和算极数术与中算极值概念萌芽

Kyokusujutsu in Wasan and Bud of ExtremumConcept in Traditional Mathematics of China

本文介绍了和算求多项式函数极大极小值方法 ,分析了和算极值方法的数理基础与立术原理 ,认为建部贤私 (16 6 4 - 1739)求多项式函数极值的费尔马方法源于《授时历》求太阳、月亮中心差问题 ,他通过观察与归纳 ,获得这类极值问题的一般性解法 ,其中求多项式函数稳定点方法与关孝和方程论的“适尽诸级法”一致 ,只不过是形式上的偶合。在上述分析的基础上 ,进一步探讨了东方传统数学中的变量数学萌芽及其未能继续发展的原因。

The paper showed the method of maximizing and minimizing a polonomial function in Wasan,analyzed the mathematical basis and the principle of establishment for the method of extremum in Wasan.The paper also held that Takebe Katahiro's (1664～1739)Fermat Method of extremizing a polynomial function had stemmed from the problem of equation of the center of the sun and the moon in Shoushi Li.Through the survey and the induction,Takebe Katahiro had acquired the genetal method of solving this kind of extremum problem.Takebe Katahiro's method of determinating a stable point of a polynomial function had been the same as the Tekijinshokyuho in Seki Takakazu's theory of equations,which was just a coincidence in form.Based on the above-mentioned analyses,the paper probed further into the reasons for the bud of variate mathematics in traditional mathematics in the Orient and the reasons why it had not been developed continuously.