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Cardano’s rule of proportional position. (Chinese. English summary) Zbl 1449.01013

Summary: Based on systematical summarization of the seven problems in Chapter 33 of Artis Magnae and careful analysis of Problem 4.1, the modern mathematical representation of the rule of proportional position is given and Cardano’s deduction of this rule is reconstructed by the elimination method for systems of linear equations with two variables in Chapter 9 of Artis Magnae. This rule reflected Cardano’s efforts to solve a type of special five-term quartic equation, through which he could transform the five-term quartic equation into a new biquadratic equation. Meanwhile, it is suggested that Cardano did not grasp the solution of general five-term quartic equation.

MSC:

01A40 History of mathematics in the 15th and 16th centuries, Renaissance

Biographic References:

Cardano, Gerolamo
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