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The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

Gerolamo Cardano's De Regula Aliza

  • Book
  • © 2015

Overview

Authors:
  1. Sara Confalonieri

    1. FB C, Bergische Universität, Wuppertal, Germany

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  • Publication in the field of didactics and history of mathematics

  • Includes supplementary material: sn.pub/extras

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XX
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  2. Introduction

    • Sara Confalonieri
    Pages 1-4

  3. Putting in context Cardano’s works and mathematics

    • Sara Confalonieri
    Pages 5-52

  4. Cardano solves equations in the Ars Magna

    • Sara Confalonieri
    Pages 53-178

  5. Cardano’s earlier encounters with some general treatments of equations

    • Sara Confalonieri
    Pages 179-242

  6. Strategies to possibly overcome the casus irriducibilis: the De Regula Aliza

    • Sara Confalonieri
    Pages 243-388

  7. Conclusions

    • Sara Confalonieri
    Pages 389-393

  8. Back Matter

    Pages 395-443
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • FB C, Bergische Universität, Wuppertal, Germany

    Sara Confalonieri

About 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.

Bibliographic Information

  • Book Title: The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

  • Book Subtitle: Gerolamo Cardano's De Regula Aliza

  • Authors: Sara Confalonieri

  • DOI: https://doi.org/10.1007/978-3-658-09275-7

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2015

  • Softcover ISBN: 978-3-658-09274-0Published: 24 March 2015

  • eBook ISBN: 978-3-658-09275-7Published: 18 March 2015

  • Edition Number: 1

  • Number of Pages: XX, 443

  • Number of Illustrations: 34 b/w illustrations

  • Topics: Epistemology, Algebra

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