花拉子米《代数学》探源  

The Preliminary Discussion about the Source of Al-Khwārizmī's Algebra

作　　者：刘琳[1] 杜瑞芝[2] 

机构地区：[1]东北财经大学津桥商学院,辽宁大连116025 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《广西民族学院学报（自然科学版）》2006年第2期53-58,86,共7页Journal of Guangxi University For Nationalities(Natural Science Edition)

基　　金：吴文俊数学与天文丝路基金资助项目(WSF2003-02)

摘　　要：关于花拉子米《代数学》的来源,历来科学史家都持有不同意见.笔者从《代数学》的形式、内容、修辞及方法等方面与古代东、西方的有关论著作了比较,并对各种不同观点进行对比分析,得到一些初步认识:《代数学》中所讨论的一次和二次方程以及某些运算技巧可能源于巴比伦.花拉子米对第四种二次方程的讨论,使用的“三率法”,对圆周率的计算以及某些术语可以在早期传入阿拉伯的印度典籍中找到出处,而在这些数学知识中有一些可能是远源于中国的(比如“三率法”).花拉子米讨论一元二次方程时所采用的算术解法与几何论证相结合的方法似乎是受希腊人推崇几何学的观念的影响,但经过仔细分析,认为他的几何证明本质上区别于欧几里得的“几何代数”,而与中国古代的“出入相补原理”更相像.通过与丢番图《算术》的比较,发现它对《代数学》没有直接的影响.《代数学》中几何篇章的内容完全是古希伯来人的一部《测量准则》的翻版,而后者中又有大量题材来源于海伦的《度量论》———一部反映了亚历山大后期希腊数学特点的著作.我们认为,在《代数学》中比较突出的反映出东西方数学并存、但以东方数学传统的影响更为突出的特点.事实上,花拉子米可能通晓中东、近东、巴比伦以及古代希腊罗马的科学遗产,他博采众长,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.On the source of al--Khwarizmi＇s Algebra, mathematicians always have held different opinions. We make comparisons with ancient east and western relevant treatises in form, content, rhetoric, method of Algebra, compare and analyze all kinds of views, finally get some preliminary cognition. Simple and quadratic equation and some skills of operation in Algebra may come from Babylon. The discussion of the fourth kind of quadratic equation , the use of ＂ rule of three ＂ , the calculation of number n and some terms in Algebra can be found in Indian classics introduced to Arab and some of these mathematical knowledge maybe comes from China （such as＂rule of three＂）. The method for solving quadratic equation which combined arithmetic solution and geometry demonstration together by al--Khwarizmi probably is influenced by Greek who praised highly geometry, but through analyzing carefully , his geometry seems different from ＂ geometrical algebra ＂ of Euclid in essence, but is similar to Chinese ancient mathematical method-- out--in complementary--like principle. Through the comparison with Arithmetica, we find it does not have direct influence on Algebra. The geometry chapter of Algebra is a reprint of Measuring Criterion and the latter has a large amount of contents stemming from Helen＇s Metrica one reflects the Greek mathematical characteristic in Alexander＇s later stage. In our opinions an outstanding characteristic in Algebra is the compatibility between east and west mathematics, with more eastern traditional mathematics influence. In fact, al--Khwarizmi may understand thoroughly Middle East, the Near East , Babylon , scientific legacy of ancient Greece and Rome, he learnt wildly from other＇s strong points, has absorbed the rational factor from both the east and western different mathematics source very wisely, thus finished his algebra work creatively.

关 键 词：花拉子米 《代数学》 《婆罗摩历算书》 《原本》 “出入相补原理” 《算术》 《测量准则》 

分 类 号：O11[理学—数学]