The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

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. 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. Contents 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 Target Groups Academics, researcher and students in the fields of mathematics, the history of mathematics, and epistemology. The Author 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.