李锐与笛卡儿符号法则

LI RUI AND THE CARTESIAN RULE OF SIGNS

本文着重研究李锐在判定代数方程正根个数方面的工作,指出他的结论是建立在增乘开方程序的算理分析之上的,同时对笛卡儿的成果来源、以及李锐的工作与当时学术风气的关系等问题提出了自己粗浅的看法。

The rule of signs for determining the number of rational roots in the theory of equations was first suggested by Rene Descartes(1596-1650) in volume three of his Geometry(1637). The same discovery was made independently by Li Rui(1768-1817), a Chinese mathematician of the Qing dynasty, who published the result in volume one of his Kai Fang Shuo(On the Solution of Equations). Li Rui's discovery of the rule of signs resulted from his research on the traditional Chinese principle of zeng cheng kai fung fa('method of solving equations'), and was also related to his use of such methods as sequencing, enumeration, analysis, synthesis and induction. Li's research went well beyond the classical Chinese algebra, and represents one of the most creative theoretical advances made in the history of mathematics during the Qing dynasty.