『大成算経』巻之八・九 日用術について (数学史の研究)

Abstract

Nichiyo-jutsu (daily calculations), volumes 8 and 9 of the Taisei Sankei (Complete Books of Mathematics), compiles the mathematical knowledge used in daily life in Japan in those days. It is based both on the mathematics which had been passed down in Japan since early times, and the mathematics introduced anew into Japan from China. It contains, for example, mathematical knowledge about the rice market, exchange of money, calculation of interest, exchange of units, fare, wages, and some questions such as how many balls are needed when piled up for a specific form. In addition, these were modified by using the 'Tengen-jutsu' (Tian yuan shu), which means an equation in China. In this article, we investigate the relation between the Taisei Sankei and the Sangakukeimou (Suanxue Qimeng) written by a Chinese mathematician Zhu Shijie. In section 5, we will focus our interest on the question of how many balls are needed when piled up for a specific form, if the base is a trapezoid. These are very particular to Takebe who is one of the authors of the Taisei Sankei.