阿尔·徒思三次代数方程正根的讨论

ON AL_TUSI'S DISCUSSION ON POSITIVE ROOTS OF CUBIC ALGEBRA EQUATIONS

讨论了阿尔·徒思三次代数方程求解（ 正根） 的方法． 考查阿尔·徒思这方面的工作，发现他的三次代数方程求解的方法已超越了传统的求解方程的几何方法． 在他的讨论中，一方面，函数的思想已贯穿始终；另一方面，就是问题转化思想． 这些正是阿尔·徒思三次方程正根的讨论与希腊几何代数的本质不同． 问题转化的思想在文艺复兴时期卡尔达诺的《大术》

In this paper, it is discussed the methods used by Sharafe al_Din al_Tusi in solving cubic algebraic equations. By investigating his work in this field, we expound his methods of solving cubic algebraic equations has exceeded the traditional geometrical methods of solving equations. In his work, on one hand, the idea of function was applied from beginning to end; on the other hand, it is embodied the concept of transformation of questions. These are main differences between the al_Tusi's discussion on the positive roots of cubic equations and Greek geometric algebra. The idea of transformation of questions was used again by G. Cardano in his works Ars magna in the Renaissance.