近世日本数学史における方程式論 : 宅間流の『遷式術』 (数学史の研究)

Abstract

The Takuma School is a school in Osaka that produced Kamata Toshikiyo (the 3rd), whose achievements should be comparable to those of Seki Takakazu, Tatebe Takahiro, and his brother Kataakira, and Matsuoka Yoshikazu (the 5th), who wrote one of the most important textbooks of the 19th century, the Complete book for arithmetic practice. In this paper, we discuss the Methods of transformation of equations written by Oka Shichibei Yukitada, who was a student of Matsuoka. After a brief overview of the Takuma School in Section 2, Sections 3 to 6 discuss the characteristics of Takuma School mathematics through an analysis of Oka's book. It has long been known that the style of expression in the Takuma school differs from that in the Seki school, but in Section 4 we discuss in more detail some of the important terms in the Takuma school (or, more precisely, in Oka's mathematics). In particular, section 5 describes Oka's transition methods of equations in detail. Section 7 briefly mentions Oka's student Asaoka Uhei, whose existence became known in 2021.