费拉里和塔塔利亚的一个争论问题

A problem debated by Ferrari and Tartaglia

目的研究费拉里和塔塔利亚1547—1548年的数学论战。方法对《大术》问题38.14进行分析。结果卡尔达诺确实没有给出该问题的一般解法。问题38.14应该有两个解,但卡尔达诺只是通过将问题38.14与问题38.13比较而观察得出了一个解。问题38.14最终导致一个五项四次方程,其预解三次方程的判别式为负,在当时没有复数系的情况下,很难相信塔塔利亚给出了该问题的代数解法。结论塔塔利亚关于卡尔达诺师徒没有解决问题38.14的断言是正确的,但他自己也不可能解决该问题。

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.