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中文摘要：
目的复原卡尔达诺关于方程变换的一条错误法则，即《大术》第7章的法则7．13的构造过程。方法依据古证复原的原则，利用数理分析的方法。结果指出卡尔达诺的错误在于忽略了一个隐合条件，其原因在于他并没有把该法则的构造进行到底，并且没有对例子进行验证。结论揭示了卡尔达诺构造法则7．13的数学思想在于，先从法则的结论出发，通过分析得到法则的假设条件，然后再以综合的方式表述法则。最后，给出了该法则的正确形式及其例子。
英文摘要：
Aim To reconstruct Cardano＇s creating of an erroneous rule, i.e. , rule 7.13, for transformation between two equations in the seventh chapter of Artis Magnae. Methods By means of principles of reconstructing ancient proofs and mathematical analysis. Results It is pointed out that Cardano＇s mistake lies in his ignorance of a latent supposition, amples. Conclusion and that his underestimation of the complexity of the rule prevents him from checking his examples. Conclusion The mathematical idea of Cardano＇s creating of rule 7. 13 is revealed as thus ：he initially gets the suppositions of the rule from the conclusion of it and then expresses the rule in a synthetic way. Finally, the correct term of rule 7.13 with its examples is given.
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