関孝和の代数方程式論 (数学史の研究)

Abstract

Seki Takakazu (?-1708) has long been known as one of the founders of mathematics in Pre- modern Japan. His personal profile, documentary legacy, and view of mathematics have been studied by numerous scholars in numerous papers. Here, I confrm that his primary interest was in the theory of algebraic equations, a topic on which he left several manuscripts. He was the first person to grasp equations systematically and abstractly as mathematical objects per se. His theory was based on the side writing" system that he developed to solve the problems set in Sawaguchi Kazuyuki's Mathematical Method Old and New (Kokon Sanpouki, 1671). It has previously been pointed out that this side writing system allowed problems to be resolved into simultaneous equations of differing degrees (simple, quadratic, etc.) which led immediately to elimination theory as a new subject of study. Seki's theory on algebraic equations has two aspects. One is still of mathematical interest today while the other belongs more to the historical context. I discuss the former quickly and the latter in rather more detail, referring to a problem treated in Seki's Method for Restoring Defective Problems (Byoudai Meichi).