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A Study on the Tibetan Arithmetic Works Found at Dunhuang

Liu Ying-hua;Beijing Tibetan Hospital,China Tibetology Research Center;  
Among the unearthed literatures from the Mogao Grottoes at Dunhuang, there are three Tibetan arith-metic works. They were written in the late Tubo dynasty, so they are the oldest extant Tibetan arithmetic works. Itcontains Chinese multiplication table with Tibetan phonetic notations at P.t.1256, and Tibetan multiplication ta-ble at P.t.1070 and B59:10.They reflect the state of Tibetan arithmetic studies at that time. The three works alsoprovide first-hand information for the study of Tibetan history of science and technology as well as the culture ex-change of Han and Tibetan people. This article contains the elucidating texts of the three works and offers theoriginal texts, their translation and the analyses of them. Moreover, a preliminary comparative study has beendone on Tibetan and Han's multiplication tables in the works unearthed at Dunhuang.
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