奥马·海亚姆《代数学》来源初探

奥马.海亚姆的《代数学》是将代数与几何结合起来解决问题的代表作,也是阿拉伯数学中最突出的成就之一.关于它的来源,在国内这方面的探讨还很少见.笔者从《代数学》的内容、方法等方面与古希腊、古代中国以及阿拉伯本土数学家的有关著作进行了比较,形成下面的一些初步的认识.奥马.海亚姆在方程代数解法后附有相应的几何证明以及将三次方程写成齐次方程的形式,这都体现了古希腊几何代数学思想的影响;通过与中国古代著作《九章算术》进行比较,我们发现《代数学》中的开方算法与中国古代方法非常相近,而与印度数学的算法相去甚远.《九章算术》中的内容可能是沿着中国-印度-阿拉伯的路线传到伊斯兰世界,并对阿拉伯数学家产生了间接的影响;同时,他继承了前辈花拉子米关于一元二次方程的解法.事实上,奥马.海亚姆博采众长,非常明智地吸收了东、西方不同数学源泉中的合理因素,从而创造性地完成了他的代数学著作.

The preliminary discussion about the source of Omar Khayyam's Algebra

Omar Khayyam's Algebra is the masterpiece of combining algebra with geometry,it is outstanding in Arabian mathematics.On the source of it,there is very little discussion interiorly.We make comparisons with relevant treatises of ancient Greece,ancient China and Arabian mathematicians in content and method of Algebra,and finally get some preliminary cognition.Omar Khayyam gave the geometrical demonstrations after algebraic solution and wrote the cubic equation as the form of homogeneous equation.It shows the influence of geometrical algebra in ancient Greece;Comparing with The Nine Chapters on the Mathematical Art,we find that the arithmetic of extraction in Algebra is similar to the method of ancient Chinese mathematics and different from the method of ancient Indian mathematics.Hence we infer that the content of The Nine Chapters on the Mathematical Art exerted the indirect influence on the Arabian mathematicians through the route of China-India-Arabia.And he inherited al-Khwarizmi's solution to quadratic equation.In fact,Omar Khayyam learnt wildly from other's strong points,had absorbed the rational factor from both the east and western mathematics source wisely,thus finished his algebra work creatively.