The Solution of The Cubic Equation
Mathematicians from del Ferro's time knew that the general cubic equation could be simplified to one of two cases called the depressed cubic equation, for positive numbers ,,:
The term in can always be removed by letting for an appropriate constant .
While it is not known today with certainty the method that del Ferro used, it is thought that he used the fact that solves the equation to conjecture that solves . This turns out to be true.
Then with the appropriate substitution of parameters, one can derive a solution to the depressed cubic:
There are conjectures about whether del Ferro worked on a solution to the cubic equation as a result of Luca Pacioli's short tenure at the University of Bologna from 1501-1502. Pacioli had previously declared in Summa de arithmetica that he believed a solution to the equation to be impossible, fueling wide interest in the mathematical community.
It is unknown whether Scipione del Ferro solved both cases or not. However, in 1925, manuscripts were discovered by Bartolotti which contained del Ferro's method and made Bartolotti suspect that del Ferro had solved both cases.
Cardano, in his book Ars Magna (published in 1545) states that it was del Ferro who was the first to solve the cubic equation, and that the solution he gives is del Ferro's method.
Read more about this topic: Scipione Del Ferro
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