元禄の中頃に成立した『算法大成』について (数学史の研究)

Abstract

The Taisei Sankei is an encyclopaedic work of Japanese mathematics compiled by three mathematicians, Seki Takakazu and his disciples, the Tatebe brothers. The compilation project began in 1683 on the initiative of the younger Takebe, Katahiro, and was completed by the elder Takebe, Kata'akira, in 1710. An interim edition in twelve volumes, entitled Sanpō Taisei, was drafted by Katahiro around 1695, but no manuscript of this edition survives. However, it is important to study the Sanpō Taisei because it is considered to be the culmination of Seki Takakazu's mathematical works. By studying the mathematical manuscripts left behind by the three mathematicians, this paper deduces which volumes of the Taisei Sankei succeed the Sanpō Taisei and how the Sanpō Taisei was compiled. We also identify the author(s) of the four manuscripts Kyūketsu Henkeisōkai, Kyūseki, Kaihō Sanshiki and Kaihō whose contents are common to some parts of the Taisei Sankei.