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亚历山大的欧几里得 - 译自《希腊化时代的科学与文化》(1)

已有 452 次阅读 2021-10-21 23:32 |个人分类:解读哥德尔不完全性定理|系统分类:科研笔记

一,译文


欧几里得的生活和工作


与新的大都市亚历山大(Alexandria)有关的最早也是最伟大的科学人物之一是欧几里德( Euclid,公元前三至一世纪),我们都知道他的名字和他的主要作品《几何原本》,但对他本人却没有确切的了解。我们所知道的一点而且是非常少的一点都是推断出来的,而且来自后期的出版物。然而,这种无知并不例外,而是常有的。人类记住了专制者和暴君,记住了成功的政治家,记住了有钱人(至少是其中的一部分),但却忘记了自己最伟大的恩人。我们对荷马、泰勒斯、毕达哥拉斯、德谟克利特(Homer, Thales, Pythagoras, Democritos),。。。了解多少?不,我们对中世纪大教堂的建筑师或莎士比亚(Shakespeare)又了解多少?过去最伟大的人不为人知,即使我们接受了他们的作品,享受了他们丰盛的祝福。


欧几里德的出生和死亡的地点和日期都不清楚,我们称他为亚历山大的欧几里德,因为那个城市是唯一一个几乎可以肯定与他有关的城市。我们聚集所有流传下来的信息,他可能是在雅典接受的教育,如果是这样的话,他是在雅典学院接受的数学训练,那是第四世纪杰出的数学学校,也是他能够容易收集到他所拥有的所有知识的唯一地方。当战争的沧桑和政治的混乱使他在雅典的工作越来越困难时,他搬到了亚历山大,在那里的第一任托,可能还有第二任托勒密托斯(Ptolematios)的统治下,他的工作蓬勃发展。两件轶事有助于揭示他的个性,据说国王托勒密托斯问他,在几何学中是否有比《几何原本》更捷径的道路,他回答说,没有通往几何学的皇家道路(there was no royal road to geometry这是一个很好的故事,就欧几里德而言,这可能不是真的,但却有永恒的效力,数学是不看人的。另一个轶事也同样精彩,有人开始向欧几里德学习几何,当他学完第一个定理后,问他: “但我学这些东西能得到什么? ”欧几里德叫来他的奴隶,说: “给他一个硬币吧,因为他必须从他所学的东西中得到好处。 ”今天仍有许多傻瓜会像欧几里德的学生那样评价教育;他们想让教育立即变得有利可图,如果按照他们的方式,教育将完全消失。


这两则轶事的记录都比较晚,第一则来自普罗克洛(Proclus),第二则来自斯托拜厄斯(Stobaios),都是在五世纪下半叶听说的,足够可信;它们在字面上可能真实,或者,如果不是,它们反映了同时代人看到的或想象的那个人物的传统形象。绝大多数的历史轶事都是这种类型的,与流行的形象一样忠实反映人物。


欧几里德与博物馆有联系吗?不是正式的,否则,这一事实会被记录下来,但如果他在亚历山大城生活,他必然熟悉博物馆及其图书馆,而这正是各种形式的知识生活的核心。然而,作为一个纯粹的数学家,他不需要任何实验室,他可以很容易地从希腊带来他所需要的所有数学卷轴;我们可以假设,好学生会自己复制他们必须知道或急于保留的文本。数学家不需要亲密的合作者,像诗人一样,他独自完成最好的工作,非常安静。另一方面,欧几里德可能一直在博物馆或自己家里教一些弟子,这是很自然的,而且Pappos阿波罗尼奥斯(Apollonios,公元前3-2年)在亚历山大受教于欧几里德的学生,也证实了这一点。这有助于确认欧几里得的日期,因为阿波罗尼奥斯生活在约262年至190年之间,于是可以推测他的老师在第三世纪上半叶。


欧几里德本人是如此鲜为人知,以至于他在很长一段时间内与另外两个人混为一谈,一个比他年长许多,另一个则年轻得多。中世纪的学者们坚持称他为梅加拉(Megara)的欧几里德,因为他们把他误认为是哲学家欧几里德,他曾是苏格拉底的弟子之一(在监狱里参加大师的详谈的信徒之一),是普拉东的朋友和梅加拉学校的创始人。这种混淆被早期的印刷商证实,直到十六世纪末。第一个在欧几里得版本中纠正这一错误的是费德里科-坎迪尼奥在他的拉丁文译本中(Pesaro1572)。另一个混乱的原因是,编辑《几何原本》的Theon of Alexandia (IV-2)被认为是结束了证明! 如果是这样的话,他才是真正的欧几里德;这个错误就像有人声称荷马构思了《伊利亚特》,但以弗所(Ephesos)的泽诺多特斯(Zenodotos)才是真正的作曲家一样深刻。



二,原文


Euclid of Alexandria


Euclid’s life and work


One of the earliest, as well as one of the greatest, men of science connected with the new metropolis, Alexandria, was Euclid (III-1 B.C.). We all know his name and his main work, the Elements of geometry, but we have no certain knowledge about himself. The little that we know - and it is very little - is inferential and of late publication. This kind of ignorance, however, is not exceptional but frequent. Mankind remembers the despots and the tyrants, the successful politicians, the men of wealth (some of them at least), but it forgets its greatest benefactors. How much do we know about Homer, Thales, Pythagoras, Democritos, …? Nay, how much do we know about the architects of the medieval cathedrals or about Shakespeare ? The greatest men of the past are unknown, even when we have received their works and enjoy their abundant blessings.


The very places and dates of Euclid’s birth and death are unknown. We call him Euclid of Alexandria, because that city is the only one with which he can be almost certainly connected. Let us put together all the information that has filtered down to us. He was probably educated in Athens and, if so, he received his mathematical training at the Academy, which was the outstanding mathematical school of the fourth century and the only one where he could have gathered easily all the knowledge that he possessed. When the vicissitudes of war and political chaos made it increasingly difficult to work in Athens, he moved to Alexandria. He flourished there under the first Ptolematios and possibly under the second. Two anecdotes help to reveal his personalty. It is said that the king (Ptolemarios Soter) 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 - an excellent story, which may not be true as far as Euclid is concerned but has an eternal validity. Mathematics is « no respecter of persons ». The other anecdote is equally good. Someone who had begun to study geometry with Euclid, when he had learned the first theorem, asked him, « But what shall I get by learning those things ? » Euclid called his slave and said, « Give him an obol, since he must gain from what he learns. » There are still many idiots today who would judge education as Euclid’s student did ; they want to make it immediately profitable, and if the are given their way, education vanishes altogether.


Both anecdotes are recorded relatively late, the first by Proclus, the second by Stobaios, both of them flourished in the second half of the fifth century; they are plausible enough; they might be literally true, or, if not, they are traditional images of the man as his contemporaries had seen him or imagined him to be. The great majority of historical anecdotes are of that kind; they are as faithful as popular imagery can be.


Was Euclid connected with the Museum ? Not officially. Otherwise, the fact would have been recorded, but if he flourished in Alexandria, he was necessarily acquainted with the museum and its Library, which were the very heart of intellectual life in all its forms. As apure mathematician, however, he did not need any laboratory and he might easily have brought from Greece all the mathematical rolls that he needed ; we may assume that good students would themselves copy the texts that they were required to know or were anxious to keep. A mathematician does not need close collaborators; like poet, he does his best work alone, very quietly. On the other hand, Euclid may have been teaching a few disciples, either in the Museum or in his own home ; this would have been natural and is confirmed by Pappos’ remark that Apollonios of Perga (III-2 a.c.) was trained in Alexandria by Euclid’s pupils. This helps to confirm Euclid’s date, for Apollonios lived from c.262 to 190; this would place the teacher of his teachers in the first half of the third century.


Euclid himself was so little known that he was confused for a very log time with two other men, one much older than himself, the other considerably younger. Medieval scholars insisted on calling him Euclid of Megara because they mistook him for the philosopher Eucleides, who had been one of Socrate’s disciples (one of the faithful who attended the master’s detail in prison), a friend of Platon’s and the founder of the school of Megara. This confusion was confirmed by the early printers until late in the sixteenth century. The first to correct the error in a Euclidean edition was Federico Commandinio in his Latin translation (Pesaro, 1572). The other confusion was caused by the fact that Theon of Alexandia (IV-2), who edited the Elements, was believed to have ended the demonstrations ! If such had been the case, he would been the real Euclid ; the error is as deep as if one claimed that Homer had conceived the Iliad but that Zenodotos of Ephesos was the real composer of it.


参考文献:

乔治·萨顿(George Sarton)与《希腊化时代的科学与文化》 http://blog.sciencenet.cn/blog-2322490-1292301.html





http://blog.sciencenet.cn/blog-2322490-1308913.html

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