抄録
The TIANYUAN-SHU "celestial element method" is the native algebra of China, the solution of higher degree equations with one unknown. In this method, the unknown is represented using "YUAN" (the element), the known term is represented using "TAI" (the taichi). This method was introduced into Japan through the work "SUAN-XUE QI-MENG" (Introduction to Mathematical Studies), written by Zhu Shi-jie in 1299. "SUAN-XUE QI-MENG" was first republished in Japan in 1658,but research into The TIANYUAN-SHU began before this time. It is thought that Masakazu Hashimoto was the first mathematician studying this method in Japan. After the 1660s, descriptions concerning the TIANYUAN-SHU started to appear in a few books written by Japanese mathematicians. Entering the 1680s, argument concerning the TIANYUAN-SHU became vigorous in Japan. An argument between Yoshinori Isomura and Kiyoyuki Shibata attracted widespread attention. Isomura tried to understand the TIANYUAN-SHU by drawing on his knowledge of Buddhism. He argued that the TIANYUAN-SHU depends on another's power, while the mathematical methods before the TIANYUAN-SHU depend on one's own power, and that the latter is preferable to the former. He thought that solving equations with the TIANYUAN-SHU corresponds to praying to Amida Buddha. Shibata argued that there was something wrong with Isomura's thinking. A person with knowledge of Buddhism is not the same as one who knows how to employ the TIANYUAN (the heaven element), and the TIANYUAN-SHU includes mathematical methods from before the system itself was developed. Isomura's thinking creates complications for beginners studying the TIANYUAN-SHU. It was Masayuki Sato who first correctly used the TIANYUAN-SHU in "Sanpo kongen ki" in 1666.
