敦煌写本《立成算经》中若干重要问题新探

New Analysis of Certain Major Problems in Dunhuang Manuscript Licheng Arithmetic Method Set

敦煌遗书计有二十余件算学写本,其中S.930V《立成算经》保存相对完整,其内容丰富,与《孙子算经》的大部分内容相类,包括对度、量、衡的规定和九九乘法表等。二十世纪三十年代李俨先生对敦煌写本《立成算经》进行了研究,此后鲜少有学者涉猎此件。通过对S.930V进行录文、梳理,并结合录文对古代算筹法、度量衡等进行研究后发现:古算筹法计数分为横式、纵式,不同数位对应不同模式的算筹,如此错落间隔,清晰计数;零作为特殊的数字,算筹在计数时会为之留有空位;度、量、衡采用十进位制,且保有敦煌地区的特色,反映出中古时期敦煌地区社会经济的状况。

In more than 20 mathematical manuscripts of Dunhuang surviving works,S.930V Licheng Arithmetic Method Set,is a relatively complete arithmetic book.Its content is rich,similar to most of the contents of SunziCalculation Classics,including the provisions of measure,quantity and balance,and the nine-nine multiplication table.In the 1930s,Mr.Li Yan studied it,but few scholars have studied it since then.The author believes that the ancient counting method is divided into horizontal and vertical,and different digits correspond to different modes of counting,with scattered intervals,clear counting.As a special number,zero is left empty when counting.The degree,quantity and measure adopt the decimal system,and retain the characteristics of Dunhuang area,reflecting the social and economic conditions of Dunhuang area in the Middle Ages.