阿拉伯与中国代数方程数值解法的比较研究──阿尔·徒思与宋元数学家比较的个案分析

A COMPARATIVE STUDY ON CHINESE AND ARABIC NUMERICAL METHODS FOR THE SOLUTION OF ALGEBRAIC EQUATIONS

该文以阿尔·徒思和宋元数学家为例，对阿拉伯与中国代数方程数值解法进行了比较研究，认为二者在方法的一般性和所讨论的根的范围上是相同的，而不同点则在于方程的布式和分类。他们分别受到各自传统开方法的启示，且又沿着不同的途径发展，即阿尔·徒思的整个计算程序力求和早期传统的开方法相吻合，而宋元数学家则对早期传统的开方术作了进一步推广和发展，沿着一条机械化、程序化的道路进展。该文还分析了为什么中国学者实现了由开高次方到高次方程数值解法的突破，而阿拉伯学者却未能实现突破的原因。

This paper discusses the numerical methods used by Arabic scholars in solving quadratic and cubic equations through comparative study. By investigating the numerical methods used by Arabic and Chinese scholars, the paper deems that they were affected by their respective traditional methods of extraction, and that their developement followed differ-ent approaches. The former strove to coincide the whole calculation procedure with the early stage traditional methods of extraction. The latter extended and developed the early stage methods of extraction, and its development followed a way of algorithmization and modeliza-tion. The paper suggests that Al-Tusi and Chinese scholars found their methods based on the early stage methods of extraction independently of each other. Moreover, it analyses the rea-son why Chinese scholars were able to make a breakthrough from higher extraction to numeri-cal methods of solving higher degree equations, but Arabic scholars were not.