中算勾股算术在17世纪日本的传播与发展

The Spread and Development of Traditional Chinese Gougu Problem in Japan in the 17th Century

勾股算术是中国传统数学的一个重要分支。17世纪以前,传入日本的中算典籍对和算产生了深远影响,使得勾股算术知识在江户时代以前就有传播。随着江户时代和算的发展,勾股算术知识逐渐成为和算中的一个重要知识分野,和算勾股算术在中算基础上获得了长足进步。17世纪日本诸多和算书皆载有勾股算术内容,并出现有关勾股问题研究的专著,部分和算家开始深入研究勾股问题。文中考察江户初期和算书中的勾股内容,追溯其中算来源,进而对17世纪和算书《股勾弦抄》与《勾股弦适等集》进行介绍和讨论,以考察江户时代前期和算勾股算术的发展。

Gougu is an important branch of traditional Chinese mathematics. The two-time transfer of Chinese classics into Japan before 17 th century has had a far-reaching impact on the Japanese mathematics. With the development of the Edo period, the knowledge of Pythagorean arithmetic has gradually became a division of an important knowledge in the Japanese mathematics, and the arithmetic of the Pythagorean has made great progress on the basis of the Chinese mathematics. In the seventeenth century, many Japanese mathematician sum books contained the arithmetic contents of Gougu, and there are monographs on the study of Gougu. Some of them begin to study the problem of Gougu in depth. This paper investigates the contents of Gougu in the early period of Edo and traces back to the source of Chinese mathematics, and then introduces and discusses the books of the 17 th century such as Problem about Gougu and The Collection of Gougu Identity, in order to investigate the development of arithmetic of Pythagorean in the early period of Edo.