《算术之钥》与中算若干问题的比较研究  

Comparative Study Between The Key to Arithmetic and Some Similar Problems in Ancient Chinese Mathematics

作　　者：郭园园[1] 

机构地区：[1]上海交通大学人文学院科学史与科学哲学系,上海200240

出　　处：《自然科学史研究》2012年第1期107-128,共22页Studies in The History of Natural Sciences

基　　金：吴文俊"数学与天文丝路基金"资助

摘　　要：15世纪初阿拉伯数学家阿尔.卡西所著的《算术之钥(》1427)与中算相似问题的比较研究向来是中国数学史界研究的热点。以往国内的研究是从二手文献入手,通过几个问题的相似性认为《算术之钥》中的相关内容受到了中国宋元数学的影响。在解读《算术之钥》阿拉伯文本的基础上,将其与中算的相似问题进行系统地比较分析之后,发现二者就这些问题在术文、方法、目的、作用等方面均有不同;且纵观阿拉伯数学史,《算术之钥》中的相关内容都延续了10至12世纪早期的阿拉伯数学传统,由此得出《算术之钥》应该没有受到中国宋元数学直接影响的结论。The comparative study between the 15^th century Arab mathematician al-Kashi＇s The Key to Arithmetic（1427） and some similar problems in ancient Chinese mathematics has always been a research focus for Chinese mathematicians. In view of previous domestic research proceeding from secondary documents and through the similarity of several issues, it is concluded that the relevant content of The Key to Arithmetic has been influenced by the mathematicians of Song and Yuan Dynasties in China. Based on the interpretation of the original Arabic document and relatively comprehensive and systematic comparative analysis, this article comes to realize that there are some obvious differences among them in terms of its text, method and intention. In the light of the history of Arab mathematics, almost all of the content of the book canT on the early tradition of Arab mathematics from the 10^th to the 12^th century. Thus, The Key to Arithmetic should not be under the direct impact of the mathematics of Song and Yuan Dynasties in China.

关 键 词：《算术之钥》 增乘开方法 立成开方法 算术三角形 

分 类 号：O112[理学—数学]