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阿基米德不是欧几里得之前的数学家

已有 1844 次阅读 2022-1-26 19:58 |个人分类:古希腊数学|系统分类:科普集锦

 

网页排版比较糟糕,大家可以直接阅读 PDF 版。


阿基米德不是欧几里得之前的数学家.pdf



 

在张卜天先生翻译的《几何原本》后记中,有这么一段话:

 

《几何原本》在思想史上有双重意义。首先,它把新的严格性标准引入了数学推理,这种逻辑严格性直到 19 世纪才被超越;其次,它朝着数学的几何化迈出了决定性一步。欧几里得之前的毕达哥拉斯学派和阿基米德,以及欧几里得之后的丢番图都表明,希腊数学也可以沿着其他方向发展。

 

无论是江西人民出版社还是商务印书馆版本都有这几句话,商务版 (https://item.jd.com/12698343.html) 在第 940 页。

 

阿基米德欧几里得之前的人物吗?古希腊人对很多数学家的生卒年都没有清晰的记录,导致一些著名数学家的生活年代都不太清楚,一个典型的例子是海 (或译希罗,Heron of Alexandria),关于他的生活年代曾经有多种说法。但是阿基米德欧几里得的生活年代次序应该还是没有太大争议的。

 

Heath 爵士英译《The Thirteen Books of the Elements Vol. 1 导论中,他是这么说的 (中文为笔者所加)

 

As in the case of the other great mathematicians of Greece, so in Euclids case, we have only the most meagre particulars of the life and personality of the man.1

 

Most of what we have is contained in the passage of Proclussummary relating to him, which is as follows: (关于欧几里得的资料大部分涵盖于 Proclus 的概述中)Not much younger than these (sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, collecting many of Eudoxustheorems, perfecting many of Theaetetus, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy


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1 这是 Heath 爵士英译《The Thirteen Books of the Elements》导论部分的第一句话,最近上海三联书店出版了冯翰翘先生的汉译全本(包括引论和大部分注释在内的版本),这句话被译为:与希腊其他伟大的数学家相比,我们所知道的欧几里得和的生活特点以及他的生平的材料都是非常贫乏的。这一翻译与原文的含义有较大差异。

 

1


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(欧几里得鼎盛期在托勒密一世之时) . For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid (阿基米德在托勒密一世之后,他提到过欧几里得) : and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than the pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.

 

This passage shows that even Proclus had no direct knowledge of Euclid s birthplace or of the date of his birth or death. He proceeds by inference. Since Archimedes lived just after the first Ptolemy, and Archimedes mentions Euclid, while there is an anecdote about some Ptolemy and Euclid, therefore Euclid lived in the time of the first Ptolemy.

 

We may infer then from Proclus that Euclid was intermediate between the first pupils of Plato and Archimedes. Now Plato died in 347/6,Archimedes lived 287212, Eratosthenes c. 284204 B.C. Thus Euclid must have flourished c.   300 B.C., which date agrees well with the fact that Ptolemy reigned from 306 to 283 B.C.

 

阿基米德的生卒年要相对清楚一些,他明确地和埃拉托色尼 (Eratosthenes) 是同时代人,而在阿基米德在其著作中提到过欧几里得。大家应该都听说过阿基米德死于古罗马士兵之手的说法,欧几里得是不可能生活在这一场战争之后的。

 

由于张卜天先生在科学史方面翻译和研究的建树,他翻译的《几何原本》有取代兰纪正、朱恩宽二先生译本的趋势。笔者所见是 2020 7 月印刷版本 (https:// item.jd.com/12698343.html) 以及江西人民出版社版本,不清楚后面的版本是否已经更正。如果没有,笔者希望商务印书馆在重印该书时,能够对上述小小的疏忽作下更正,特别是针对中学生的版本 (http://product.dangdang.com/29115001.html)


  或许它已被改了,因为我看到上述当当网的页面上有这么一句介绍:

 

      被誉为力学之父的阿基米德是他的学生。

 

只是笔者愚钝,还真无法想象阿基米德做过欧几里得的学生。

 

另外,关于现有几个汉译《几何原本》的诸多翻译问题,笔者以后有时间再慢慢聊。


 



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