On the Chūsan-shiki by tactician Arisawa Munesada (Study of the History of Mathematics 2019)

"Study of the History of Mathematics 2019". September 2-4, 2019. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The Chūsan-shiki is a small monograph of bout Napier's bones which was written by Arisawa Munesada (1690-1752) in 1725. Author Arisawa was a samurai who served as a tactician under the Kaga domain (in present day Ishikawa prefecture). He wrote many military treatises in his life, also he has been studied mathematics and astronomical calendar in his young age. In this monograph he classified calculation method into three types of Wasan, Karasan and Kōmōsan. According to his emphasize Wasan is calculation method using Soroban (Chinese abacus), Karasan is Chinese classical calculation method using counting rods for solving equation and Kōmōsan is calculation method depend on Napier's bones. And Arisawa Munesada stressed that calculation using Napier's bones is the easiest way to get the answer quickly and without making error even if one does not kwon multiplication. In this paper we discuss that, first, what kind of mathematical ideas as a samurai or a tactician did he has, second why did he classify calculation method into three types, finally what mathematical book did he learn Napier's bones from