内容概述
关于丢番图的生平仅知他活跃于亚历山大城；《希腊诗选》一则铭文题给出传奇细节：童年占一生 1/6，青年 1/12，单身汉 1/7 时间，结婚 5 年后得子，儿子比父早死 4 年、享年恰为父一半。设 x 为去世年龄，列方程解得 x=84。
中文正文
84° 丢番图生平
关于丢番图的生平，我们只确切地知道他曾活跃于亚历山大城。不过，《希腊诗选》（Greek Anthology）中的一个题，似乎能给我们一点儿细节。《希腊诗选》（或《帕拉廷诗选》（Palatine Anthology），大约是语法家梅特罗多勒斯（Metrodorus）在公元 500 年左右汇集的）[4]中有 46 个铭文形式的问题。有关丢番图的问题大意是这样说的："丢番图的童年经过了生命的六分之一，青年经过了十二分之一，又做了七分之一的单身汉。结婚五年后生下一个儿子，儿子比父亲先死四年，年纪是他的一半。（问儿子死时丢番图多大年纪？）"
假如我们把"年纪是他的一半"理解为"年纪是他父亲享年的一半"，那么，令 x 为丢番图去世时的年龄，我们很容易得到方程
x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
结果是 x=84。于是，丢番图过了 14 年的童年，7 年的青春时光，12 年的单身汉，33 岁时结婚，5 年后，在他 38 岁时有了一个儿子，80 岁时，他 42 岁的儿子死了。假如我们把"年纪是他的一半"理解为"年纪正好是他父亲当时年纪的一半"，结果就不同了，而且出现了分数年。根据这样的解释，丢番图是在 65⅓ 岁时死的，而儿子是 30⅔ 岁时死的。既然丢番图那么喜欢整数，我们还是让他的生命更长久些吧。
英文正文
84° Diophantus's personal life. Beyond the fact that Diophantus flourished at Alexandria, nothing certain is known about his life. There is, however, a problem in the Greek Anthology that purports to give us some details. The Greek, or Palatine, Anthology is a collection of forty-six number problems, in epigrammatic form, assembled about 500 A.D. by the grammarian Metrodorus. The problem concerning Diophantus appears as the following epitaphic summary: "Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor. Five years after his marriage was born a son who died four years before his father, at half his father's age. [How old was Diophantus when he died?]"
If we interpret the phrase "at half his father's age" to mean "at half his father's final age," then, letting x denote Diophantus's age at death, we easily obtain the equation
x/6 + x/12 + x/7 + 5 + x/2 + 4 = x,
which gives x = 84. It then follows that Diophantus spent fourteen years in childhood, seven more in youth, and twelve more as a bachelor, thus marrying when he was thirty-three. Five years later, at the age of thirty-eight, he had a son who died at the age of forty-two when his father was eighty years old. If we should interpret the phrase "at half his father's age" to mean "when he was just half the age of his father," a different solution is obtained with the various episodes occurring at fractional years. Under this interpretation, Diophantus died when 65⅓ years old and his son when 30⅔ years old. Out of regard for Diophantus's love of integers, let us allow him and his son the longer spans of life.
英语学习拓展
常用词汇
flourish音标/ˈflʌrɪʃ/
活跃；繁荣。
原文用法：Diophantus flourished at Alexandria
anthology音标/ænˈθɒlədʒi/
选集；诗选。
原文用法：the Greek Anthology
purport音标/pɜːˈpɔːt/
声称；意指。
原文用法：purports to give us some details
epigrammatic音标/ˌepɪɡræˈmætɪk/
警句式的；铭文体的。
原文用法：in epigrammatic form
assemble音标/əˈsembl/
汇编；收集。
原文用法：assembled about 500 A.D.
grammarian音标/ɡrəˈmeəriən/
语法学家。
原文用法：by the grammarian Metrodorus
epitaphic音标/ˌepɪˈtæfɪk/
墓志铭的。
原文用法：the following epitaphic summary
bachelor音标/ˈbætʃələ/
单身汉。
原文用法：one seventh more as a bachelor
interpret音标/ɪnˈtɜːprɪt/
解读；理解。
原文用法：If we interpret the phrase ... to mean ...
fractional音标/ˈfrækʃənl/
分数的；非整数的。
原文用法：occurring at fractional years
同义词与近义词
常用短语与固定搭配
- beyond the fact that...：除了……这一事实之外。原文用法：Beyond the fact that Diophantus flourished at Alexandria, nothing certain is known about his life.
- purports to do sth.：声称做某事；意在……。原文用法：a problem ... that purports to give us some details
- appear as...：呈现为；表现为。原文用法：The problem concerning Diophantus appears as the following epitaphic summary
- letting x denote...：令 x 表示……。原文用法：letting x denote Diophantus's age at death
- out of regard for...：出于对……的尊重/考虑。原文用法：Out of regard for Diophantus's love of integers
- it follows that...：由此得出；随之而来的是。原文用法：It then follows that Diophantus spent fourteen years in childhood...
常用句式
- There is, however, a problem in ... that ...：然而，……中有一个问题，它……。原文例句：There is, however, a problem in the Greek Anthology that purports to give us some details.
- If we interpret ... to mean ..., then ...：如果我们把……理解为……，那么……。原文例句：If we interpret the phrase "at half his father's age" to mean "at half his father's final age," then, letting x denote Diophantus's age at death, we easily obtain the equation ...
- It then follows that ...：于是可以推出……。原文例句：It then follows that Diophantus spent fourteen years in childhood, seven more in youth, and twelve more as a bachelor...
长难句解析
If we should interpret the phrase "at half his father's age" to mean "when he was just half the age of his father," a different solution is obtained with the various episodes occurring at fractional years.
- 主干：a different solution is obtained（被动语态）。
- 条件状语：If we should interpret ... to mean ... 中，should 表虚拟语气，表示假设性情况；to mean 不定式作宾语补足语，说明 interpret 的内容。
- 伴随状语：with the various episodes occurring at fractional years 为 with 复合结构，occurring 为现在分词，修饰 episodes。
- 逻辑关系：作者提出另一种解读方式，指出这种理解会导致各阶段时间出现分数值（不够"整齐"）。
语言使用特点
- 作者使用 should 虚拟语气（If we should interpret...）来委婉提出另一种假设，体现学术写作的审慎态度。
- 句末 "let us allow him and his son the longer spans of life" 以幽默收尾，赋予冷冰冰的方程以人文温度——这是数学史叙事特有的笔法。
迁移练习
- 用英文简要复述丢番图墓志铭的内容（包含所有分数比例）。
- 用 If we interpret ... to mean ... 结构写一句你对某个歧义短语的两种理解。
- 将"丢番图在亚历山大城度过了他的一生"翻译成英文，使用 flourish 一词。
点击展开参考答案
- Diophantus passed one sixth of his life in childhood, one twelfth in youth, one seventh as a bachelor; five years after his marriage he had a son who predeceased him by four years at half his father's age.
- Example: If we interpret "cheap" to mean "low quality," then the product is not worth buying; if we interpret it to mean "low price," it may be a good deal.
- Diophantus flourished at Alexandria, where he spent his life as a mathematician.