The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations
The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

Author: Sara Confalonieri

Publisher:

Published: 2015

Total Pages:

ISBN-13: 9783658092764

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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. 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.

The Telling of the Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations
The Telling of the Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

Author: Sara Confalonieri

Publisher:

Published: 2013

Total Pages: 750

ISBN-13:

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Solving cubic equations by a formula that involves only the elementary operations of sum, product, and exponentiation of the coefficients is one of the greatest results in 16th century mathematics. This was achieved by Girolamo Cardano's Ars Magna in 1545. Still, a deep, substantial difference between the quadratic and the cubic formula exists: while the quadratic formula only involves imaginary numbers when all the solutions are imaginary too, it may happen that the cubic formula contains imaginary numbers, even when the three solutions are anyway ail real (and different). This means that a scholar of the time could stumble upon numerical cubic equations of which he already knew three (real) solutions and the cubic formula of which actually contains square roots of negative numbers. This will be lately called the "casus irreducibilis". Cardano's De Regula AJiza (Basel, 1570) is (at least, partially) meant to try to overcome the problem entailed by it. Its (partial) analysis is the heart of this dissertation.

The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations
The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations

Author: Sara Confalonieri

Publisher: Springer

Published: 2015-03-18

Total Pages: 458

ISBN-13: 3658092750

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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.

Explorations and False Trails
Explorations and False Trails

Author: Jens Høyrup

Publisher: Springer Nature

Published: 2024

Total Pages: 150

ISBN-13: 3031481585

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This book provides a unique perspective on the history of European algebra up to the advent of Viète and Descartes. The standard version of this history is written on the basis of a narrow and misleading source basis: the Latin translations of al-Khwārizmī, Fibonacci's Liber abbaci, Luca Pacioli's Summa, Cardano's Ars magna -- with neither Fibonacci nor Pacioli being read in detail. The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Viète's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps. This book traces the meandering development of all these techniques along with the mostly ignored but very important parenthesis function, by means of detailed readings of all pertinent sources, including the abacus and cossic algebra and French algebra from Chuquet to Gosselin. It argues for a necessary distinction between abbreviating glyphs and genuine symbols serving within a symbolic syntax, which allows it to trace the emergence of symbolic calculation. Characterization of the mathematical practice of the environment within which Viète and Descartes moved allows for an explanation of how these two figures did not even need to invent abstract coefficients but rather received them as a gift.

The Art of Science
The Art of Science

Author: Rossella Lupacchini

Publisher: Springer

Published: 2014-07-22

Total Pages: 220

ISBN-13: 3319021117

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In addition to linear perspective, complex numbers and probability were notable discoveries of the Renaissance. While the power of perspective, which transformed Renaissance art, was quickly recognized, the scientific establishment treated both complex numbers and probability with much suspicion. It was only in the twentieth century that quantum theory showed how probability might be molded from complex numbers and defined the notion of “complex probability amplitude”. From a theoretical point of view, however, the space opened to painting by linear perspective and that opened to science by complex numbers share significant characteristics. The Art of Science explores this shared field with the purpose of extending Leonardo’s vision of painting to issues of mathematics and encouraging the reader to see science as an art. The intention is to restore a visual dimension to mathematical sciences – an element dulled, if not obscured, by historians, philosophers, and scientists themselves.

Mastering the History of Pure and Applied Mathematics
Mastering the History of Pure and Applied Mathematics

Author: Toke Knudsen

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-06-04

Total Pages: 272

ISBN-13: 3110769964

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The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.

A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case (Classic Reprint)
A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case (Classic Reprint)

Author: James Lockhart

Publisher: Forgotten Books

Published: 2017-12-22

Total Pages: 88

ISBN-13: 9780484474153

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Excerpt from A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case The following rules are necessary to a right understanding of the method contained in this work, and serve to facilitate the requisite Operations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

METHOD OF APPROXIMATING TOWARD
METHOD OF APPROXIMATING TOWARD

Author: James 1763-1852 Lookhart

Publisher: Wentworth Press

Published: 2016-08-28

Total Pages: 104

ISBN-13: 9781372423598

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Oxford Studies in Early Modern Philosophy, Volume X
Oxford Studies in Early Modern Philosophy, Volume X

Author: Donald Rutherford

Publisher: Oxford University Press

Published: 2021

Total Pages: 249

ISBN-13: 0192897446

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Oxford Studies in Early Modern Philosophy is an annual series, presenting a selection of the best current work in the history of early modern philosophy. It focuses on the seventeenth and eighteenth centuries - the extraordinary period of intellectual flourishing that begins, very roughly, with Descartes and his contemporaries and ends with Kant. It also publishes papers on thinkers or movements outside of that framework, provided they are important in illuminating early modern thought. The articles in OSEMP will be of importance to specialists within the discipline, but the editors also intend that they should appeal to a larger audience of philosophers, intellectual historians, and others who are interested in the development of modern thought.