Introduction

Abstract

Solving cubic equations by a formula that involves only the elementary operations of sum, product, and exponentiation of the coefficients is one of the greatest results in 16^th century mathematics. At that time, the solution of quadratic equations was a well-mastered issue and the attention was driven on searching a generalisation to the cubic case. This was achieved by Girolamo Cardano’s Ars Magna in 1545. Still, a deep, substantial difference between the quadratic and the cubic formulae exists: while the quadratic formulae only involve imaginary numbers when all the solutions are imaginary too, it may happen that the cubic formulae contain imaginary numbers, even when the three solutions are all real (and different). This means that one could stumble upon numerical cubic equations of which he already knew three (real) solutions, but its cubic formula actually contains some square roots of negative numbers. This will be later called the ‘casus irreducibilis’.