敦煌汉藏文献中所存九九表研究  

A Study on Multiplication Tables from Chinese and Tibetan Dunhuang Manuscripts

作　　者：杨宝玉[1] 刘英华[2] Yang Baoyu;Liu Yinghua

机构地区：[1]中国社会科学院古代史研究所 [2]中国藏学研究中心北京藏医院

出　　处：《中国社会科学院大学学报》2023年第6期90-105,155,共17页Journal of University of Chinese Academy of Social Sciences

摘　　要：本文首先据传世文献和考古发现归纳了作为算学重要基础的九九表变化演进的基本脉络,继而梳理了敦煌藏经洞所出汉文和藏文文书中近20件九九表的现存状况与主要特征,论证了敦煌汉文文书可将对九九表从小到大表述顺序出现的可证时间提前至少200多年;分析指出敦煌藏文文书表明除了我们熟知的36句式、45句式、81句式,我国古代的九九表还有64句式,认为很可能早在10世纪时就已有"大九九"而非迟至明代以后;还论及九九表与以乘法口诀为引句的算表的概念界定问题,并以九九表研究为例,重申了敦煌文献对我国古代科技史研究的重要意义。Based on handed down documents and archaeological discoveries,this paper first summarizes the basic context of the evolution of multiplication tables as an important foundation of mathematics,and discusses the current condition and main characteristics of nearly twenty multiplication tables from Chinese and Tibetan Dunhuang manuscripts,demonstrating that the Chinese manuscripts can advance the date of the appearance of the multiplication formula in ascending order by at least 200 years.This paper thereafter points out that in addition to the known 36,45 and 81 sentence patterns,the Tibetan manuscripts also contain a 64 sentence pattern in the ancient multiplication table.Therefore,there is a reasonable belief that a complete multiplication table existed as early as the 1oth century,significantly predating the previous consensus of Ming Dynasty.It further discusses the difference between the multiplication table and Suanbiao(calculation table)with multiplication formula as the quotation.Finally,taking the multiplication table as an example,this paper reaffirms the significance of Dunhuang manuscripts for the study on the history of science and technology in ancient China.

关 键 词：敦煌汉藏文献 九九表 算表 算学史 

分 类 号：C256[社会学]