The Flos of Leonardo turns on the second question set by John of Palermo, which required the solution of the cubic equation x 3 -{-2x'-}-lox = 20.
Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.
This contest over, Tartalea redoubled his attempts to generalize his methods, and by 1541 he possessed the means for solving any form of cubic equation.
He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.
Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation.
