The Unattainable Attempt To Avoid The Casus Irreducibilis For Cubic Equations

Download or read book The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations written by Sara Confalonieri and published by Springer. This book was released on 2015-03-18 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations written by Sara Confalonieri and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Explorations and False Trails written by Jens Høyrup and published by Springer Nature. This book was released on 2024 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Art of Science written by Rossella Lupacchini and published by Springer. This book was released on 2014-07-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mastering the History of Pure and Applied Mathematics written by Toke Knudsen and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-06-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Oxford Studies in Early Modern Philosophy, Volume X written by Donald Rutherford and published by Oxford University Press. This book was released on 2021 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Galois Theory Through Exercises written by Juliusz Brzeziński and published by Springer. This book was released on 2018-03-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.