印度正弦表与唐代正切函数表之比较

A comparative study between Indian sine table and tangent table of Buddhist monk Yi Xing

为澄清印度正弦表与唐代僧一行 (683～ 72 7年 )正切函数表的关系 ,采用中、印数学比较的方法 ,分析唐代传入中国的印度《九执历》中所载印度正弦表的构造方法 ,并与僧一行所编《大衍历》中的晷影差分表比较。结论指出 :僧一行的数表没有利用传入中国的正弦表的结果推算 。

To clarify the relationship between the Indian sine table and the tangent table of the Buddhist monk Yi Xing(683～727A.D.) in the Tang Dynasty, the method of the mathematical compare between the ancient China and India was adopted. An analysis was made on the constructive method of the Indian sine table in the Jiuzhi Calendar(九执历) and the difference table of solar shadows in Dayan Calendar(大衍历). On the basis of a comparative studybetween the two tables, the conclusion was drawn that Yi Xing did not take advantage of the results of the Indian sine table to calculate the lengths of solar shadows.