从岳麓书院藏秦简《数》看上古时代盈不足问题的发展

The Development of the Problems of the Excess and Deficit in the Early Period of China:An Investigation Based on the Shu on the Qin Bamboo Strips Preserved at Yuelu Academy

对岳麓书院藏秦简《数》中的盈不足问题进行新的校释,解决了一些疑难问题;并与《九章算术》《算数书》等相对照,研究了上古时代盈不足问题的发展.指出《数》进一步证明盈不足问题的产生可以追溯到秦代和先秦时期,《数》对《九章》盈不足问题在文本上没有直接影响,《九章》在先秦的祖本或其衍生本的盈不足方法很可能对《数》有间接或直接的影响.通过将《九章》“盈不足”章第15题及《算数书》和《数》的相关内容进行对比和分析,指出前人认为是古人错误地把此题归入“盈不足”章的观点,是不妥当的;《九章》编者在为“盈不足”章选材时具有高度的一致性.

The new collations and new interpretations were given for the materials about the yingbuzu (excess and deficit) in the book Shu (On Numbers) on the Qin bamboo strips preserved at Yuelu Academy and some difficult and complicated problems were clarified in this paper.Together with the corresponding materials in the Jiuzhang Suanshu (Nine Chapters on Mathematical Procedures) and the Suanshu Shu (A Book on Numbers and Computation),we investigated the development of the yingbuzu problems in early China.The textual analysis revealed that the problems of yingbuzu could be traced back to the Qin Dynasty and the Pre-Qin period according the Shu,the Shu had no textual influence on the Jiuzhang Suanshu,while the solution methods of yingbuzu in the pre-Qin ancestors or its derivatives in the Jiuzhang Suanshu was likely to have direct or indirect influence on the Shu.After comparing and analyzing the 15th problem of the “Yingbuzu” in the Jiuzhang Suanshu with corresponding problem in the Shu and the Suanshu Shu,we realized that the opinion of some scholars that ancients had carelessly put this problem into the “Yingbuzu” chapter was not appropriate and held that the composers of the Jiuzhang Suanshu maintained high degree of consistency with the Shu and the Suanshu Shu in selection of problems for the chapter.