9~10世纪伊斯兰世界两部代数著作的比较研究

A Comparative Study on Al-Khwārizmī's Algebra and Abū Kāmil's Algebra

花拉子米的《代数学》首次给出一元二次方程的一般解法,从此方程的解法成为代数学的基本特征,并为代数学的发展提供了方向.艾布.卡米勒是继花拉子米之后第一位著有代数著作的数学家,他的《代数书》被视为《代数学》的评注书,所给出的解法更具一般性和系统性,所选例题也更多样化;而且,当遇到具无理系数的方程时,作者放弃了几何证明,具有明显的算术化趋势.两部著作传入欧洲后,大部分内容被纳入斐波那契的《实用几何》中,因此得以广泛的流传.

Al-Khwārizmī＇s Algebra first gave all the solutions to the quadratic equations. From then on, the solution to the equations is considered to be the basic characteristic of algebra. It provided development direction of algebra. After Al-Khwārizmī, Abū Kāmil is the first algebraist who wrote books about algebca. Comparing with Al-Khwārizmī＇s Algebra, we find that Abū Kāmil^s Algebra is considered to be the commentatory of Al-Khwārizmī＇s Algebra. Besides Abū Kāmil gave the more general, more systemic methods of the solution to queadratic equation with more various examples. When the coefficients of quadratic equations were irrational numbers, Abū Kāmil abandoned the geometry demonstration showing the trend of arithmetization. After their works were introduced to Europe, most of their contents were brought into Practica Geornetriae written by Fibonacci and became prevalent.