敦煌本藏文算书九九表再探

Restudy on Tibetan Multiplication Tables in Dunhuang Manuscripts

敦煌文献中已鉴别出4种藏文九九表,其中,P.t.1256是由藏文字母拼写的汉文“小九九”表,ITJ764、P.t.1070和B59:10是藏文九九表,包括了不同编排形式的“小九九”表和“大九九”表。ITJ764尾题人名“■”,为藏文九九表溯源和断代提供了重要依据。对这4篇写本做转录,对残缺的内容做推拟还原,并给出译文和评析,初步结论是:敦煌藏文九九表有大、小两类4种,与汉文“小九九”表作用一致,编排方式有别,藏文九九表抄写者和使用者并不限于藏族。这些藏文算学文献实物,为研究藏族科技史和汉藏文化交流史提供了第一手资料。

Four manuscripts of multiplication table have been identified from Tibetan manuscripts of Dunhuang grottoes. The P. t. 1256 is a transliteration of Chinese original with Tibetan alphabets,and the other three,ITJ764,P. t. 1070 and B59: 10 are indeed in Tibetan,which include different forms of simplified format and complex format. The name of Chinese author mentioned at the end of ITJ764 is helpful in traceability and chronology research of it. Along with restoration of the missing parts translations and interpretations of these four manuscripts,we can make a preliminary conclusion that the Dunhuang multiplication table have four types which belong to complex and simplified in format separately. There are visible differences in format between Tibetan and Han multiplication tables of Dunhuang. Tibetans seem to prefer the complex format while the Han prefer simplified ones. The users of these multiplication tables are not limited to Tibetans. These physical Tibetan arithmetic documents are first-hand materials for the study of Tibetan history as well as cultural interchange history between Han and Tibetan communities.