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The Westernization of Chinese Mathematics - A Case Study on the Development of the Duoji Method

Tian Miao (CAS, Beijing)

Western mathematics was transmitted into China in the Late Ming and Early Qing Period. It had a great impact on the development of Chinese mathematics. After 1840's, many Western mathematical books, including Elias Loomis's Elements of Analytical Geometry and the Differential and Integral Calculus, Augustus De Morgan's Elements of Algebra and William Wallace's Fluxions and Algebra in the eighth edition of Encyclopedia Britannica, were translated into Chinese. Therefore, Chinese mathematicians began to be familiar with the modern symbolic algebra, calculus and some other branches of Western mathematics. At the same time, some high officials and scholars were impressed by the destructive power of Western weapons. As the skill in the manufacture of fire-arms was derived from the study of mathematics, so they energetically encouraged the study and education of mathematics. Therefore, there were many mathematicians and a great deal of mathematical works in late Qing Dynasty. By the study on these works, we can get a clear view of the Westernization of Chinese Mathematics. In this article, I would like to give a detailed study on the development of the Duoji method (the method of calculating the summation of finite series), in order to show how the method of traditional mathematics was transformed into the Western one.

There are three reasons why I choose the Duoji method as the main subject. The first is that the Duoji is one of the most important branch of the traditional mathematics, so the study on the development of the method is very important. The second is that the Duoji method is the only field in which late Qing mathematicians had made advanced achievements in the world. The third is that up to 1860, there was hardly influence on the Duoji method, despite the fact that the Western mathematics had already transmitted into China in early 17th century. Therefore the study on this subject would give a view of how Western mathematics affected the Chinese mathematics in 1860 - 1910. The conclusions of this article are as follows:

  1. Based on the study of Zhu Shijie's Siyuan yujian, Wang Lai's Dijian shuli and Li Shanlan's

    Duoji bilei, I would like to discuss about the style and the structure of the works, which deal with

    the Duoji method.

  2. Based on the study of Liu Yicheng's Jianyian suangao, I will study the traditional procedure of

    Duoji method.

  3. Based on the study on the Tongwenguan suanxue keyi, Cui Caoqing's Duoji yi de and Zhang

    Xi's Duiduo shu, I point out that the method of Duoji had already been transformed into Western

    mathematical ones.

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