关于“大衍术”源流的算例分析  

AN ANALYSIS OF THE TEXT ON THE ORIGIN AND DEVELOPMENT OF THE DAYAN METHOD

作　　者：王荣彬[1] 徐泽林[1] 

机构地区：[1]武汉大学数学系,西北大学数学系

出　　处：《自然科学史研究》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

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.

关 键 词：大衍术 通其率术 方程术 数书九章 

分 类 号：O112[理学—数学]