内容概述
故事介绍古印度数学家善用“反演法”求解算术问题：从已知结果出发，逐步使用原运算的逆运算倒推回去。文中引用 6 世纪老阿利耶波多（Aryabhata）提出的一个著名算题，先按反演法逆向算出答案，再给出相应的现代方程，说明古今方法本质相同。
中文正文
92° 反演法
印度人是天才的算术家，对代数有着重要贡献。他们用反演法解决了许多算术问题，也就是通过一点已知的信息逆向地求出问题的答案。例如6世纪时老阿利耶波多（Aryabhata）提出的一个问题：“一个妙目顾盼的美少女问我，你既知反演妙法，那我问你，什么数乘以3，再加乘积的3/4，再除以7，再减商的1/3，再自乘，再减52，再开方，再加8，再除以10，结果等于2？”根据反演法，我们从数2开始逆向计算。于是，$((2)(10)-8)^2+52=196$，$\sqrt{196}=14$，$(14)(3/2)(7)(4/7)/3=28$，即答案。可以看到，问题要除以10，我们就乘以10，问题要加8，我们就减8，问题要开方，我们就乘方，等等。正是因为用相反的运算来取代原来的运算，所以有了“反演”的名称。其实，用现代方法来解，我们也是这样做的：
\frac{(\sqrt{[(2/3)(7/4)(3x)/7]^2-52})+8}{10}=2为了解这个方程，我们两边同乘以10，然后减去8，然后平方，等等。
英文正文
92° Inversion. The Hindus were gifted arithmeticians and made significant contributions to algebra. Many of the arithmetic problems were solved by the method of inversion, where one works backward from a given piece of information. Consider, for example, the following problem given during the sixth century by the elder Aryabhata: "Beautiful maiden with beaming eyes, tell me, as thou understandst the right method of inversion, which is the number which multiplied by 3, then increased by 3/4 of the product, then divided by 7, diminished by 1/3 of the quotient, multiplied by itself, diminished by 52, by the extraction of the square root, addition of 8, and division by 10 gives the number 2?" By the method of inversion we start with the number 2 and work backward. Thus $[(2)(10) - 8]^2 + 52 = 196$, $\sqrt{196} = 14$, $(14)(3/2)(7)(4/7)/3 = 28$, the answer. Note that where the problem instructed us to divide by 10 we multiply by 10, where we were told to add 8 we subtract 8, where we were told to extract a square root we take the square, and so forth. It is the replacement of each operation by its inverse that accounts for the name inversion. It is, of course, just what we would do if we were to solve the problem by modern methods. Thus, if we let $x$ represent the sought number, we have
\{\sqrt{[(2/3)(7/4)(3x)/7]^2 - 52} + 8\}/10 = 2.To solve this we multiply both sides by 10, then subtract 8 from each side, then square both sides, and so forth.
英语学习拓展
常用词汇
arithmeticians音标/əˌrɪθməˈtɪʃənz/
算术家。
原文用法：The Hindus were gifted arithmeticians and made significant contributions to algebra.
contributions音标/ˌkɒntrɪˈbjuːʃənz/
贡献。
原文用法：The Hindus were gifted arithmeticians and made significant contributions to algebra.
inversion音标/ɪnˈvɜːrʒən/
反演，逆向。
原文用法：Many of the arithmetic problems were solved by the method of inversion.
quotient音标/ˈkwoʊʃənt/
商。
原文用法：then divided by 7, diminished by 1/3 of the quotient.
extraction音标/ɪkˈstrækʃən/
提取，开方。
原文用法：by the extraction of the square root.
instructed音标/ɪnˈstrʌktɪd/
指示，要求。
原文用法：Note that where the problem instructed us to divide by 10 we multiply by 10.
accounts音标/əˈkaʊnts/
解释，说明。
原文用法：It is the replacement of each operation by its inverse that accounts for the name inversion.
sought音标/sɔːt/
所求的。
原文用法：if we let x represent the sought number.
同义词与近义词
对应核心词汇 arithmetician。
arithmetician 侧重“算术专家”，mathematician 泛指“数学家”，范围更广。
原文用 arithmeticians 突出古印度人在算术计算上的天赋。
对应核心词汇无，但均表示“减少”。
diminish 较书面，常用于数学语境；decrease 最常用；reduce 强调“降低到更小”。
对应核心词汇：sought
对应核心词汇 sought。
sought 是 seek 的过去分词，作形容词用，意为“被寻找的”，常见于数学文本；required 强调“必需的”；desired 强调“期望的”。
常用短语与固定搭配
- method of inversion：反演法。原文用法：Many of the arithmetic problems were solved by the method of inversion.
- work backward：逆向工作，倒推。原文用法：By the method of inversion we start with the number 2 and work backward.
- accounts for：解释……的原因。原文用法：It is the replacement of each operation by its inverse that accounts for the name inversion.
- both sides：两边。原文用法：To solve this we multiply both sides by 10.
- and so forth：等等，诸如此类。原文用法：then square both sides, and so forth.
常用句式
- Pattern: It is ... that ...（强调句）：正是……。原文例句：It is the replacement of each operation by its inverse that accounts for the name inversion.（正是用逆运算取代每一步运算，解释了“反演”这一名称的由来。）
- Pattern: Consider, for example, ...：例如，考虑……。原文例句：Consider, for example, the following problem given during the sixth century by the elder Aryabhata.
- Pattern: where ...：在……情况下；在那里。原文例句：Many of the arithmetic problems were solved by the method of inversion, where one works backward from a given piece of information.
长难句解析
The Hindus were gifted arithmeticians and made significant contributions to algebra.
- 主干：The Hindus were gifted arithmeticians（印度人是天才的算术家）。
- 并列谓语：made significant contributions to algebra（对代数做出了重大贡献）。
- 理解要点：句中 gifted 作形容词，意为“有天赋的”；make contributions to 是固定搭配，表示“对……做出贡献”。
It is the replacement of each operation by its inverse that accounts for the name inversion.
- 主干：强调句 It is ... that ...，被强调部分是 the replacement of each operation by its inverse（用逆运算取代每一步运算）。
- 从句/结果：accounts for the name inversion（解释了“反演”名称的由来）。
- 理解要点：replacement ... by ... 表示“用……替换……”；account for 表示“解释、说明”。
语言使用特点
- 文本为数学史叙述，时态以一般过去时和一般现在时为主。
- 频繁使用被动语态和强调句，突出数学概念和方法。
- 引用阿利耶波多的问题时使用古英语第二人称 thou understandst，增加历史感，阅读时不必逐字模仿，但需注意其语法形式。
迁移练习
- 用 account for 仿写一句：解释你为什么喜欢某种学习方法。
- 把原文中的强调句 It is the replacement of each operation by its inverse that accounts for the name inversion. 改写成普通陈述句。
- 用 work backward 描述一次你通过倒推解决实际问题的经历。
点击展开参考答案
- （示例）His curiosity accounts for his success in science experiments.
- （示例）The replacement of each operation by its inverse accounts for the name inversion.
- （示例）When I forgot the original price of a discounted item, I worked backward from the final bill to find it.