中日方程论之比较

鼎盛于宋元时代的中算方程论在和算与清代数学中又有着新的不同发展,从和算这一角探讨中算方程论之特质与局限性,具有重要意义。该文通过对中日方程论之基础及发生机制的数理分析,比较了和算与清代方程论的不同成就及其成因,认为增乘开方法是中日方程论的基础,和算开方代数化与清代数学研究的注释性是造成中日方程论发展迥异的根本原因。

A COMPARISON OF THE THEORY OF EQUATIONS BETWEEN CHINA AND JAPAN

The theory of equations, which was in full bloom in the Song and Yuan Dynas-ties, made a new progress different from wasan and the mathematics of the Qing Dynasty. Itis of great significance to approach its characteristics and limitations from wasan angles.Analysing the basis and operation of it between China and Japan, this paper points out that thezeng-cheng method for the extraction of roots was the basis. And the chief reason why thetheory of equations in the two countries developed differently was the extraction of roots inwasan and the annotation in the mathematical research of the Qing Dynasty.