A problem debated by Ferrari and Tartaglia

Journal of Northwest University 01/2010; 40:560-564.


Aim: To study the mathematical debates between Ferrari and Tartaglia in 1547—1548. Methods: Analyzing problem 38. 14 of Artis Magnae.
Results: Cardano indeed does not give the general solution of that problem. Problem 38. 14 should have two solutions,but Cardano only gives one by observation after comparing problem 38. 14 and problem 38. 13. Problem 38. 14 leads to a quartic equation at last,whose resolvent cubic equation is of a negative discriminant. Without the complex number system,it is unbelievable that Tartaglia could give the algebraic solution of that problem. Conclusion: It is correct that Tartaglia asserts that Cardano and his pupil have not resolved the problem. However,he himself could not resolve it either.

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