任占鹏

内容摘要：关于敦煌写本《算经》的编撰年代，有唐代说、五代说以及唐五代说，笔者结合韩延《夏侯阳算经》，将其编撰年代推定在唐代宗建中元年之后的中晚唐或后唐。《算经》类算书的源流，前人多追溯至晋代的《孙子算经》。笔者通过对比，认为北大秦简《算书》甲篇是《孙子算经》《算经》的源头，其内容和结构对后世算书的编撰有很大影响;《算经》分门别类的编撰体式，是受北朝《算书》的影响，而北朝《算书》上承《孙子算经》。由此，《算经》类算书的源流和发展脉络愈加明晰。

关键词：敦煌写本;《算经》;《孙子算经》;北大秦简《算书》甲篇;北朝《算书》

中图分类号：G256.1  文献标识码：A  文章编号：1000-4106（2021）06-0107-09

On the Codification Era and Origins of the Suan Jing from

Dunhuang Documents

REN Zhanpeng

（Headquarters for Education， Hiroshima University， Higashi Hiroshimashi， Hiroshima 7398511， Japan）

Abstract：Scholars of Dunhuang Studies have traced the compilation of the Dunhuang manuscript Suan Jing， an ancient book on mathematics， either to the Tang dynasty， the Five Dynasties， or the period of overlap between the two dynasties. By comparing the text with Xiahouyang Suan Jing recorded by Han Yan， the author of this paper concludes that the Suan Jing was compiled in the mid to late Tang dynasty， either after the first year of the Jianzhong era or during the Later Tang period. The origins of arithmetic books like the Suan Jing have traditionally been traced back to the Sun Tzu Suan Jing from the Jin Dynasty. It is through similar historical comparison and analysis that the author believes that the “Jia” chapter of the Suan Shu （a similar mathematical treatise） from the Qin dynasty bamboo slips collected at Peking University is the source of both Sun Tzu Suan Jing and Suan Jing， and that the contents and structure of this earlier compilation had a crucial influence on the compilation of books on mathematics created in later times. The compilation style of Suan Jing was clearly influenced by the Suan Shu of the Northern Dynasty， which in turn inherited its structure from Sun Tzu Suan Jing. This process of inheritance is highly suggestive for the origins and development of Chinese treatises on mathematics.

Keywords：Dunhuang manuscript; Suan Jing; Sun Tzu Suan Jing; “Jia” chapter of Suan Shu in the Qin bamboo slips; Suan Shu of the Northern Dynasties

《算经》，史籍未载，作者不明，幸赖敦煌莫高窟藏经洞得以保存了6个卷号的写本，可以缀合为两件，为P.3349+S.5859、S.19+羽37+Дx.3903+

S.5779{1}。缀合后的两件写本的内容依旧残缺，按照现存内容可以分为三部分：一是序文，二是以筹算识位法和乘除法、九九乘法歌、大数法、度量衡制为主的传统基础算学知识，三是“均田法第一”。一直以来学界多围绕《算经》的内容和价值展开探讨，且多涉及与《孙子算经》《夏侯阳算经》《五曹算经》的对比，先后有李俨[1]、那波利贞[2]、李倍始（U.J.Libbrecht）[3]、赵承泽[4]、许康[5]、李并成[6]、王进玉[7]、宫岛一彦[8]、王渝生[9]、李迪[10]、刘钝[11]、邓文宽[12]等先贤的研究成果可供参考。

本文在先贤的基础上，欲就以下两个方面的问题展开讨论：首先是《算经》的编撰年代。李俨、那波利贞、许康、宫岛一彦、郝春文、王进玉虽对此提出了自己的观点，但尚无定论，现在主要有唐代说、五代说以及唐五代说。……