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双语句库分类列表：
数学:
Its applications extend beyond the physical sciences into, for example, biology and economics.
它的应用已超越了物理学的范围而进入到生物学和经济学这类学科的范畴
属类：自然科学-数学-
In mathematics, the power to which a base must be raised to yield a given number (e.g., the logarithm to the base 3 of 9, or log3^9, is 2, because 3^2 = 9).
在数学上指的是，为了产生一个给定的数，一个基数必须自乘的次数(例如，9对于基数3的对数，即log3^9是2，因为3^2=9)。
属类：自然科学-数学-
A common logarithm is a logarithm to the base 10. Thus, the common logarithm of 100 (log 100)is 2, because 10^2 = 100. Logarithms to the base e, in which e = 2.71828…, called natural logarithms (ln), are especially useful in calculus.
常用对数是对于基数为10的对数。于是，100的常用对数(log100)是2，因为102=100。对于基数为e(e=2.71828...)的对数叫做自然对数(ln)，在微积分中特别有用。
属类：自然科学-数学-
Logarithms were invented to simplify cumbersome calculations, since exponents can be added or subtracted to multiply or divide their bases. These processes have been further simplified by the incorporation of logarithmic functions into digital calculators and computers. See also John Napier.
发明对数是为了简化繁琐的计算，因为用幂指数的相加或相减可以等同于它们的基数的相乘或相除。将对数函数加进数字计算器和计算机后，这些过程就被进一步简化了。
属类：自然科学-数学-
In the philosophy of mathematics, the thesis that all mathematical propositions are expressible as or derivable from the propositions of pure logic.
在数学哲学中，认为数学是从逻辑推导出来的一种论点。
属类：自然科学-数学-
In mathematics, a topological space with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical dynamics. .
数学中指装配了一族局部坐标系的拓扑空间，这些局部坐标系之间由特定的坐标变换相互联系。流形出现于代数几何、微分方程式和经典动力学中。
属类：自然科学-数学-
They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.
它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。
属类：自然科学-数学-
mathematics: Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation
数学:关于结构、序和关系的科学，由计数、度量和描述物体形状等基本实践演化而来，涉及逻辑推理和数量计算。
属类：自然科学-数学-
Since the 17th century mathematics has been an indispensable adjunct to the physical sciences and technology, to the extent that it is considered the underlying language of science.
从17世纪以来，数学一直是物理科学和技术必不可少的助手。从这种程度上说，它被认为是科学的潜在语言。
属类：自然科学-数学-
Among the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics, Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, and trigonometry.
数学的主要分支有:代数学、分析、算术、组合学、欧几里德几何和非欧几里德几何、赛局论、数论、计算数学、最优化、机率论、集合论、统计学、拓扑学和三角学。
属类：自然科学-数学-
Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods
对数学理论和数学方法的范围提出科学的质问。
属类：自然科学-数学-
It began with Euclid’s Elements as an inquiry into the logical and philosophical basis of mathematics-in essence, whether the axioms of any system (be it Euclidean geometry or calculus)can ensure its completeness and consistency.
开始于欧几里德的《几何原本》，对数学的逻辑和哲学基础提出质问。其基本点是，任何系统的公理(例如欧几里德几何或微积分)是否可以保证它的完整性和一致性。
属类：自然科学-数学-
In the modern era, this debate for a time divided into three schools of thought :logicism, formalism, and intuitionism
在近代，经过一段时间的争论，分成了三派思想:逻辑主义、形式主义和直觉主义。
属类：自然科学-数学-
Logicists supposed that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer
逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来，称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在
属类：自然科学-数学-
"Formalists believed mathematics to be the manipulation of configurations of symbols according to prescribed rules, a "game" independent of any physical interpretation of the symbols."
形式主义相信数学是按照预先规定好的规则来操纵一些符号的配置，是与这些符号的任何物理解释无关的一种"游戏"
属类：自然科学-数学-
Intuitionists rejected certain concepts of logic and the notion that the axiomatic method would suffice to explain all of mathematics, instead seeing mathematics as an intellectual activity dealing with mental constructions independent of language and any external reality.
直觉主义否认某些逻辑概念，公理方法的注释已经足够解释数学的全部，而不把数学看作是处理与语言和任何外部现实无关的思想构造的一种智力活动。
属类：自然科学-数学-
In the 20th century, G?del’s theorem ended any hope of finding an axiomatic basis of mathematics that was both complete and free from contradictions.
在20世纪，哥德尔定理终止了寻找数学公理基础的任何希望，因为数学本身既是完整的，也是没有矛盾的
属类：自然科学-数学-
Branch of logic, founded by Stanisaw Leniewski, that studies class expressions and the relations between parts and wholes.
逻辑的一门分支，由莱希涅夫斯基所创立，这一分支试图理清分类表达方式并将部分与整体的关系加以理论化。
属类：自然科学-数学-
In mathematics, a set of objects equipped with a concept of distance.
数学中指一组带有距离概念的对象的集合
属类：自然科学-数学-
The objects can be thought of as points in space, with the distance between points given by a distance formula, such that: (1)the distance from point A to point B is zero if and only if A and B are identical,
可以把这些对象想成是空间中的点，两点之间的距离由距离公式给定，于是:(1)只有当A和B是重合的时候，A到B的距离才为零
属类：自然科学-数学-
| 1 | 它的应用已超越了物理学的范围而进入到生物学和经济学这类学科的范畴 | Its applications extend beyond the physical sciences into, for example, biology and economics. |
|
| 2 | 在数学上指的是，为了产生一个给定的数，一个基数必须自乘的次数(例如，9对于基数3的对数，即log3^9是2，因为3^2=9)。 | In mathematics, the power to which a base must be raised to yield a given number (e.g., the logarithm to the base 3 of 9, or log3^9, is 2, because 3^2 = 9). |
|
| 3 | 常用对数是对于基数为10的对数。于是，100的常用对数(log100)是2，因为102=100。对于基数为e(e=2.71828...)的对数叫做自然对数(ln)，在微积分中特别有用。 | A common logarithm is a logarithm to the base 10. Thus, the common logarithm of 100 (log 100)is 2, because 10^2 = 100. Logarithms to the base e, in which e = 2.71828…, called natural logarithms (ln), are especially useful in calculus. |
|
| 4 | 发明对数是为了简化繁琐的计算，因为用幂指数的相加或相减可以等同于它们的基数的相乘或相除。将对数函数加进数字计算器和计算机后，这些过程就被进一步简化了。 | Logarithms were invented to simplify cumbersome calculations, since exponents can be added or subtracted to multiply or divide their bases. These processes have been further simplified by the incorporation of logarithmic functions into digital calculators and computers. See also John Napier. |
|
| 5 | 在数学哲学中，认为数学是从逻辑推导出来的一种论点。 | In the philosophy of mathematics, the thesis that all mathematical propositions are expressible as or derivable from the propositions of pure logic. |
|
| 6 | 数学中指装配了一族局部坐标系的拓扑空间，这些局部坐标系之间由特定的坐标变换相互联系。流形出现于代数几何、微分方程式和经典动力学中。 | In mathematics, a topological space with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical dynamics. . |
|
| 7 | 它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。 | They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations. |
|
| 8 | 数学:关于结构、序和关系的科学，由计数、度量和描述物体形状等基本实践演化而来，涉及逻辑推理和数量计算。 | mathematics: Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation |
|
| 9 | 从17世纪以来，数学一直是物理科学和技术必不可少的助手。从这种程度上说，它被认为是科学的潜在语言。 | Since the 17th century mathematics has been an indispensable adjunct to the physical sciences and technology, to the extent that it is considered the underlying language of science. |
|
| 10 | 数学的主要分支有:代数学、分析、算术、组合学、欧几里德几何和非欧几里德几何、赛局论、数论、计算数学、最优化、机率论、集合论、统计学、拓扑学和三角学。 | Among the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics, Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, and trigonometry. |
|
| 11 | 对数学理论和数学方法的范围提出科学的质问。 | Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods |
|
| 12 | 开始于欧几里德的《几何原本》，对数学的逻辑和哲学基础提出质问。其基本点是，任何系统的公理(例如欧几里德几何或微积分)是否可以保证它的完整性和一致性。 | It began with Euclid’s Elements as an inquiry into the logical and philosophical basis of mathematics-in essence, whether the axioms of any system (be it Euclidean geometry or calculus)can ensure its completeness and consistency. |
|
| 13 | 在近代，经过一段时间的争论，分成了三派思想:逻辑主义、形式主义和直觉主义。 | In the modern era, this debate for a time divided into three schools of thought :logicism, formalism, and intuitionism |
|
| 14 | 逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来，称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在 | Logicists supposed that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer |
|
| 15 | 形式主义相信数学是按照预先规定好的规则来操纵一些符号的配置，是与这些符号的任何物理解释无关的一种"游戏" | "Formalists believed mathematics to be the manipulation of configurations of symbols according to prescribed rules, a "game" independent of any physical interpretation of the symbols." |
|
| 16 | 直觉主义否认某些逻辑概念，公理方法的注释已经足够解释数学的全部，而不把数学看作是处理与语言和任何外部现实无关的思想构造的一种智力活动。 | Intuitionists rejected certain concepts of logic and the notion that the axiomatic method would suffice to explain all of mathematics, instead seeing mathematics as an intellectual activity dealing with mental constructions independent of language and any external reality. |
|
| 17 | 在20世纪，哥德尔定理终止了寻找数学公理基础的任何希望，因为数学本身既是完整的，也是没有矛盾的 | In the 20th century, G?del’s theorem ended any hope of finding an axiomatic basis of mathematics that was both complete and free from contradictions. |
|
| 18 | 逻辑的一门分支，由莱希涅夫斯基所创立，这一分支试图理清分类表达方式并将部分与整体的关系加以理论化。 | Branch of logic, founded by Stanisaw Leniewski, that studies class expressions and the relations between parts and wholes. |
|
| 19 | 数学中指一组带有距离概念的对象的集合 | In mathematics, a set of objects equipped with a concept of distance. |
|
| 20 | 可以把这些对象想成是空间中的点，两点之间的距离由距离公式给定，于是:(1)只有当A和B是重合的时候，A到B的距离才为零 | The objects can be thought of as points in space, with the distance between points given by a distance formula, such that: (1)the distance from point A to point B is zero if and only if A and B are identical, |
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