Chinese Mathematicians In HangZhou In Late Qing Dynasty

It is in the middle ages of the 19th century that westernization of Chinese mathematics in late Qing Dynasty is the most significant phase. During this period, though China governed by Qing suffered much from both external aggressions and internal rebels, mathematics obtained many important achievements in the process of digesting western knowledge. For example, expanding trigonometric functions into their power series is the main work of mathematics from the beginning to the end of the late Qing Dynasty, with which many important results were given. And modifying the methods in SHU LI JING YUN(????)for calculating logarithms is another field paid much attention to by Chinese mathematicians. Studying Chinese.mathematics in this period has been hot points of the history of mathematics, and especially there are a great many research achievements about mathematicians, such as XIANG Mingda, XU Youren, DAI Xu, LI Shanlan, XIA Luanxiang, and so on, and their works in JiangSu and ZheJiang provinces. However, those achievements mainly focus on individuals or interpretation of some mathematical contents, and there is little about the fundamental factors and necessary conditions why the achievements could be gotten under the serious circumstance that China suffered the defend of the Opium War and the loss of governing of nearly half country due to the Tai Ping rebel, but mathematics still developed so much. Meanwhile, you could hardly see research about the communications among mathematicians in the areas around Hangzhou City. Though there is so much research about the mathematical works, there are still some contents untouched. By discussing the social environment of the Qing Dynasty at that time, the thesis analyzes the physical and cultural foundation based on which the mathematician party was established in the area around Hangzhou City, and gives some driving factors of mathematics development. Moreover, through studying the origin contents of those mathematicians, based on the comparison of the materials and achievements of other scholars, some new results are gained. The thesis is divided into five chapters. In Chapter 1, the author mainly talks about the meanings of choosing such subject and the new results of the thesis. In Chapter 2, the author introduces the social environment of the late Qing Dynasty at that time briefly. The Qing government dealt with internal continuous uprisings all over the country on one hand, and on the other hand it had to defend the aggression produced by other capitalism countries. During the defending process, Qing governors gradually recognized the importance of scientists and technicians, which objectively makes the mathematics develop. And the western mathematics and some related mathematicians at that time are briefly introduced in this chapter. Finally, the physical and cultural foundation on which the mathematician party was established in the area around Hangzhou City is explained. In Chapter 3, which is one important part of the thesis, the author mainly introduces XIANG Mingda, XU Youren, DAI Xu, XIA Luanxiang's the works. Based on analyzing the original contents, author discusses the XU Youren's method about "calculating tangent given arc", points out that DAI Xu actually got the Taylor's series of (?) at x0 in his extracting method, gives a new viewpoint different from some other scholars. After studying the record materials about those mathematicians, author analyzes their characteristics. In Chapter 4, which is another important part of the thesis, author exclusively discusses LI Shanlan and his achievements. Based on studying the contents of DUO JI BI LEI(????) and other scholars' results, the author summarizes the its properties. For his "JIAN ZHUI" method, the author gives some new results as well as some new viewpoints. For example, the formula for area still holds even though the graph changes its shape, and "JIAN ZHUI" method is an algebraic method, and LI Shanlan divided two infinite series earlier than DAI Xu, which are the important contents of this chapter. Finally, taking OUTLINES OF ASTRONOMY and TAN TIAN(??),through comparing the relative contents between the origin version and the translation version, author evaluates LI's translation. The last chapter includes the conclusions of the whole thesis. Firstly, author points out the influence of Confucianism and Taoism. Secondly, the communications among Chinese mathematicians and their loving mathematics at that time are other driving factors for mathematics development. Then that the governors of Qing Dynasty gradually recognized the importance of scientists and technicians objectively makes the mathematics develop. Finally, the author picks out some mistakes in Shu Li Jing Yun(??????)and his viewpoints appear there.