SOAS Research Online

Abstract

I will consider the Influence of Chinese mathematics on Seki Kowa. For this purpose, my thesis is constructed in four parts, introduction, I the studies of editions; Shu. Shu. Jiu Zhang and Yang Hui Sum. Fa, II the conception and extension of method for making magic squares, and III the analysis for solving indeterminate equations. In the introduction, I will explain some similarities between Chinese mathematics in the Song dynasty and Seki Kowa's works. It will become clear that the latter was influenced by Chinese mathematics. Then I introduce some former opinions concerning which Chinese mathematical book influenced him. I shall show that two Chinese mathematical books, Shi Shu. Jiu Zhang and Yang Hai Suan Fa, are particularly important. Some Chinese mathematical books were republished and studied by Japanese mathematicians, but these two books were not accessible to Japanese mathematicians. Thus we must study them for considering questions of influence. I will consider two subjects, the treatment of magic squares in Yang Hui Suan Fa in chapter H and the method of solving indeterminate equations in Shu Shu Jiu Zhang in chapter III. Before considering the contents of these subjects, we must know more about the available versions of these two books in chapter I, otherwise we cannot know whether Seki Kowa could have obtained them. It seems certain that Seki Kowa studied the Yang Hui Sum Fa, but I cannot know whether he studied the Shu Shu Jiu Zhang. However, Seki Kowa's method of solving indeterminate equations is very similar to that of Qin Jiushao, especially when their methods of changing negative constants into positive are similar. Thus I would like to propose that Seki Kowa studied the Chinese method of solving indeterminate equations.