内容概述
泰勒斯在埃及时利用影子测量金字塔高度，赢得赞誉。关于这件事有两个版本：较早的版本由亚里士多德的学生耶洛尼姆斯讲述，说泰勒斯在自身影子与身高等长时测量金字塔影长；较晚的版本由普卢塔克讲述，说泰勒斯立了一根木棍，利用“金字塔高与棍高之比等于金字塔影与棍影之比”来求解。两个版本都忽略了一个现实困难：如何获得金字塔影子的实际长度（即从影子顶点到塔底中心的距离）。由此引出“泰勒斯疑难”：设计一种仅基于影子观测和相似三角形、且不依赖纬度和具体时间的方法来确定金字塔高度。原书图 4 提示可用相隔数小时的两次影子观测来解决。
中文正文
31° 泰勒斯疑难
据说泰勒斯在埃及住过一段时间，他根据影子来计算金字塔的高度，赢得了赞誉。故事有两个版本。较早的一个是亚里士多德的学生耶洛尼姆斯（Hieronymus）讲的。故事说，泰勒斯在自己的影子和自己的身高一样时，发现了金字塔影子的长度。后来的故事是普卢塔克（Plutarch）讲的，说泰勒斯立了一根木棍，而且发挥了下列事实：“金字塔的高度与木棍高度之比，等于金字塔的影子与木棍的影子之比。”两个故事都没提到一个很现实的困难：如何在那两种情形下获得金字塔影子的长度（从影子的顶点到塔底中心的距离）。
这个难题引出所谓的泰勒斯疑难：在影子观测和相似三角形的基础上，找一个方法来确定金字塔的高度。图 4 提出了一个解决办法（读者也许有兴趣来完成它），它需要观测两个相隔若干小时的影子。
英文正文
31° The Thales puzzle. It has been reported that Thales resided for a time in Egypt, and there evoked admiration by calculating the height of a pyramid by means of shadows. Two versions of the story have been given. The earlier account, furnished by Hieronymus, a pupil of Aristotle, says that Thales noted the length of the shadow of the pyramid at the moment when his own shadow was the same length as himself. The later version, given by Plutarch, says that Thales set up a stick and employed the fact that “the [height of the] pyramid was to the [length of the] stick as the shadow of the pyramid to the shadow of the stick.” Both of these versions fail to mention the very real difficulty, in either case, of obtaining the length of the shadow of the pyramid (that is, the distance from the apex of the shadow to the center of the base of the pyramid).
The above unaccounted-for difficulty has given rise to what might be called the Thales puzzle: Devise a method, based on shadow observations and similar triangles and independent of latitude and specific time of day or year, for determining the height of a pyramid. Figure 4 suggests a solution—that the reader may care to complete—requiring two shadow observations spaced a few hours apart.
英语学习拓展
常用词汇
reside音标/rɪˈzaɪd/
居住；停留。
原文用法：Thales resided for a time in Egypt…
evoke音标/ɪˈvəʊk/
引起；赢得。
原文用法：there evoked admiration by calculating the height of a pyramid…
pyramid音标/ˈpɪrəmɪd/
金字塔。
原文用法：the height of a pyramid…
account音标/əˈkaʊnt/
叙述；描述。
原文用法：The earlier account, furnished by Hieronymus…
furnish音标/ˈfɜːnɪʃ/
提供；供给。
原文用法：furnished by Hieronymus…
employ音标/ɪmˈplɔɪ/
使用；采用。
原文用法：employed the fact that…
unaccounted-for音标/ʌnəˈkaʊntɪd fɔː(r)/
未予解释的；未加说明的。
原文用法：The above unaccounted-for difficulty…
devise音标/dɪˈvaɪz/
设计；想出。
原文用法：Devise a method…
observation音标/ˌɒbzəˈveɪʃn/
观测；观察。
原文用法：shadow observations…
latitude音标/ˈlætɪtjuːd/
纬度。
原文用法：independent of latitude…
同义词与近义词
常用短语与固定搭配
- reside for a time in：在某地居住一段时间。原文用法：Thales resided for a time in Egypt…
- evoke admiration by：通过……赢得赞赏。原文用法：evoked admiration by calculating the height…
- by means of：借助；通过。原文用法：by means of shadows.
- set up a stick：立一根木棍。原文用法：Thales set up a stick…
- employ the fact that：利用……这一事实。原文用法：employed the fact that…
- fail to mention：没有提到。原文用法：Both of these versions fail to mention…
- give rise to：引起；导致。原文用法：has given rise to what might be called the Thales puzzle.
- spaced a few hours apart：相隔数小时。原文用法：two shadow observations spaced a few hours apart.
常用句式
- Pattern: It has been reported that …：据报道……。原文例句：It has been reported that Thales resided for a time in Egypt…
- Pattern: … was to … as … was to …：……与……之比等于……与……之比。原文例句：the [height of the] pyramid was to the [length of the] stick as the shadow of the pyramid to the shadow of the stick.
- Pattern: … fail to mention …：……没有提到……。原文例句：Both of these versions fail to mention the very real difficulty…
长难句解析
Both of these versions fail to mention the very real difficulty, in either case, of obtaining the length of the shadow of the pyramid (that is, the distance from the apex of the shadow to the center of the base of the pyramid).
- 主干：Both of these versions fail to mention the difficulty.
- 修饰与从句：
- very real 修饰 difficulty； - in either case 为插入语，指两种版本中的任何一种； - of obtaining the length of the shadow of the pyramid 为介词短语，说明困难的具体内容； - that is, the distance from the apex of the shadow to the center of the base of the pyramid 为同位语，解释“影子的长度”的含义。
- 逻辑关系：句子指出两个传统版本共同的缺陷——都没有说明如何获得金字塔影子的实际长度。
语言使用特点
- 使用被动语态和正式动词（如 resided, evoked, furnished, employed），体现数学史叙事的客观性；
- 用 It has been reported that … 等句式表达传说或二手记载；
- 比例句式 A was to B as C was to D 是几何文献中的经典表达。
迁移练习
- 用 “It has been reported that …” 介绍一个你听说的历史故事。
- 解释为什么泰勒斯测金字塔需要知道“从影子顶点到塔底中心的距离”。
- 翻译：两个版本都没有提到，在任一情况下，获得金字塔影子长度所面临的现实困难。
- 用 “… was to … as … was to …” 描述两个相似三角形的对应边关系。
点击展开参考答案
- （示例）It has been reported that Archimedes once used mirrors to set enemy ships on fire.
- （示例）Because the similar-triangle method requires the ratio of heights to equal the ratio of shadow lengths. To use the pyramid's shadow length, we must know where the shadow ends relative to the center of the pyramid's base.
- Both of these versions fail to mention the very real difficulty, in either case, of obtaining the length of the shadow of the pyramid.
- （示例）The height of the tree was to the height of the stick as the shadow of the tree to the shadow of the stick.