Distributivity-like Results in the Medieval Traditions of Euclid's Elements PDF Download
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Author: Leo Corry
Publisher: Springer Nature
ISBN: 3030796795
Category : Science
Languages : en
Pages : 88
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Book Description
This book provides a fresh view on an important and largely overlooked aspect of the Euclidean traditions in the medieval mathematical texts, particularly concerning the interrelations between geometry and arithmetic, and the rise of algebraic modes of thought. It appeals to anyone interested in the history of mathematics in general and in history of medieval and early modern science.
Author: Leo Corry
Publisher: Springer Nature
ISBN: 3030796795
Category : Science
Languages : en
Pages : 88
Get Book Here
Book Description
This book provides a fresh view on an important and largely overlooked aspect of the Euclidean traditions in the medieval mathematical texts, particularly concerning the interrelations between geometry and arithmetic, and the rise of algebraic modes of thought. It appeals to anyone interested in the history of mathematics in general and in history of medieval and early modern science.
Author: Leo Corry
Publisher: Springer Nature
ISBN: 3031115384
Category : Science
Languages : en
Pages : 79
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Book Description
This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century. Its focus is on Book II of the Elements and the ways in which algebraic symbolism and methods, especially as recently introduced by François Viète and his followers, took center stage as mediators between the two realms, and thus offered new avenues to work out that relationship in idiosyncratic ways not found in earlier editions of the Euclidean text. Texts examined include Robert Recorde's Pathway to Knowledge (1551), Henry Billingsley’s first English translation of the Elements (1570), Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot (both published in 1631), Isaac Barrow’s versions of the Elements (1660), and John Wallis Treatise of Algebra (1685), and the English translations of Claude Dechales’ French Euclidean Elements (1685). This book offers a completely new perspective of the topic and analyzes mostly unexplored material. It will be of interest to historians of mathematics, mathematicians with an interest in history and historians of renaissance science in general.
Author: Leo Corry
Publisher:
ISBN: 9783030796808
Category :
Languages : en
Pages : 0
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Book Description
This book provides a fresh view on an important and largely overlooked aspect of the Euclidean traditions in the medieval mathematical texts, particularly concerning the interrelations between geometry and arithmetic, and the rise of algebraic modes of thought. It appeals to anyone interested in the history of mathematics in general and in history of medieval and early modern science.
Author: Ruth Glasner
Publisher: Springer Nature
ISBN: 3319773038
Category : Mathematics
Languages : en
Pages : 293
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Book Description
This volume offers a new English translation, introduction, and detailed commentary on Sefer Meyasher 'Aqov, (The Rectifying of the Curved), a 14th-century Hebrew treatise on the foundation of geometry. The book is a mixture of two genres: philosophical discussion and formal, Euclidean-type geometrical writing. A central issue is the use of motion and superposition in geometry, which is analyzed in depth through dialog with earlier Arab mathematicians. The author, Alfonso, was identified by Gita Gluskina (the editor of the 1983 Russian edition) as Alfonso of Valladolid, the converted Jew Abner of Burgos. Alfonso lived in Castile, rather far from the leading cultural centers of his time, but nonetheless at the crossroad of three cultures. He was raised in the Jewish tradition and like many Sephardic Jewish intellectuals was versed in Greek-Arabic philosophy and science. He also had connections with some Christian nobles and towards the end of his life converted to Christianity. Driven by his ambition to solve the problem of the quadrature of the circle, as well as other open geometrical problems, Alfonso acquired surprisingly wide knowledge and became familiar with several episodes in Greek and Arabic geometry that historians usually consider not to have been known in the West in the fourteenth century. Sefer Meyasher 'Aqov reflects his wide and deep erudition in mathematics and philosophy, and provides new evidence on cultural transmission around the Mediterranean.
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: L. Corry
Publisher: Springer Science & Business Media
ISBN: 1402027788
Category : Science
Languages : en
Pages : 542
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Book Description
David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.
Author: James J. Tattersall
Publisher: Cambridge University Press
ISBN: 9780521585316
Category : Mathematics
Languages : en
Pages : 420
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Book Description
This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 0387226761
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Author: Ian Mueller
Publisher: Courier Dover Publications
ISBN:
Category : Mathematics
Languages : en
Pages : 404
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Book Description
A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Author: Lindsay Childs
Publisher: Springer Science & Business Media
ISBN: 1468400657
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.
