摘要
一、秦九韶在《数书九章》(1247)提出的"大衍求一术"(一次同余式解法),在世界数学史上占有重要地位,这一点已为学术界所公认。他同时也是世界上第一个考虑一次同余式理论中模数两两互素的问题,对这个问题,学术界的观点是不一致的,在具体方法的解释上也存在一些不同的看法。本文拟从历史的角度谈谈个人的意见。在"大衍总数术"中,秦九韶把"问数"(非两两互素的模数)分为四类:"元数"(整数)、"收数"(小数)、"通数"(分数)和"复数"(10的倍数)。其中"收数"和"通数"都可化成"
The author considers that there are two steps in Qin Jiushao's basic methods to find the Dingshu (the modul): The first, finding the Deng (G. C. D.) of one number and another continuously, using it to divide the Ji instead of the Ou (or divide the Ou instead of the Ji); the second, finding the Deng of one number and another continuously, using the Deng to divide the Ji instead of the Ou, and return to multiply the latter or otherwise.In this method, the word Ji means the odd times G. C. D., and the word Ou means the even times G. C. D., their meaning being evolved from the method of divining in the Yi Jing Xi Ci Zhuan.In this method, finding the G. C. D. of one number and another continuously, using the G. C. D. to divide the one instead of another has its origin in the method of Shao Guang in the Jiu Zhang Suan Shu.
出处
《自然科学史研究》
1987年第4期293-298,共6页
Studies in The History of Natural Sciences
