刘徽《重差》从《九章算术》注本分离的时代问题——基于李俨编史观启示的研究

On the Time When Liu Hui’s Chongcha Separated from His Annotated Book of The Nine Chapters on Mathematical Procedures——A study based on Li Yan’s conception of historiography

刘徽《重差》是远距离测算高、深、广、远的重要著作,原缀于其《九章算术》注本末章“勾股”之下,后单行乃至以《海岛算经》之名行世。《重差》何时分离为史家所关注,主流观点认为始于唐代并更名为《海岛算经》。通过辨析前人研究的得失,提出李俨的编史观和他提到的史料对解决此问题有重要价值;证明《重差》至迟在公元540年左右确有信都芳的分离本,也存在祖冲之时代已有分出本的可能性;阐明《重差》获得《海岛》之名不晚于初唐,可能早于李淳风注释十部算经之时,而唐代数学教育和科举制度对《重差》分出本(特别是以《海岛算经》之名)的通行有重要作用;指出对文献流传过程中的分合,不能拘泥于非此即彼的观念,必须充分考虑其复杂性。

Liu Hui’s Chongcha(重差,double differences)is an important work on the survey of height,depth,width and distance from a distant place.It was originally placed under“Gougu勾股”,the last chapter of Jiuzhang Suanshu Zhu(《九章算术》注,Liu Hui’s annotated book of The Nine Chapters on the Mathematical Procedures),later spread separately and renamed Haidao Suanjing(海岛算经,Sea Island Mathematical Classic).Concerning Chongcha’s separation,the mainstream view by the historians is that it was in Tang dynasty when the separation began and when Chongcha was renamed as Haidao Suanjing.By analyzing the previous studies,the authors proposed that Li Yan(李俨)’s methodology of historiography and the sources he mentioned are of great value in addressing this question.The authors demonstrated that there was a separate version of Chongcha at the time of Xindu Fang(信都芳)around 540 C.E.at the latest,and there was also the possibility that it had separated edition(s)at the period of Zu Chongzhi(祖冲之).The authors indicated that the renaming was no later than the early Tang dynasty,and even probably earlier than Li Chunfeng(李淳风)’s Annotations to the ten mathematical classics(十部算经);while Tang’s mathematical educational system and the imperial examination system played an important role in the popularity of separated edition of Chongcha(especially titled“Haidao Suanjing”).At last,the authors pointed out that,concerning separation or combination in the literature evolvement,one cannot be bound by the notion of either one or the other,but must take full account of the complexity.