『大成算経』における開方 (The study of the history of mathematics 2016)

Abstract

Since it is the writing which accomplishes the core of the Seki style mathematics developed in Japan, Taisei Sankei by Kowa Seki, Kataakira Takebe, and Katahiro Takebe is investigated with much concern. However, about the relation between evaluation of the Front of Volume which described the algorithm by abacus calculation systematically, and evaluation of the Middle of Volume which investigated the algorithm which solves high order simultaneous equations, and the End of Volume, It is not solved enough. In this paper, I summarized the actual condition of the Taisei Sankei from comparison with the Unified Lineage of Mathematical Methods which is the classic document which described the algorithm by abacus calculation systematically. And I considered the directivity of algebraic investigation from comparison with the Tongwen Suanzhi which introduced Western arithmetic to China.