The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

Sara Confalonieri graduated in Philosophy at the Università degli Studi di Milano, in Mathematics at the Université Paris 6, and in Epistemology at the Université Paris 7, where she also obtained the PhD degree in history of mathematics on cubic equations during the Renaissance. At present, she takes part in a project on history of the didactic of mathematics in the 18th century at the Bergische Universität in Wuppertal as a post-doctoral researcher.

Inter-Dependencies Between the Families of Cubic Equations in the Ars Magna.- Ars Magna, Chapters XI-XXIII and the Casus Irreducibilis.- Getting Acquainted with the De Regula Aliza.- The Method of the Splittings in Aliza, Chapter I.

"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)