《九九乘法歌》的传播与演变--以出土文献为中心

The Dissemination and Development of Nine-Nine Multiplication Song——Centering on Unearthed Documents

通过秦汉简牍,可知当时已经形成了固定的三十八句的《九九乘法歌》,以横向分列书写方式为主,汉代出现了纵向书写方式和仅有乘积的歌诀,并可知该歌诀随着秦汉时期疆域的拓展而传播到了河西地区和南海郡。通过楼兰文书,可知魏晋时期出现了四十五句的乘法歌,并传播到了西域地区。通过敦煌吐鲁番写本,可知唐代四十五句的乘法歌已经成为常态,书写形式以纵向为主,不仅出现了大写数字本、吐蕃文本及“大九九”,而且还在歌诀中加入平方、加法、除法运算及数码,呈现了唐五代宋初敦煌及西域地区的算术教育状况。通过日本木简,可知八世纪四十五句的乘法歌已经在日本各地普及。

Through the Qin and Han Bamboo Slips,it can be known that a fixed thirty-eight-sentence Nine-Nine Multiplication Song in horizontal writing form was created at that time and there appeared the Nine-Nine Table in vertical writing form with only the result of the multiplication in the Han Dynasty.With the expansion of the territory during the Qin and Han Dynasties,it was quickly spread to the Hexi and Nanhai regions.Through Loulan Manuscripts,we can see that the forty-five-sentence Multiplication Song appeared during the Wei and Jin Dynasties and was spread to the Western Regions.Through the Dunhuang and Turpan Manuscripts,it can be found that the forty-five-sentence Song in vertical writing form became the norm in the Tang Dynasty.During the Tang and Five Dynasties,the capital number version,the Tibetan version and the eighty-one-sentence Nine-Nine Song appeared,and the Counting symbol,addition,division,and square were added to the Nine-Nine Song.These manuscripts show the state of mathematics education in Dunhuang and the Western Regions at that time.From Japanese Bamboo Slips,we can see that the forty-five-sentence Song was popularized all over Japan in the eighth centuries.