摘要
意大利数学家斐波那契(Fibonacci,C.1170-C.1250)在《计算之书》(Liber Abaci,1202)中首次利用多重双假设法求解多元线性方程组问题,成为之后三百多年欧洲数学家处理此类问题的标准算法。德国数学家克拉维乌斯(Clavius,1538-1612)在《算术实践概要》(Epitome Arithmeticae Practicae,1583)中运用二重双假设法求解三元线性方程组问题时,发现了求解公式的一致性,开始对斐波那契的方法做出重要简化。该文通过对比二者求解的异同,对克拉维乌斯的方法如何简化运算给出了量化分析,解释了克拉维乌斯双假设法求解公式一致性的数学原理,并进一步提出,他可能是基于对4个特殊三元线性方程组问题的计算结果进行分析和归纳,从而发现了求解公式的一致性。
In 1202,Italian mathematician Fibonacci(C.1170-C.1250)published Liber Abaci,in which the system of linear equations was solved by multi-fold double false positions for the first time in Europe.This method became the standard algorithm until the late 16 th century when European mathematicians treated with such problems.In 1583,German mathematician Clavius(1538—1612)dealt with the system of 3-variable linear equations by the method of two fold double false positions in his Epitome Arithmeticae Practicae,he discovered the consistence of the solution formula of double false positions,which became the earliest simplification to Fibonacci′s method.By comparing the similarities and differences between the methods,this paper presents a quantitative analysis of how Clavius′simplified method works,and explains the mathematical principles of Clavius′consistence of the solution formula,and proposes that Clavius′discovery of the consistency of solution formula may be based on analysis and induction of the concrete mean results during his solution of 4 special systems of 3-variable linear equations.
作者
刘迪
赵继伟
LIU Di;ZHAO Jiwei(Institute for Advanced Studies in History of Science,Northwest University,Xi′an 710127,China)
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2019年第6期970-976,共7页
Journal of Northwest University（Natural Science Edition）
基金
国家自然科学基金资助项目(11571276,11501444)
关键词
二重双假设法
斐波那契
克拉维乌斯
一致性
线性方程组
the method of twofold double false positions
Fibonacci
Clavius
consistence
system of linear equations
