On Development of Ancient Chinese Mathematics - from the ''Shu" of Yuelu Academy to the Ten Computational Canons of Tang Dyansty

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K00269
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 01080:Sociology of science, history of science and technology-related
• Research Institution: Osaka Sangyo University
• Principal Investigator: Tamura Makoto 大阪産業大学, 全学教育機構, 教授 (40309175)
• Co-Investigator(Kenkyū-buntansha): 張替 俊夫 大阪産業大学, 全学教育機構, 教授 (50309176)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 科学史 / 数学史 / 中国古代数学 / 『九章算術』 / 『海島算経』 / 『緝古算経』 / 句股術 / 3次方程式

Outline of Final Research Achievements

Towards the books "Haidao Suanjing", "Sunzi Suanjing", "Zhang Qiujian Suanjing", "Wucao Suanjing", and "Jigu Suanjing", we have added mathematical and cultural-historical considerations, and published as articles their translations into Japanese and their annotations.
We explianed that the methods of "Haidao Suanjing" is the combination of the same techniques as in the problems 17 - 24, Chapter 9 of "Nine Chapters of Mathematical Arts", which is particular version of Proposition 43, Volume 1 of Euclid's "Elements". We also showed that the solution method for cubic equations described in "Jigu Suanjing" is a generalization of the method to extract cubic root described in "Nine Chapters", and on the other hand, clarified the gap between them.
Furthermore, we clarified the reason why the existence of the positive solution of its cubic equation is guaranteed.

Free Research Field

科学技術史

Academic Significance and Societal Importance of the Research Achievements

以前の研究課題による秦漢期の成果と合わせ、本研究によって秦代から唐代に至る中国数学の研究資料の用に足る訳注がそろったことになる。その多くは完訳としては初めてであろう。
恩恵の一例として、前漢の『算数書』での平方根の近似分数、後漢の『九章算術』の開平方・開立方、三国魏の劉徽注による開帯従平方（2次方程式）、唐の『緝古算経』の開帯従立方（3次方程式）という展開が、一貫して図形の取り尽くしという考え方によるものであったこと、それぞれの段階にある困難とが明らかになった。