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中文摘要：
基于对卡尔达诺关于三次方程的一般法则和《大术》第6章的命题的分析,复原了卡尔达诺关于三次方程的17条特殊法则的构造过程,由此揭示出隐藏在这些法则背后的数学思想和方法,阐明了卡尔达诺对这些法则所作的模糊暗示的意义,并指出其综合叙述方式与这些法则的构造过程并不完全一致。另外,根据对这些特殊法则的适用范围的分类讨论,认为卡尔达诺构造这些特殊法则的目的并非专为解决三次方程的不可约情形。
英文摘要：
Based on the analysis of Cardano＇s general rules for cubic equations and the propositions in the sixth chapter of Artis Magnae,Cardano＇s 17 special rules for cubic equations are reconstructed.Hence his mathematical ideas and methods behind these rules are revealed,and his vague indications on these special rules are clarified.It is pointed out that Cardano＇s synthetic statement of the rules does not quite accord with the procedure of the reconstructions of relative rules.Meanwhile,according to the discussion on the applicable cases of these special rules by means of taxonomic approach,Cardano＇s intention is argued as rather the special rules themselves than the methods on the irreducible cases of cubic equations.
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