内容概述
本篇讲述古代印度数学文献《巴克沙里手稿》（Bakhshali manuscript）中所使用的“试位法”（rule of false position，亦称 regula falsi）。手稿于 1881 年在今巴基斯坦西北边境省巴克沙里村附近出土，书写于桦树皮之上，年代约在公元初几个世纪。故事通过一道“四人依次成倍数捐赠、总额 132”的例题，完整演示了试位法的操作：先假设一个方便的数值，按比例算出各部分之和，再与实际总和比较，由比值还原出真实答案。
中文正文
99° 巴克沙里手稿的试位法
巴克沙里手稿是一部古老的印度数学著作，据信是在公元初的几个世纪里书写在桦树皮上的。它于 1881 年出土，地点离巴克沙里村不远，即今巴基斯坦的西北边境省一带。这部手稿显示出对算术、代数以及所谓“试位法”的惊人造诣。
下面是从手稿中引出的一道例题。
某人作了一次捐赠。第二个人捐的是第一个人的两倍，第三个人捐的是第二个人的三倍，第四个人捐的是第三个人的四倍。他们四人一共捐了 132。问每人各捐了多少？
按照试位法，先假设一个方便的数值。设第一个人捐了 1。那么第二个人捐了 2，第三个人捐了 3 × 2 = 6，第四个人捐了 4 × 6 = 24。这些数额加起来是 1 + 2 + 6 + 24 = 33。但实际的总额应当是 132；而 132 ÷ 33 = 4。于是第一个人捐了 1 × 4 = 4，第二个人捐了 2 × 4 = 8，第三个人捐了 6 × 4 = 24，第四个人捐了 24 × 4 = 96。这些数额加起来正是 4 + 8 + 24 + 96 = 132。
英文正文
99° False position in the Bakhshali manuscript.
The Bakhshali manuscript, an ancient Hindu work on mathematics, is believed to have been composed on birch bark during the early centuries of our era. It was unearthed in 1881, not far from the village of Bakhshali, in what is now the North-West Frontier Province of Pakistan. The manuscript reveals a surprisingly advanced knowledge of arithmetic, algebra, and the so-called rule of false position.
The following is an example taken from the manuscript.
A certain person made a donation. The second gave twice as much as the first, the third gave three times as much as the second, and the fourth gave four times as much as the third. All together they gave 132. How much did each give?
By the rule of false position one assumes a convenient value. Let the first have given 1. Then the second gave 2, the third gave 3 × 2 = 6, and the fourth gave 4 × 6 = 24. These amount to 1 + 2 + 6 + 24 = 33. But the total should be 132; and 132 ÷ 33 = 4. Therefore the first gave 1 × 4 = 4, the second gave 2 × 4 = 8, the third gave 6 × 4 = 24, and the fourth gave 24 × 4 = 96. These amount to 4 + 8 + 24 + 96 = 132.
英语学习拓展
常用词汇
manuscript音标/ˈmænjəskrɪpt/
手稿；原稿。
原文用法：False position in the Bakhshali manuscript.
birch音标/bɜːrtʃ/
桦树；桦木。
原文用法：composed on birch bark
unearthed音标/ʌnˈɜːrθt/
被发掘；被出土。
原文用法：It was unearthed in 1881
convenient音标/kənˈviːniənt/
方便的；便利的。
原文用法：one assumes a convenient value
assume音标/əˈsuːm/
假设；假定。
原文用法：one assumes a convenient value
donation音标/doʊˈneɪʃn/
捐赠；捐献。
原文用法：A certain person made a donation
amount音标/əˈmaʊnt/
总计；合计。
原文用法：These amount to 33
同义词与近义词
对应核心词汇：unearthed
对应核心词汇：unearthed。
辨析：三者都表示“发现、找到”，但 unearthed 带有“从地下发掘”的意味，专指考古或文物出土；discovered 更泛用，可指任何新发现；found 最口语、最普通。
原文用 unearthed 恰当地呼应了手稿在村旁被挖出的情境。
对应核心词汇：assume
对应核心词汇：assume。
辨析：assume 与 suppose 在“假设”义上近义，但 assume 更强调把某前提当作成立来推演（试位法正是如此）；presume 则带有“基于既有证据推定”的语气。
本故事“one assumes a convenient value”用 assume 最准确。
常用短语与固定搭配
- rule of false position：试位法（亦称 regula falsi）。原文用法：the so-called rule of false position，是整篇故事的核心术语。
- as much as：和……一样多，常用于比较倍数结构。原文用法：twice as much as the first、three times as much as the second，构成“n 倍于……”的递进表达。
- amount to：总计为；合计达。原文用法：These amount to 1 + 2 + 6 + 24 = 33，用于汇总各项之和。
- not far from：离……不远。原文用法：not far from the village of Bakhshali，描述出土地点的相对位置。
常用句式
- Pattern "is believed to have been + 过去分词"：结构说明：表达“据信曾……”，用于学术上不确定的历史判断，比直接陈述更严谨。原文例句：is believed to have been composed on birch bark。
- Pattern "n times as much as …"：结构说明：表示“是……的 n 倍”，常用于逐层倍增的并列句。原文例句：The second gave twice as much as the first。
长难句解析
The Bakhshali manuscript, an ancient Hindu work on mathematics, is believed to have been composed on birch bark during the early centuries of our era.
- 主干：The Bakhshali manuscript ... is believed to have been composed on birch bark. - 修饰与从句：an ancient Hindu work on mathematics 为同位语，说明手稿性质；during the early centuries of our era 为时间状语。 - 逻辑关系：主句陈述“据信曾被书写于桦树皮上”，同位语补充身份，时间状语限定年代。
语言使用特点
- 多用被动与 “be believed to” 等客观化表达，体现学术叙述的严谨与克制。
- 倍数比较用 "n times as much as" 逐层递进，结构清晰、节奏明快，适合描述比例关系。
- 连接词 But、Therefore 引导推理转折，使试位法的推导过程逻辑连贯、易于跟读。
迁移练习
- 用英语复述试位法的三步：assume a convenient value → compute the assumed total → multiply by the ratio (actual ÷ assumed)。
- 写出“第三个人捐的是第二个人的三倍”（提示：three times as much as the second）。
- 模仿 "is believed to have been + 过去分词" 结构，造一个关于某件文物被发现的句子。
点击展开参考答案
- （复述步骤即答案）assume a convenient value → compute the assumed total → multiply by the ratio (actual ÷ assumed).
- The third gave three times as much as the second.
- 示例：The pottery is believed to have been made in the Tang dynasty.