The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

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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.ContentsInter-Dependencies Between the Families of Cubic Equations in the Ars Magna Ars Magna, Chapters XI-XXIII and the Casus IrreducibilisGetting Acquainted with the De Regula AlizaThe Method of the Splittings in Aliza, Chapter ITarget Groups Academics, researcher and students in the fields of mathematics, the history of mathematics, and epistemology.The AuthorSara 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.
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.
Publication in the field of didactics and history of mathematics Includes supplementary material: sn.pub/extras

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Sara Confalonieri

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Gerolamo Cardano casus irreducibilis cubic equations cubic formula renaissance algebra

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“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)

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