摘要
基于对《大术》第7章关于三项方程变换法则的几何证明的构造性特点分析,总结了卡尔达诺的构造思想,并按照其方法把他针对三项三次方程的证明自然地推广到一般三项方程.由此认为,卡尔达诺在《大术》中的几何证明大多区别于经典的综合证明,而属于以分析为基础的验证.他对涉及高次方程的几何证明一般是通过具体例子来展示一般方法,但是,他针对特殊情形的证明方法具有一般性.另外,在方法论上指出,古证复原方法也适用于历史上存在的几何证明.
Based on the analysis of the constructive characteristics of the geometric demonstrations on the transformation between two three-term equations in the seventh chapter of Cardano＇s Artis Magnae, his constructive idea is summarized, and his demonstration on the case of the cubic equation is generalized to the general case by his own method. It is concluded that the most of the demonstrations in Cardano＇s Artis Magnae are different from classical synthetic proofs and are based on analytic deduction. Although the general method of his demonstrations about the cases of high degree equations is usually shown by concrete examples, his demonstrations on special cases are universal. Besides, it is pointed out that the reasonable reconstructive method is adaptive to the domain of historic geometric proofs.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第6期14-18,共5页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(10771169)
关键词
卡尔达诺
几何证明
变换法则
古证复原
Cardano
geometric demonstration
transformation rule
reasonable reconstruction
