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), whi
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Sara Confalonieri
The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations Gerolamo Cardano’s De Regula Aliza
Sara Confalonieri Bergische Universität Wuppertal Germany Dissertation Université Paris 7 Diderot, 2013
ISBN 978-3-658-09274-0 ISBN 978-3-658-09275-7 (eBook) DOI 10.1007/978-3-658-09275-7 Library of Congress Control Number: 2015933836 Springer Spektrum © Springer Fachmedien Wiesbaden 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci¿cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro¿lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speci¿c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Spektrum is a brand of Springer Fachmedien Wiesbaden Springer Fachmedien Wiesbaden is part of Springer Science+Business Media (www.springer.com)
Foreword The present work comes from my dissertation [55], supervised by Marco Panza (directeur) and Massimo Galuzzi (co-directeur), defended at the Université Diderot Paris 7 on October 12, 2013. It has been improved according to the remarks and observations that I have received from the viva examiners Sabine Rommevaux (président), Veronica Gavagna (rapporteur), Klaus Volkert (rapporteur), Paolo d’Alessandro, Jeffrey Oaks, and my two supervisors. The dissertation was originally composed of two parts. Only the first one is contained in the present work. The second part is a compared Latin transcription of the 1570 and 1663 editions of the De Regula Aliza and a partial English translation; this has been omitted since it will hopefully give rise to a critical edition of Cardano’s treatise. For their support and help, I want to express my gratitude to Marco Panza and Klaus Volkert. I am indebted to Massimo Galuzzi, Veronica Gavagna, and Sabine Rommevaux for their outstanding advice. A special thank goes to Paolo D’Alessandro, Jeffrey Oaks, David Rabouin, Jackie Stedall, Pier Daniele Napolitani, the SPHERE group in Paris, Jens Høyrup, and Antoni Malet.
Notations and more For a modern reader it is almost impossible – or at least it is really hard work – to account for Cardano’s time mathematics without reverting to some sort of formalism.
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