内容概述
埃拉托色尼用简洁而巧妙的办法测出了地球周长。他知道夏至正午时尼罗河畔的昔兰尼城阳光垂直入射，地上直立木棍没有影子，深井也能照见井底；同时刻的亚历山大城却有 1/50 圆周的太阳倾角。他还估出两城相距约 5000 个古希腊长度单位 stadia，按比例即得地球周长为 250 000 stadia，约合 25 000 英里，与今天实测的约 24 900 英里惊人接近。这一测量没用望远镜，也无需漂洋过海，是几何与三角最经典的早期应用之一。
中文正文
80° 埃拉托色尼丈量地球
关于埃拉托色尼，人们至今还喜闻乐道的也许是他丈量地球的故事。尽管埃拉托色尼的测量带着点儿运气，基本思想却是简洁、独特而科学的，即使只学过最初等的几何和三角的同学，也能理解和欣赏。
埃拉托色尼知道，在夏至日的正午，垂直树立在昔兰尼（埃及尼罗河畔的一个城市）地上的木棍儿没有影子。实际上，在同一个时刻的同一个地方，人们还发现，深井里的水将阳光垂直反射到向井底张望的眼睛。另一方面，在同一天的正午，人们也看到，亚历山大城的高高石柱却投下了影子，说明那里的太阳光线相对于垂直方向有 1/50 个圆周的倾斜角度。这样，埃拉托色尼就发现昔兰尼在亚历山大的正南方，距离约 5000 个古希腊长度单位（stadia）（图 10 描绘了他的意思）。根据简单比例，我们有
地球的周长 : 5000 = 1 : 1/50
于是，
地球周长 = 250 000 stadia
我们有理由假定一个古希腊长度单位大约等于 1/10 英里。这就是说，地球的周长近似为 25 000 英里。
有意思的是，地球的大小就这么简单而精确地确定下来了，不用望远镜，也不用跋山涉水或漂洋过海。
英文正文
80° Eratosthenes' measurement of the earth. Perhaps the best story that has come down to us about Eratosthenes concerns his determination of the size of the earth. Though there seems to be an element of fortuitousness in Eratosthenes' measurements, the basic idea is simple, ingenious, scientific, and appreciable by students of even the most elementary geometry or trigonometry class.
Eratosthenes learned that at noon, at the summer solstice, a vertical rod held at Syene, a city on the Nile in Egypt, casts no shadow. This fact was confirmed by noting that at that time and place the water in a deep well reflected the sun's rays directly back into the eyes of an observer looking into the well. On the other hand, at noon on the same day, a tall pillar at Alexandria was noted to cast a shadow which showed that the sun's rays there were inclined 1/50 of a complete circle to the vertical. Now Eratosthenes knew that Syene lay directly south of Alexandria, at a distance of 5000 stadia. The situation we have described is pictured in Figure 10. From a simple proportion we then have
circumference of earth : 5000 = 1 : 1/50.
It follows that
circumference of earth = 250,000 stadia.
There is reason to suppose that a stadium had a length of about one tenth of a mile. This leads to 25,000 miles as the approximate circumference of the earth.
It is interesting that the size of the earth was so simply and so accurately determined without the use of a telescope and without traveling any great distance on land or sea.
英语学习拓展
常用词汇
circumference音标/səˈkʌmfərəns/
周长。
原文用法：the approximate circumference of the earth
solstice音标/ˈsɒlstɪs/
至日；夏至或冬至。
原文用法：at the summer solstice
vertical音标/ˈvɜːtɪkəl/
垂直的。
原文用法：a vertical rod held at Syene
shadow音标/ˈʃædəʊ/
影子。
原文用法：casts no shadow
incline音标/ɪnˈklaɪn/
倾斜。
原文用法：the sun's rays there were inclined 1/50 of a complete circle（正文中为 inclined）。
proportion音标/prəˈpɔːʃən/
比例。
原文用法：From a simple proportion we then have
stadium音标/ˈsteɪdɪəm/
古希腊长度单位 stadium 的复数形式为 stadia。
原文用法：a stadium had a length of about one tenth of a mile
approximate音标/əˈprɒksɪmət/
近似的。
原文用法：the approximate circumference of the earth
elementary音标/ˌelɪˈmentəri/
初等的。
原文用法：even the most elementary geometry or trigonometry class
trigonometry音标/ˌtrɪɡəˈnɒmɪtri/
三角学。
原文用法：elementary geometry or trigonometry class
同义词与近义词
对应核心词汇：vertical
对应核心词汇：vertical。
辨析：vertical 指与水平面垂直；perpendicular 强调两条线成 90°；upright 指竖直、直立，语气更日常。
对应核心词汇：approximate
对应核心词汇：approximate。
辨析：approximate 为正式用语，表示“近似的”；rough 更口语，强调粗略；estimated 侧重“估计的”。
常用短语与固定搭配
- summer solstice：夏至。原文用法：at noon, at the summer solstice。
- cast a shadow：投下影子。原文用法：a vertical rod ... casts no shadow / a tall pillar ... was noted to cast a shadow。
- lie directly south of：位于……的正南方。原文用法：Syene lay directly south of Alexandria。
- at a distance of：距离为……。原文用法：at a distance of 5000 stadia。
- it follows that：由此得出。原文用法：It follows that circumference of earth = 250,000 stadia。
常用句式
- There is reason to suppose that ...：有理由认为……。原文例句：There is reason to suppose that a stadium had a length of about one tenth of a mile.
- A is inclined B to the vertical：A 相对于垂直方向倾斜 B。原文例句：the sun's rays there were inclined 1/50 of a complete circle to the vertical。
长难句解析
Eratosthenes learned that at noon, at the summer solstice, a vertical rod held at Syene, a city on the Nile in Egypt, casts no shadow.
- 主干：Eratosthenes learned that ... a vertical rod ... casts no shadow。
- 修饰与从句：that 引导宾语从句；从句中 at noon, at the summer solstice 为时间状语；held at Syene 为过去分词短语修饰 rod；a city on the Nile in Egypt 为 Syene 的同位语。
- 逻辑关系：说明埃拉托色尼所知观测事实的时间、地点与条件。
语言使用特点
- 科学史叙述常使用 it is interesting that ...、there is reason to suppose that ... 等评价性句型，既陈述事实又表达作者的赞叹。
- 涉及测量时，作者使用 approximately、about 等限定词，体现对历史数据不确定性的尊重。
迁移练习
- 用英文复述埃拉托色尼测量地球周长的三个关键数据：角度、距离、结果。
- 用 It is interesting that ... 写一句你对古代测量的感想。
- 将“夏至正午时，一根垂直的竿子没有影子”翻译成英文。
点击展开参考答案
- The sun's rays at Alexandria were inclined 1/50 of a full circle; Syene was about 5000 stadia south of Alexandria; therefore the circumference of the earth was about 250,000 stadia, or roughly 25,000 miles.
- Example: It is interesting that the ancient Greeks could estimate the size of the earth with such simple tools.
- At noon at the summer solstice, a vertical rod casts no shadow.