On the Origin and Formation of Tenzan in Early Modern Japanese Mathematics

Abstract

Tenzan 点竄 is a Japanese mathematical term from the Edo period. It spread after the publication of Shūki-Sanpō, which was written by ARIMA Yoriyuki. Although Tenzan became a candidate for the translation of algebra, its origin has not been well studied. This essay considers the origin and formation of Tenzan based on examples of mathematicians.

 The previous research that has evaluated Tenzan as algebra often focuses on the relationship between Tenzan and Endan. However, this study shows that Endan was initially interpreted as “an account” and subsequently considered as the solution of Fukudai. Therefore, Endan is not related to Tenzan.

This essay also suggests that mathematicians had different interpretations of Tenzan. MATSUNAGA Yoshisuke related Tenzan to bōsyohō. IRIE Syūkei, who defined Tenzan as “revealing the hidden,” had much in common with the views on mathematics by SEKI Takakaze and TAKEBE Katahiro. Moreover, Irie influenced Arima, and Arima’s description was based on the Irie’s definition. In addition, Arima appended bōsyohō, which explained how to write a numerical formula to Tenzan in Shūki-Sanpō. As a result, later mathematicians and previous research might have considered Tenzan the same as bōsyohō, which was also algebra.