
六面体 hexahedron
平行六面体 parallelepiped
立方体 cube
七面体 heptahedron
八面体 octahedron
九面体 enneahedron
十面体 decahedron
十一面体 hendecahedron
十二面体 dodecahedron
二十面体 icosahedron
多面体 polyhedron
棱锥 pyramid
棱柱 prism
棱台 frustum of a prism
旋转 rotation
轴 axis
圆锥 cone
圆柱 cylinder
圆台 frustum of a cone
球 sphere
半球 hemisphere
底面 undersurface
表面积 surface area
体积 volume
空间 space
坐标系 coordinates
坐标轴 x-axis, y-axis, z-axis
横坐标 x-coordinate
纵坐标 y-coordinate
原点 origin
双曲线 hyperbola
抛物线 parabola
三角 trigonometry
正弦 sine
余弦 cosine
正切 tangent
余切 cotangent
正割 secant
余割 cosecant
反正弦 arc sine
反余弦 arc cosine
反正切 arc tangent
反余切 arc cotangent
反正割 arc secant
反余割 arc cosecant
相位 phase
周期 period
振幅 amplitude
内心 incentre(BrE), incenter(AmE)
外心 excentre(BrE), excenter(AmE)
旁心 escentre(BrE), escenter(AmE)
垂心 orthocentre(BrE), orthocenter(AmE)
重心 barycentre(BrE), barycenter(AmE)
内切圆 inscribed circle
外切圆 circumcircle
统计 statistics
平均数 average
加权平均数 weighted average
方差 variance
标准差 root-mean-square deviation, standard deviation
比例 propotion
百分比 percent
百分点 percentage
百分位数 percentile
排列 permutation
组合 combination
概率，或然率 probability
分布 distribution
正态分布 normal distribution
非正态分布 abnormal distribution
图表 graph
条形统计图 bar graph
柱形统计图 histogram
折线统计图 broken line graph
1. Differentiate both sides of the equation and we get...
Integrate both sides of the equation and we get...
2. Differentiating both sides of the equation , we get...
Integrating both sides of the equation , we get...
3. Add (A) to (B) and we have…
(其中(A) 、(B)为某些表达式，如不等式、等式、方程等，下同)
4．Subtract (B) from (A) and we have …
5. Multiplying each term of the equation by …, we obtain…
6. Dividing the equation through by ..., we have ...
7. (A) and (B) together give …
(A) and (B) together yield …
(A) and (B) together imply …
8. Comparing (A) with (B), it is easy to see that …
9. Substituting (A) into (B), we obtain …
10. Eliminating (the parameter) t from (A) and (B),we have …
11. By introducing a new variable …, we can then rewrite (A) as follows
By introducing a new variable …, we can then rewrite (A) in the following form
12. By a simple calculation, we obtain from (A) …
定理证明过程中常见的短语和句子
1.下面的句型可用来表达“根据什么即可得到什么”的意思
According to definition , it follows …
According to hypothesis , it follows …
According to asssumptions, it follows …
According to theorem(N), it follows …
According to lemma (A) , it follows …
According to corollary (B) , it follows …
According to the remark , it follows …
According to the fact that … , it follows …
(可以把上面的“according to ”换成“ by” )
Since …, it follows …
2. 如果一个论断可以通过一些简单运算或简单推理而获得，由于这些运算或推理比较简单，读者可以自行推算，因而只需直接写出论断来，这时可用下面句型：
(1) It is easy to see that …
It is easy to show that …
It is easy to prove that …
It is easy to verify that …
It is easy to check that …
(2) It can easily be seen that …
It can easily be shown that …
It can easily be proved that …
It can easily be verified that …
It can easily be checked that …
3.如果所要提及的结论比较显浅，或是众所周知，无需作进一步的证明，这时可用下面句型：
(1) It is clear that …
It is obvious that …
It is evident that …
It is well-known that …
(2) Clearly, …
Obviously, …
Evidently,…
4.为了证明一个定理有时需要引进辅助函数，这时可用下面句型：
Let us first define the function…
Let us introduce a new function…
Let us consider the function…
Let us first investigate the function…
Let …
Set…
Define…
Put…
Consider…
5. 在一个定理中，有几个结论需要证明，其中有些结论比较明显，可不用证明，仅需证明余下结论即可，这时可用下面句型：
Since (A) and (B) are obvious, we need only prove (C).
Since (A) and (B) are trivial, we need only prove (C).
Since (A) and (B) are trivial, it suffices to prove (C)
6. 为了证明一个定理，有时我们并不是直接去证明，而是证明一个新的论断，一旦新的论断得到证明，已给定理不难由此而得证，这时可用下面句型：
以下各句用于新的论断被证明之前：
The theorem will be proved if we can show…
The result will be proved if we can show…
The theorem will be proved by showing that…
If we can prove…then the theorem follows immediately.
以下各句用于新的论断被证明之后：
The theorem is now a direct consequence of what we have proved.
The theorem follows immediately from what we have proved.
The theorem is now evident from what we have proved.
It is evident to see that the theorem holds.
7.在证明过程中，有时要用到一些早已学过的知识或技巧，这时可用下面句子，以提醒读者：
Recall that…
Notice that…
Note that…
Observe that…
In order to prove the theorem, we need the knowledge of …
In order to obtain the following equation, we need…
8. 如果需要证明的定理的假设条件是一般条件，但是，只要定理在特殊条件下成立，就不难推出定理在一般条件下也成立，这时仅需要在特殊情况下去证明定理就够了，为此可用下面句型：
Without loss of generality, we may consider…
Without loss of generality, we may assume…
Without loss of generality, we may prove the theorem in the case…
It suffices to prove the theorem in the case…
We need only consider the case…
For simplicity, we may take…
9. 如果待证的论断可用以前用过的相似的方法或步骤进行证明，则可用下面句型：
This theorem can be proved in the same way as shown before.
This statement can be proved in a similar way as shown before.
This theorem can be proved by the same method as employed in the last section.
This theorem can be completed by the method analogous to that used above.
Using the same argument as in the proof of theorem N, we can easily carry out the proof of this theorem.
We now proceed as in the proof of theorem N.
We shall adopt the same procedure as in the proof of theorem N.
10. 如果我们用的是反证法，则其开头及结尾可用下面句型：
If the statement(or assertion, conclusion) were false(or not true, not right) then…
If the assertion would not hold, then…
This is contrary to…
This contradicts the fact that…
This leads to a contradiction.
11. 表示定理已证毕或者把前面所证的总结为一结论
We have thus proved the theorem.
This completes the proof.
The proof of the theorem is now completed.
It is now obvious that the theorem holds.
Thus we have derived that …
Consequently, we infer that…
Thus we conclude that…
Thus we are led to the conclusion that …
Thus we arrive at the conclusion that …
Thus we can summarize what we have proved as the following theorem.
12. 其它
There exist(s)…such that…
We claim…in fact…
We are now in a position to…
If otherwise…
Provided that…
(variables) 二元方程
（方程的）解solution
……的充要条件是…… … if and only if … |
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