摘要
刘益在中国古代数学史上最先引入系数可为负数的方程，并突破了方程首项系数必须为1的限制。以往人们认为有了增乘开方法，只要知道正负数的四则运算便可十分容易地推广到高次方程的数值解。因此，对增乘开方法给予了高度的重视，而对刘益工作的意义未予足够的肯定。该文分析研究了刘益的直田演段问题，指出方程系数域的推广，蕴涵着观念上的革新，是中算家有关高次方程数值解法领域发展进程中的一个关键步骤。
It was Liu Yi who first studied the equation with negative coefficients, and broke through the limit of the leading coefficient having to be 1 in the history of mathematics in ancient China. People used to consider that the Zheng-Cheng Method for the Extraction of Roots can be extended to the solution of numerical higher equations easily with the knowledge of four arithmetic operations for negative quantity. Thus, there are full of praises to the Zheng-Cheng Method while the significance of Liu Yi's work is ignored. This paper deals with the problems of dividing a rectangle by Liu Yi. It points out that there exists new concept in Liu's work which is a key in the field of ancient Chinese mathematicians' research for solving numerical higher equations.
出处
《自然科学史研究》
CSCD
1999年第1期28-35,共8页
Studies in The History of Natural Sciences
关键词
刘益
正负开方术
议古根源
古代数学
清代
Liu Yi, Zheng-Cheng Method for the extraction of roots, Yi Gu Gen Yuan
