不确定性的困惑与NP理论分享 http://blog.sciencenet.cn/u/liuyu2205 平常心是道

博文

欧几里得传统- 译自《希腊化时代的科学与文化》(5)

已有 1483 次阅读 2021-10-30 01:22 |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


与第五公设有关的传统已经被提及,可以从《几何原本》的时代一直追溯到我们的时代,这只是传统的一小部分。然而,欧几里得传统,即使只限于数学,也因其连续性和许多传承者的伟大而引人注目。古代传统包括PappersIII-2)等人,亚历山大的TheonIV-2),ProclosV-2),SichemMarinosV-2),SimpliciosVI-1),那时的《几何原本》完全是希腊语写的,一些西方学者,如CensorinusIII-1)和BoethiusVI-1),将《几何原本》的部分内容从希腊文翻译成拉丁文,但他们的努力所剩无几,人们无法谈论任何完整的翻译,也无法谈论任何一个涵盖大部分内容的《几何原本》。还有更糟糕的事情要讲,直到12世纪,西方还流传着各种手抄本,其中只有欧几里得的命题,没有论证。有一种说法是,欧几里德本人并没有给出证明,这些证明是在七个世纪之后才由Theon提供的。没有比这更好的误解例子了,因为如果欧几里得不知道他的定理的证明,他就不可能把它们放在逻辑顺序中,而这种秩序是《几何原本》的精髓和伟大之处,但中世纪的学者们却没有看到,或者至少在阿拉伯注释者打开他们的眼界之前没有看到。


《几何原本》很快就从希腊文翻译成了叙利亚文; al-Hajjaj ibn YusufIX-1)为Harun al-Rashidcaliph 788-809)首次将其从叙利亚文翻译成了阿拉伯文, al-Hajjajal-Mamuncaliph 813-833)修订了他的翻译。第一个对欧几里得感兴趣的阿拉伯哲学家可能是 al-KindiIX-1),但他的兴趣集中在光学上,在数学上则延伸到非欧几里得主题,如印度数字。在随后的250年里(第九至第十一世纪),阿拉伯数学家一直非常接近欧几里得,他们是代数学家,还有几何学家,并出版了其他译本和许多评论。在九世纪末之前,Muhammad ibn Musaal-Mahanial-NairiziThabit ibn QurraIshaq ibn HunainQusta ibn Luqa用阿拉伯语重新翻译和讨论了欧几里。十世纪前25年,Abu Uthman Said ibn Yaqub al-Dimishqi迈出了一大步,他用Pappos的注释(希腊文的注释已经丢失)翻译了第十卷,这增加了阿拉伯人对第十卷内容(不可通约的分类)的兴趣,基督教牧师Nazif ibn YumnX-2)的新译本以及Abu Jafar al-KhazinX-2)和Muhammad ibn And al-Baqi al-BaghdadiXI-2)的评论见证了这一点。我的阿拉伯清单很长,但却很不完整,因为我们必须假设这个时代的阿拉伯数学家都熟悉《几何原本》并讨论过欧几里得。例如,据说Abu-l-Wafa写了一篇评论,但已经失传。


我们现在可以打断阿拉伯的故事,回到西方。西方学者将《几何原本》从希腊文直接翻译成拉丁文的努力并不奏效;很可能在他们对欧几里得的兴趣日益浓厚的时候,他们的希腊文知识却减少了,几乎降到了零。从阿拉伯文翻译的人开始出现,他们必然会遇到欧几里得的手稿。 达尔马提亚人 HermannXII-1)、John O’CreatXII-1)和Gerard of CremonaXII-2)都曾努力将这些手稿拉丁化,但除了Adelard of BathXII-1),没有理由相信翻译工作已经完成。然而,十二世纪的拉丁文气候并不像九世纪以来的阿拉伯文气候那样对几何学研究有利。事实上,我们必须等到十三世纪初才能看到欧几里得天才的拉丁文复兴,而这种复兴要归功于Leonardo of PisaXIII-1),他以斐波那契(Fibonacci)的名字更出名。然而,在他写于1220年的《几何实践》中,斐波那契并没有继续《几何原本》,而是写了另一部关于图形划分的欧几里得著作,该著作已经失传。


同时,希伯来语的传统由Judah ben Solomon ha-KohenXIII-1)开始,由Moses ibn TibbonXIII-2)、Jacob ben Mahir ibn YibbonXIII-2)和Levi ben GersonXIV-1)继续。Abu-l-Faraj恢复了叙利亚语传统,他被称为BarhebraeusXIII-2),于1268年在马拉加天文台讲授欧几里得;不幸的是,叙利亚语传统的恢复也是它的终结,因为Abu-l-Faraj是最后一位重要的叙利亚语作家;他死后,叙利亚语逐渐被阿拉伯语取代。


阿拉伯科学的黄金时代也在减弱,尽管在十三世纪仍有一些杰出的欧几里得人,如Qaisar ibn abi-l-QasimXIII-1)、Ibn al-LubudiXIII-1)、Nasir al-din al-TusiXIII-2)、Muhyi al-din al-MaghribiXIII-2)、Qutb al-din al-ShiraziXIII-2),甚至在十四世纪也有。我们可以忽略晚期的阿拉伯和犹太数学家,因为现在主要的河流是在西方流淌。


Adelard的拉丁文本由 Giovanni CampanoXIII-2)修订,Campano的修订本在最早的《几何原本》印刷版中得到了永生(威尼斯:Ratdolt1482)(图7)。它被Leonardus de BasileaGulielmus de Papia重印(Vicenza1491)。只有这两本incunabulaKlebs, 383),都是由阿拉伯文翻译的拉丁文。第一个从希腊文翻译的拉丁文版本是由威尼斯人巴Bartolommeo Zamberti1493年完成的,并由 Joannes Tacuinus 印刷(威尼斯,1505年)(图8)。下一个版本也是拉丁文,由Joannes Tacuinus印刷(威尼斯,1509年)(图9)。希腊文princepsSimon Grynaeus编写,献给英国数学家和神学家Cuthbert Tunstall,并由Johann Herwagen印刷(巴塞尔,1533年)(图10)。第一个英译本由剑桥大学圣约翰学院的Henry Billingsley爵士翻译,他曾是伦敦市长,并由 John Dee 作序出版(伦敦;John Day1570)(图11)。由Nasir al-din al-Tusi修订的Aravic文本的princepsTypographia Medicea(罗马,1594)出版(图12)。


其余的故事在此不必多说。从1482年开始到现在还没有结束的欧几里得版本的清单是巨大的,欧几里得传统的历史是几何学历史的一个重要组成部分。


就初等几何学而言,《几何原本》是唯一一本直到我们今天仍可使用的教科书的例子,想想看吧! 二十二个世纪的变化,战争,革命,各种灾难,但我们仍然可以通过欧几里得来学习几何。



二,原文


The Euclidean tradition



The tradition concerned with the fifth postulate has already been referred to; it can be traced from the time of the Elements until our own. That is only a small part of the tradition, however, the Euclidean tradition, even if restricted to mathematics, is remarkable for its continuity and the greatness of many of its bearers. The ancient tradition includes such men as Pappers (III-2). Theon of Alexandria (IV-2), Proclos (V-2), Marinos of Sichem (V-2), Simplicios (VI-1). It was wholly Greek. Some Western scholars, such as Censorinus (III-1) and Boethius (VI-1), translated parts of the Elements from the Greek into Latin, but very little remains of their efforts and one cannot speak of any complete translation, nor of any one covering large part of the Elements. There is much worse to be said; various manuscrits circulated in the West until as late as the twelfth century which contained only the propositions of Euclid without demonstrations. The story was spread that Euclid himself had given no proofs and that these had been supplied only seven centuries later by Theon. One could not find a better example of incomprehension, for if Euclid had not known the proofs of his theorems, he would not have been able to put them in logical order. That order is the very essence and the greatness of the Elements, but medieval scholars did not see it, or at least did not see it until their eyes had been opened by Muslim commentators. 


The Elements was soon translated from Greek into Syriac; it was first translated from Syriac into Arabic ibn Yusuf (IX-1) for Harun al-Rashid (caliph 788-809) and al-Hajjaj revised his translation for al-Mamun (caliph 813-833). The first Muslim philosopher to be interested in Euclid was probably al-Kindi (IX-1), but his interest was centered upon the Optics and in mathematics it extended to non-Euclidean topics, such as the Hindu numerals. During the 250 years that followed  (cent. IX to XI), the Muslim mathematicians kept very close to Euclid, the algebraist and student of numbers as well as the geometer, and published other translations and many commentaries. Before the end of the ninth century, Euclid was retranslated and discussed in Arabic by Muhammad ibn Musa, al-Mahani, al-Nairizi. Thabit ibn Qurra, Ishaq ibn Hunain, Qusta ibn Luqa. A great step forward was made in the first quarter of the tenth century by Abu Uthman Said ibn Yaqub al-Dimishqi, who translated Book X with Pappos’s commentary (the Greek of which is lost). This increased Arabic interest in the contents of Book X (classification of incommensurable lines) as witnessed by the new translation of Nazif ibn Yumn (X-2), a Christian priest, and by the commentaries of Abu Jafar al-Khazin (X-2) and Muhammad ibn And al-Baqi al-Baghdadi (XI-2). My Arabic list is long yet very incomplete, because we must assume that every Arabic mathematician of this age acquainted with the Elements and discussed Euclid. For example, Abu-l-Wafa (X-2) is said to have written a commentary which is lost.


We may now interrupt the Arabic story and return to the West. The efforts made by Western scholars to translate the Elements directly from Greek into Latin had been ineffective; it is probable that their knowledge of Greek diminished and dwindled almost to nothing at the very time when their interest in Euclid was increasing. Translators from the Arabic were beginning to appear and these were bound to come across Euclidean manuscripts. Efforts to Latinize these were made by Hermann the Dalmatian (XII-1), John O’Creat (XII-1), and Gerard of Cremona (XII-2), but there is no reason to believe that the translation was completed, except by Adelard of Bath (XII-1). However, the Latin climate was not as favorable to geometric research in the twelfth century as the Arabic climate had proved to be from the ninth century on. Indeed, we have to wait until the beginning of the thirteenth century to witness a Latin revival of the Euclidean genius, and we owe that revival to Leonardo of Pisa (XIII-1), better known under the name of Fibonacci. In his Practice geometriae, written in 1220, Fibonacci did not continue the Elements, however, but another Euclidean work on the Division of figures, which is lost. 


In the meanwhile, the Hebrew tradition was begun by Judah ben Solomon ha-Kohen (XIII-1) and continued by Moses ibn Tibbon (XIII-2), Jacob ben Mahir ibn Yibbon (XIII-2), and Levi ben Gerson (XIV-1). The Syriac tradition was revived by Abu-l-Faraj; called Barhebraeus (XIII-2), who lectured on Euclid at the observatory of Maragha in 1268; unfortunately, this revival of the Syriac tradition was also the end of it, because Abu-l-Faraj was the last Syriac writer of importance; after his death, Syriac was gradually replaced by Arabic.


The golden age of Arabic science was also on the wane, though there remained a few illustrious Euclideans in the thirteenth century, like Qaisar ibn abi-l-Qasim (XIII-1), Ibn al-Lubudi (XIII-1), Nasir al-din al-Tusi (XIII-2), Muhyi al-din al-Maghribi (XIII-2), Qutb al-din al-Shirazi (XIII-2), and even in the fourteenth century. We may overlook the late Muslim and Jewish mathematicians, for the main river was now flowing in the West.


Adelard’s Latin text was revised by Giovanni Campano (XIII-2), and Campano’s revision was immortalised in the earliest printed edition of the Elements (Venice: Ratdolt, 1482) (Fig. 7). It was reprinted by Leonardus de Basilea and Gulielmus de Papia (Vicenza, 1491). There are only these two incunabula (Klebs, 383), both Latin from the Arabic. The first Latin translation from the Greek was made by the Venetian, Bartolommeo Zamberti, in 1493, and printed by Joannes Tacuinus (Venice, 1505) (Fig. 8). The next edition, also Latin, was printed by Joannes Tacuinus (Venice, 1509) (Fig. 9). The Greek princeps was prepared by Simon Grynaeus, dedicated to the English mathematician and theologian, Cuthbert Tunstall, and printed by Johann Herwagen (Basel, 1533) (Fig. 10). The first English translation was made by Sir Henry Billingsley, of St. John’s College, Cambridge, sometime lord mayor of London, and published with a preface by John Dee (London; John Day, 1570) (Fig. 11). The princeps of the Aravic text as revised by Nasir al-din al-Tusi was published by the Typographia Medicea (Rome, 1594) (Fig. 12).


The rest of the story need not be told here. The list of Euclidean editions, which began in 1482 and is not ended yet, is immense, and the history of the Euclidean tradition is an essential part of the history of geometry. 


As far as elementary geometry is concerned, the Elements of Euclid is the only example of a textbook that has remained serviceable until our own day. Think of that! Twenty-two centuries of changes, wars, revolutions, catastrophes of every kind, yet it still us profitable to study geometry in Euclid. 


参考文献:

1】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

2】张卜天译本,兰纪正、朱恩宽译本。




https://blog.sciencenet.cn/blog-2322490-1310075.html

上一篇:非欧几里得几何 - 译自《希腊化时代的科学与文化》(4)
下一篇:徐光启与利玛窦的《几何原本》译本赏析
收藏 IP: 91.165.191.*| 热度|

1 杨正瓴

该博文允许注册用户评论 请点击登录 评论 (0 个评论)

数据加载中...

Archiver|手机版|科学网 ( 京ICP备07017567号-12 )

GMT+8, 2024-3-28 23:38

Powered by ScienceNet.cn

Copyright © 2007- 中国科学报社

返回顶部