Sara Confalonieri presents an overview of Cardano's mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano's algebraic works, the De Regula Aliza (1570), which displays the attempts to overcome the difficulties entailed by the casus irreducibilis. Notably some of Cardano's strategies in this treatise are thoroughly analyzed. Far from offering an ultimate account of De Regula Aliza, by one of the most outstanding scholars of the 16th century, the present work is a first step towards a better understanding.
"Sara Confalonieri presents the most complete analysis every attempted of Cardano's Ars magna as well as of Cardano's valiant attempts to bypass the cases where the cubic formula includes square roots of negative numbers, the so-called casus irreducibilis. ... a reference guide that will be useful whenever one is studying Cardano's work. ... This work will stand as a monument to Cardano's attempts to solve cubic equations." (Victor J. Katz, Mathematical Reviews, December, 2015)
"Sara Confalonieri's The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations: Gerolamo Cardano's De Regula Aliza, based on the first part of her 2013 dissertation, is a welcome addition to the literature on Gerolamo Cardano. ... There is much to absorb and study in this treatise. And I look forward to reading the results of Confalonieri's future work related to the subjects presented here." (Joel Haack, MAA Reviews, June, 2015)
"Sara Confalonieri's The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations: Gerolamo Cardano's De Regula Aliza, based on the first part of her 2013 dissertation, is a welcome addition to the literature on Gerolamo Cardano. ... There is much to absorb and study in this treatise. And I look forward to reading the results of Confalonieri's future work related to the subjects presented here." (Joel Haack, MAA Reviews, June, 2015)