徐光启Xu Guangqi

徐光启（或徐光启）也被称为Hsu Kuang-ch'i。他受过天文学和历法计算的教育，在科举考试中获得了最高等级。他地位日益显赫，最终成为明朝朝廷的首辅大臣。在此之前，他曾在利玛窦门下学习西方文化，但在我们解释他们共同的工作之前，我们应该引用[6]中关于背景的叙述来设定场景：-

尽管明朝（1368-1644）的政治历史黯淡，但中国在许多领域取得了进步，包括贸易和工业、科学技术、哲学和文学，这主要归功于人民的智慧和努力。经济发展在长江流域尤为显著。因此，像徐光启这样的人物在这个“文艺复兴”时期出现是自然的结果。……[徐光启]在明朝朝廷度过了长达四分之一世纪的政治上相当徒劳的部长生涯。也正是在明朝的最后几十年，中国人首次通过耶稣会士接触到了欧洲科学。耶稣会士意图在这个古老的帝国传播天主教信仰，为了赢得民众，他们首先努力获得受过教育阶层的青睐和追随。作为一种权宜之计，他们带来了各种中国未知的新技术小工具和仪器，以及科学理论，尽管这些理论并非都是当时欧洲的最新知识，但对一些受过教育的中国人来说仍然足够新颖和具有吸引力。

事实上，中国数学已经衰落了一段时间。徐光启深知这一点，并将衰落归因于学者忽视实学以及数学与术数之间的混淆。13世纪李冶以如此娴熟的技巧阐述的用于解方程的辉煌的“天元”或“系数阵列法”或“天元术”在中国已不再被理解。中国人在代数方面取得的显著进展已基本被遗忘，曾经用代数解决的实用问题此时却用临时方法解决。甚至九章算术也几乎无人知晓，徐光启本人从未读过这部辉煌的中国经典，而数学十大经典被认为已经失传。在这个中国数学的薄弱时期，利玛窦等学者带来了欧洲数学。

利玛窦是一位耶稣会士，曾在罗马师从克里斯托佛·克拉乌学习。他于1582年抵达中国东海岸的澳门。他定居在广东省肇庆，并开始学习中文。他还努力了解中国文化。1589年，利玛窦迁往韶州，并开始向中国学者教授他从老师克里斯托佛·克拉乌那里学到的数学思想。他与自己的一名学生瞿汝夔一起翻译了欧几里得的Elements的第一卷。利玛窦于1595年试图访问北京，但发现该城对外国人关闭，于是转而前往南京，并从1599年起居住在那里。他在那里提交了关于Elements第一卷的论文，但这部初步著作现已失传。利玛窦在南京受到欢迎，这鼓励他再次尝试访问北京，他于1601年成行。这一次他被允许在城中居住，并从那时起以此地为家。他向中国学生教授数学，其中一位就是高级官员徐光启。

徐光启成为第一个将欧洲书籍翻译成中文出版的中国本土人士。他与利玛窦合作，翻译了关于数学、水力学和地理学的西方书籍。欧几里得的Elements的前六卷于1607年由利玛窦和徐光启翻译成中文。他们采用了克里斯托佛·克拉乌于1574年首次出版的欧几里得的Elements的拉丁文评注本。作为一个有趣的注脚，我们指出他们将“克里斯托佛·克拉乌”翻译成中文意为“钉子”，因此他们将克里斯托佛·克拉乌称为“丁先生”！他们的翻译方法在[3]中描述如下：-

翻译技巧涉及利玛窦向[徐光启]口头解释原文内容，然后徐光启写下他所理解的内容。……利玛窦和徐光启的翻译完全遵循克里斯托佛·克拉乌著作的顺序；然而，它远没有那么冗长……

这些书中的数学方法对当时中国读者来说一定显得完全陌生，因为他们对该学科的方法如此截然不同。徐光启在译本的序言中写道：-

这本书中有四件事是不必要的；不必怀疑，不必假设新的猜想，不必检验，不必修改。此外，这本书中有四件事是不可能的。不可能删除任何特定的段落，不可能反驳它，不可能缩短它，也不可能把它放在它前面的内容之前，反之亦然。

显然，徐光启完全皈依了西方思想，但大多数其他中国数学家坚持他们传统的思维方式，质疑对他们来说荒谬的东西，如“点没有部分”。中国数学方法一直非常实用，为了试图将Elements融入这一传统，徐光启在他的序言中解释了内容如何应用于历法问题、音乐和技术。大多数读者仍然不信服。然而，徐光启不得不为点、曲线、平行线、锐角、钝角等发明的新中文术语（这些概念对中国数学来说是陌生的，没有对应的中文词汇）很快成为中国数学的一部分，几何图形的风格也是如此，特别是徐光启选择用来标记它们的字符。

从某种意义上说，徐光启对中国数学造成了损害。他被利玛窦皈依基督教，并采取了中国文化劣于西方的立场，特别是在我们上面指出的数学传统方面。这是一个巨大的遗憾，因为尽管显然从知识传播中学到了很多，但没有必要通过不同的方法贬低中国人的杰出成就。徐光启写道：-

西方的规则与我们的不同，我们没有。东方的规则与西方相同的都是正确的，与西方不同的都是错误的。……因此，尽管《算经十书》失传了，这并不遗憾，因为它们不过是破鞋。

他预测很快中国的每个人都会学习Elements，在这一点上他大体上是正确的，因为西方学校在中国建立，其中学习几何原本是必修课。

利玛窦在中国的主要目标是使中国人皈依基督教。许多在中国和欧洲基督教会中的人认为他利用西方数学、科学和技术作为实现皈依的不合理手段。利玛窦本人觉得改革中国历法是最有效的步骤，从而“证明”基督教的力量。的确，历法改革问题已经困扰了中国人200年，但尽管提出了各种建议，天文局一直谨慎，什么也没做。徐光启在遇到利玛窦之前就已经对历法改革感兴趣，所以他很快参与了辩论。

西方天文学和历法方法在利玛窦去世后不久取得了重大成功，当时它准确预测了1610年12月15日的日食。另一次日食预测在1629年，中国政府举行了一场竞赛，以确定谁能给出最准确的时间预测。做出了三种不同的预测，一种来自大统中国传统学派，一种来自伊斯兰历法学派，一种来自徐光启领导的新方法学派，该学派使用欧洲方法。对1629年6月21日日食的最准确预测是由徐光启做出的，皇帝随后任命他负责历法改革。四位欧洲耶稣会士协助徐光启，但改革过程在他1633年去世时尚未完成，由李天经接手。

在他生命的最后几年，徐光启是明朝朝廷中一位极具影响力的人物。明朝正受到满族的攻击，满族是12世纪曾作为金朝统治中国北方的女真部落的后裔。徐光启坚信欧洲的一切都优越，他说服明朝皇帝让他的军队采用先进的欧洲火炮来对抗满族。这一策略起初有效，但在徐光启死后崩溃了，因为满族学会了欧洲的炼铁技术并自己获得了西方武器。1644年，明朝被他们击败。

Xu Guangqi (or Xu Guang-qi) is also known as Hsu Kuang-ch'i. He obtained the highest level in the civil-service examination having been educated in astronomy and calendar computation. He rose in importance to eventually become the leading minister in the Imperial Court of the Ming Dynasty. Before this he had studied Western culture under Matteo Ricci but, before we explain their work together, we should set the scene by quoting from [6] concerning the background:-

In spite of the dismal political history of the Ming Dynasty (1368-1644), China progressed in many fields including trade and industry, science and technology, philosophy and literature, mainly owing to the wisdom and effort of the people. The economic development was especially marked in the Yangtze Valley. It was therefore a natural consequence that figures like Xu Guang-qi and others appeared during this period of 'Renaissance'. ... [Xu Guang-qi] led a long, but politically rather futile, ministerial life for a quarter of a century in the Imperial Court of the Ming Dynasty. It was also during these last decades of the Ming Dynasty that the Chinese first came into contact with European science through the Jesuits. The Jesuits were intent on spreading the Catholic faith in the old Empire, and in order to win over the people, they endeavoured first to gain the favour and the following of the educated class. As an expedient means they brought in various new technological gadgets and apparatus unknown to China, as well as scientific theories which were, though not all of them up-to-date knowledge at the time in Europe, nonetheless of a sufficient novelty and attraction to some educated Chinese.

In fact Chinese mathematics had been in a period of decline for some time. Xu Guang-qi was well aware of this and attributed the decline to academics neglecting practical learning and also to a confusion between mathematics and numerology. The brilliant "tian yuan" or "coefficient array method" or "method of the celestial unknown" for solving equations which had been expounded with such skill by Li Zhi in the 13th century was no longer understood in China. The remarkable progress which the Chinese had made in algebra had been largely forgotten, and practical problems which had been solved by algebra were by this time solved by ad hoc means. Even the Nine Chapters on the Mathematical Art was almost unknown, and Xu Guang-qi himself had never read the brilliant Chinese classic, while The Ten Classics were thought to have been lost. Into this weak period in Chinese mathematics came European mathematics brought by scholars such as Ricci.

Ricci was a Jesuit who had studied in Rome under Clavius. He arrived at Macau on the east coast of China in 1582. He settled in Chao-ch'ing, Kwangtung Province, and began his study of Chinese. He also worked at acquiring understanding of Chinese culture. In 1589 Ricci moved to Shao-chou and began to teach Chinese scholars the mathematical ideas that he had learnt from his teacher Clavius. Together with one of his students, Qu Rukui, he translated the first book of Euclid's Elements. Ricci attempted to visit Peking in 1595 but, finding the city closed to foreigners, he went instead to Nanking where he lived from 1599. There he presented his essay on the first book of the Elements but this preliminary work is now lost. Ricci was well received in Nanking and this encouraged him to try again to visit Peking which he did in 1601. This time he was allowed to live in the city and he made this his home from that time. He taught mathematics to Chinese students and one of these was the high-ranking public official Xu Guang-qi.

Xu Guang-qi became the first native of China to publish translations of European books into Chinese. Collaborating with Ricci he translated Western books on mathematics, hydraulics, and geography. The first six books of Euclid's Elements were translated into Chinese in 1607 by Ricci and Xu Guang-qi. They took the Latin commentary on Euclid's Elements first published by Clavius in 1574. As an amusing note, we remark that their translation of "Clavius" into Chinese meant "nail" so they referred to Clavius as "Mr Ding"! Their method of translation is described in [3]:-

The translation technique involved Ricci explaining the contents of the original text orally to [Xu Guang-qi] who would then write down what he had understood. ... Ricci and Xu Guang-qi's translation respects the order of Clavius's work completely; however, it is much less verbose ...

The approach to mathematics in these books must have seemed totally alien to Chinese readers whose approach to the subject had been so radically different. Xu Guang-qi wrote in the foreword to the translation:-

Four things in this book are not necessary; it is not necessary to doubt, to assume new conjectures, to put to the test, to modify. In addition four things in this book are impossible. It is impossible to remove any particular passage, to refute it, to shorten it, or to place it before that which precedes it, or vice versa.

Clearly Xu Guang-qi was a total convert to Western thinking but most other Chinese mathematicians stuck to their traditional way of thinking, questioning what to them was absurd such as "a point has no part". The Chinese approach to mathematics had been highly practical and to try to fit the Elements into that tradition Xu Guang-qi explained in his preface how the contents had application to the problem of the calendar, to music and to technology. Most readers remained unconvinced. However the new Chinese terminology which Xu Guang-qi had to invent for point, curve, parallel line, acute angle, obtuse angle etc. (these concepts being alien to Chinese mathematics, there were no Chinese words for them) soon became part of Chinese mathematics, as did the style of the geometric figures, in particular the characters Xu Guang-qi chose to label them.

In one sense Xu Guang-qi did a disservice to Chinese mathematics. He was converted to Christianity by Ricci and adopted the position that Chinese culture was inferior to that of the West, in particular, as we indicated above, in their mathematical tradition. This was a great shame, for although clearly much had to be learnt from the transmission of knowledge, there was no need to talk down the fine achievements of the Chinese through a different approach. Xu Guangqi wrote:-

Rules in the West different from ours we do not have. Rules in the East that are the same as in the west are all right, those different from those in the west are all wrong. ... Therefore though The Ten Mathematical Classics are lost, this is not a pity, for they were nothing but worn-out shoes.

He predicted that soon everyone in China would be studying the Elements and in this he was largely correct since Western schools were set up in China in which the study of the elements was a compulsory topic.

Ricci's main aim in China was to convert the Chinese to Christianity. Many, both in China and in the European Christian Church, felt that he used Western mathematics, science and technology as an unreasonable means to achieve conversions. Ricci himself felt that reforming the Chinese calendar would be the most effective step that could be taken, so "proving" the power of Christianity. Indeed the question of calendar reform had occupied the Chinese for 200 years but, despite various proposals being made, the Bureau of Astronomy had been cautious and done nothing. Xu Guang-qi was already interested in calendar reform before he met Ricci, so he was soon involved in the debate.

The Western approach to astronomy and the calendar scored a major success shortly after Ricci died when it accurately predicted the eclipse of 15 December 1610. Another eclipse was predicted for 1629 and a competition was held by the Chinese government to determine who could give the most accurate prediction of its timing. Three different predictions were made, one by the Da Tong traditional Chinese school, one by the Islamic calendar school, and one by the New Method School led by Xu Guang-qi which used European methods. The most accurate prediction for the eclipse of 21 June 1629 was made by Xu Guang-qi and the emperor then appointed him take charge of calendar reform. Four European Jesuits assisted Xu Guang-qi but the reform process had not been completed on his death in 1633 and was taken over by Li Tang-jing.

During the last few years of his life Xu Guang-qi was an extremely influential figure at the Imperial Court of the Ming Dynasty. The Ming were under attack by from the Manchu who were descendants of the Juchen tribes who had ruled North China as the Chin dynasty in the 12th century. Xu Guang-qi, with his strong belief in the superiority of all things European, persuaded the Ming emperor to have his army adopt advanced European artillery against the Manchu. Initially effective, the strategy collapsed after Xu Guang-qi's death when the Manchu learned European iron-smelting technology and acquired Western arms themselves. The Ming dynasty was defeated by them in 1644.