萨拉夫·丁·图西三次方程数值解的研究

A Study on Sharaf al-Dīn al-Tūsī's Numerical Solution of Cubic Equations

文章在全面解读阿拉伯数学家萨拉夫·丁·图西（Sharaf alDin al-Tusi，1135～1213）《方程》（1209年）一书的基础上，着重分析了其中的三次方程数值解法，得出它们是在已有开方算法的基础上有规律性地构造出来。另还将其与同时代中算家秦九韶的相似算法作比较，得出二者的核心算法相同，但是由于各自数学传统的差异又表现出明显的不同。该研究对于进一步认识图西三次方程数值解算法的构造思想以及探究中阿数学在相似问题上各自的特点与传统有积极意义。

This article analyzes the numerical solutions of cubic equations based on comprehensive interpretations of ＂Equations＂ （1209） by Sharaf al-Din al-Tusi （1135 - 1213 ）. The results show that the algorithms were constructed from existing methods of extracting roots. The article also compares the algorithms by al-Tusi and Qin Jiushao. Results indicate that the cores of the two algorithms were the same, though they were significantly different due to differences in the mathematical traditions. The present study is significant in understanding the numerical solutions of the cubic equations by al-Tusi. It also contributes to investigations of the features and traditions of such mathematical algorithms in China and Arabic countries.