摘要
通过分析秦九韶《数书九章》（１２４７年）“治历演纪”题算例，证明了所谓“通其率”算法在中算史上是确实存在的，指出历家相传有一种解一次同余式的一般性算法程序，秦氏称之为大衍术，并将之规范为大衍求一术，而历家推演历元的“方程术”与大衍术在算理上是一致的。并给出了“方程术”演算程序的一种推测。
Analysing the problem Zhili Yanji (searching the number of years between the beginning of the grand cycle and the year given by calendar makers , called Shangyan Jinian , in making calendars) in the book Shushu Jiuzhang (Mathematical Treatise in Nine Sections , A. D. 1247) by the celebrated Song mathematician Qin Jiushao , this paper proves that a mathematical method , known as Tongqilu , existed indeed in the history of mathematics in China. It also points out that the calendar makers had a traditional calculation program handed down for solving congruences called Dayanshu by Qin Jiushao who improved it into a standardized method named Dayan qiuyishu (lit. the great extension method of searching unity) . The authors consider that the mathematical principles of Dayanshu and Fangchengshu (a part of the method for searching Shangyuan Jinian)are identical. The paper goes a step fur- ther to conjecture how the calculation program of Fangchengshu worked.
出处
《自然科学史研究》
CSCD
1998年第1期47-54,共8页
Studies in The History of Natural Sciences
基金
中国博士后科学基金
关键词
大衍术
通其率术
方程术
数书九章
Dayanshu , Tongqilushu , Fangchengshu , Qin Jiushao
