Cardano’s constructive geometric demonstration. (Chinese. English summary)

J. Shaanxi Norm. Univ., Nat. Sci. Ed. 36, No. 6, 14-18 (2008).

Summary: 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.