橋本伝兵衛正数とその伝書 (The study of the history of mathematics 2016)

Abstract

HASHIMOTO Denbee Masakazu is the first mathematician who understood and taught the "Tengen-jutsu" ("Tianyuan-shu" method). He has been recognized an originator of the advanced mathematics in Kyoto and Osaka area. His son HASHIMOTO Yoshitaka and SAWAGUCHI Kazuyuki are known as his pupils. It is said that SAWAGUCHI Kazuyuki's book of Kokon Sampoki was also written by HASHIMOTO. Many questions in the Kokon Sampo-ki weren't solved by the "Tengen-jutsu" method. The first mathematician who solved these questions was SEKI Takakazu, at his book of Hatsubi Sampo. Neither the year of his birth nor the year of his death are known. According to historical materials he was living from Kan'ei era(1624-1644) to Meireki era(1655-1658). He wasn't a warrior but the merchant class, conversely the Samurai warrior mathematicians, HISADA Gentetsu, HOSHINO Sanenobu, and TAKEBE Katahiro who tried to understand the Suanxue Qimeng. HASHIMOTO was respected as the first person who understood the Suanxue Qimeng and spread the Tengen-jutsu". Until now HASHIMOTO's mathematics was almost unknown. By this study whole of HASHIMOTO and his works became clear.