The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations PDF Download
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Author: Sara Confalonieri
Publisher: Springer
ISBN: 3658092750
Category : Philosophy
Languages : en
Pages : 458
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Book Description
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.
Author: Sara Confalonieri
Publisher: Springer
ISBN: 3658092750
Category : Philosophy
Languages : en
Pages : 458
Get Book Here
Book Description
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.
Author: Sara Confalonieri
Publisher:
ISBN: 9783658092764
Category :
Languages : en
Pages :
Get Book Here
Book Description
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.
Author: Jens Høyrup
Publisher: Springer Nature
ISBN: 3031481585
Category : Algebra
Languages : en
Pages : 150
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Book Description
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.
Author: Rossella Lupacchini
Publisher: Springer
ISBN: 3319021117
Category : Mathematics
Languages : en
Pages : 220
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Book Description
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.
Author: Toke Knudsen
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110769964
Category : History
Languages : en
Pages : 272
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Book Description
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.
Author: Donald Rutherford
Publisher: Oxford University Press
ISBN: 0192897446
Category : Philosophy
Languages : en
Pages : 249
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Book Description
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.
Author: Juliusz Brzeziński
Publisher: Springer
ISBN: 331972326X
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Author: R. Bruce King
Publisher: Springer Science & Business Media
ISBN: 0817648496
Category : Mathematics
Languages : en
Pages : 159
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Book Description
The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist
Author: Lindsay N. Childs
Publisher: Springer Science & Business Media
ISBN: 1441987029
Category : Mathematics
Languages : en
Pages : 540
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Book Description
An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.
Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 9780198534464
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
