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Author: Ad Meskens Publisher: Springer Science & Business Media ISBN: 3034606435 Category : Mathematics Languages : en Pages : 214
Book Description
In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations. In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.
Author: Ad Meskens Publisher: Springer Science & Business Media ISBN: 3034606435 Category : Mathematics Languages : en Pages : 214
Book Description
In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations. In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.
Author: Benno Artmann Publisher: Springer Science & Business Media ISBN: 1461214122 Category : Mathematics Languages : en Pages : 352
Book Description
Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.
Author: Ulrich Felgner Publisher: Springer Nature ISBN: 3031273044 Category : Mathematics Languages : en Pages : 314
Book Description
»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.
Author: C.C.W. Taylor Publisher: Taylor & Francis ISBN: 100094381X Category : Philosophy Languages : en Pages : 521
Book Description
This first volume in the series traces the development of philosophy over two-and-a-half centuries, from Thales at the beginning of the sixth century BC to the death of Plato in 347 BC.
Author: Michael Fried Publisher: BRILL ISBN: 9004350993 Category : Literary Criticism Languages : en Pages : 512
Book Description
This volume contains a historically sensitive analysis and interpretation of Apollonius of Perga's Conica, one of the greatest works of Hellenistic mathematics. It provides a long overdue alternative to H. G. Zeuthen's Die Lehre von den Kogelschnitten im Altertum.
Author: Euclid Publisher: Museum Tusculanum Press ISBN: 9788772898155 Category : Literary Collections Languages : en Pages : 276
Book Description
This is a scholarly contribution to an area -- the history of Greek geometrical analysis -- that is still insufficiently understood. At the time of Zeuthen, and even up to the middle of the last century, it was fashionable to treat the Data algebraically. Taisbak has abandoned this approach completely, arguing that it does nothing to help us to understand either the development of the work or the reasons for its having been copied, studied, and quoted for more than two millennia. We must bear a queer sort of frustration that affects us everywhere in the Data: we get very little information, hardly any 'knowledge' of the givens. And why not? Probably because 'knowing' geometrical objects was problematic in those days when the concept of 'given' came into being, and the consequences of incommensurability was just being understood. Next to nothing is known of these items, and very little that is worth knowing: length, size, distance -- any of the attributes that can be spoken of by means of numbers. Although there have been two recent translations of the Data, this one is unique in providing, as well, an extensive commentary, which provides the insights gained from three decades of studying the work. The book is meant as a coherent and understandable account of what could have been going on in Euclid's mind, and some reasons for believing that that is what actually was going on in his mind.
Author: John J. Cleary Publisher: BRILL ISBN: 900424784X Category : Philosophy Languages : en Pages : 639
Book Description
John J. Cleary (1949–2009) was an internationally recognised authority in many aspects of ancient philosophy. As well as penetrating and original studies of Plato, Aristotle, and Proclus, he was particularly interested in the philosophy of mathematics, and ancient theories of education. The essays included in this collection display Cleary’s range of expertise and originality of approach. Cleary was especially attentive to the problems involved in the interpretation of a philosophical text: in his reading of Plato he recognised the special status of dialogue as a privileged mode of philosophical writing. His underlying concern was the open-ended character of philosophy itself, to be pursued with intellectual rigour and respect both for the question and one’s interlocutor. These collected essays are representative of John Cleary’s philosophical life’s work.
Author: B.E. Babich Publisher: Springer Science & Business Media ISBN: 9401717672 Category : Science Languages : en Pages : 496
Book Description
This richly textured book bridges analytic and hermeneutic and phenomenological philosophy of science. It features unique resources for students of the philosophy and history of quantum mechanics and the Copenhagen Interpretation, cognitive theory and the psychology of perception, the history and philosophy of art, and the pragmatic and historical relationships between religion and science.
Author: Ad Meskens
Author: Ad Meskens
Author: Benno Artmann
Author: Ian Mueller
Author: Ulrich Felgner
Author: C.C.W. Taylor
Author: Ivor Grattan-Guiness
Author: Michael Fried
Author: Euclid
Author: John J. Cleary
Author: B.E. Babich