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Symbols, Impossible Numbers, and Geometric Entanglements

Author: Helena M. Pycior

Publisher: Cambridge University Press

Published: 1997-05-13

Total Pages: 40

ISBN-13: 9780521481243

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Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

Book Synopsis Symbols, Impossible Numbers, and Geometric Entanglements by : Helena M. Pycior

Download or read book Symbols, Impossible Numbers, and Geometric Entanglements written by Helena M. Pycior and published by Cambridge University Press. This book was released on 1997-05-13 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

Around Caspar Wessel and the Geometric Representation of Complex Numbers

Author: Jesper Lützen

Publisher: Kgl. Danske Videnskabernes Selskab

Published: 2001

Total Pages: 306

ISBN-13: 9788778762368

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Book Synopsis Around Caspar Wessel and the Geometric Representation of Complex Numbers by : Jesper Lützen

Download or read book Around Caspar Wessel and the Geometric Representation of Complex Numbers written by Jesper Lützen and published by Kgl. Danske Videnskabernes Selskab. This book was released on 2001 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Thomas Reid on Mathematics and Natural Philosophy

Author: Thomas Reid

Publisher: Edinburgh University Press

Published: 2017-07-28

Total Pages: 512

ISBN-13: 0748643397

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Reconstructs Reid's career as a mathematician and natural philosopher for the first time

Book Synopsis Thomas Reid on Mathematics and Natural Philosophy by : Thomas Reid

Download or read book Thomas Reid on Mathematics and Natural Philosophy written by Thomas Reid and published by Edinburgh University Press. This book was released on 2017-07-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstructs Reid's career as a mathematician and natural philosopher for the first time

Blindness and Enlightenment: An Essay

Author: Kate E. Tunstall

Publisher: Bloomsbury Publishing USA

Published: 2011-08-18

Total Pages: 251

ISBN-13: 1441175431

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Blindness and Enlightenment presents a reading and a new translation of Diderot's Letter on the Blind. Diderot was the editor of the Encyclopédie, that Trojan horse of Enlightenment ideas, as well as a novelist, playwright, art critic and philosopher. His Letter on the Blind of 1749 is essential reading for anyone interested in Enlightenment philosophy or eighteenth-century literature because it contradicts a central assumption of Western literature and philosophy, and of the Enlightenment in particular, namely that moral and philosophical insight is dependent on seeing. Kate Tunstall's essay guides the reader through the Letter, its anecdotes, ideas and its conversational mode of presenting them, and it situates the Letter in relation both to the Encyclopedie and to a rich tradition of writing about and, most importantly, talking and listening to the blind.

Book Synopsis Blindness and Enlightenment: An Essay by : Kate E. Tunstall

Download or read book Blindness and Enlightenment: An Essay written by Kate E. Tunstall and published by Bloomsbury Publishing USA. This book was released on 2011-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blindness and Enlightenment presents a reading and a new translation of Diderot's Letter on the Blind. Diderot was the editor of the Encyclopédie, that Trojan horse of Enlightenment ideas, as well as a novelist, playwright, art critic and philosopher. His Letter on the Blind of 1749 is essential reading for anyone interested in Enlightenment philosophy or eighteenth-century literature because it contradicts a central assumption of Western literature and philosophy, and of the Enlightenment in particular, namely that moral and philosophical insight is dependent on seeing. Kate Tunstall's essay guides the reader through the Letter, its anecdotes, ideas and its conversational mode of presenting them, and it situates the Letter in relation both to the Encyclopedie and to a rich tradition of writing about and, most importantly, talking and listening to the blind.

Algebraic Art

Author: Andrea K. Henderson

Publisher: Oxford University Press

Published: 2018

Total Pages: 231

ISBN-13: 0198809980

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Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. Drawing on literature, art, and photography, it explores how the Victorian mathematical conception of form still resonates today.

Book Synopsis Algebraic Art by : Andrea K. Henderson

Download or read book Algebraic Art written by Andrea K. Henderson and published by Oxford University Press. This book was released on 2018 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. Drawing on literature, art, and photography, it explores how the Victorian mathematical conception of form still resonates today.

From Discrete to Continuous

Author: K. Neal

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 182

ISBN-13: 940170077X

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In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

Book Synopsis From Discrete to Continuous by : K. Neal

Download or read book From Discrete to Continuous written by K. Neal and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

The Cambridge History of Science: Volume 3, Early Modern Science

Author: David C. Lindberg

Publisher: Cambridge University Press

Published: 2003

Total Pages: 833

ISBN-13: 0521572444

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An account of European knowledge of the natural world, c.1500-1700.

Book Synopsis The Cambridge History of Science: Volume 3, Early Modern Science by : David C. Lindberg

Download or read book The Cambridge History of Science: Volume 3, Early Modern Science written by David C. Lindberg and published by Cambridge University Press. This book was released on 2003 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of European knowledge of the natural world, c.1500-1700.

British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750)

Author: Leo Corry

Publisher: Springer Nature

Published: 2022-09-12

Total Pages: 79

ISBN-13: 3031115384

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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.

Book Synopsis British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) by : Leo Corry

Download or read book British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) written by Leo Corry and published by Springer Nature. This book was released on 2022-09-12 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Isaac Newton on Mathematical Certainty and Method

Author: Niccolo Guicciardini

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 449

ISBN-13: 0262291657

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An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

Book Synopsis Isaac Newton on Mathematical Certainty and Method by : Niccolo Guicciardini

Download or read book Isaac Newton on Mathematical Certainty and Method written by Niccolo Guicciardini and published by MIT Press. This book was released on 2011-08-19 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

The Cult of Pythagoras

Author: Alberto A. Martinez

Publisher: University of Pittsburgh Press

Published: 2012-10-30

Total Pages: 289

ISBN-13: 0822978539

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In this follow-up to his popular Science Secrets, Alberto A. Martinez discusses various popular myths from the history of mathematics: that Pythagoras proved the hypotenuse theorem, that Archimedes figured out how to test the purity of a gold crown while he was in a bathtub, that the Golden Ratio is in nature and ancient architecture, that the young Galois created group theory the night before the pistol duel that killed him, and more. Some stories are partly true, others are entirely false, but all show the power of invention in history. Pythagoras emerges as a symbol of the urge to conjecture and "fill in the gaps" of history. He has been credited with fundamental discoveries in mathematics and the sciences, yet there is nearly no evidence that he really contributed anything to such fields at all. This book asks: how does history change when we subtract the many small exaggerations and interpolations that writers have added for over two thousand years? The Cult of Pythagoras is also about invention in a positive sense. Most people view mathematical breakthroughs as "discoveries" rather than invention or creativity, believing that mathematics describes a realm of eternal ideas. But mathematicians have disagreed about what is possible and impossible, about what counts as a proof, and even about the results of certain operations. Was there ever invention in the history of concepts such as zero, negative numbers, imaginary numbers, quaternions, infinity, and infinitesimals? Martinez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the actual origins of mathematical concepts. Martinez argues that an accurate history that analyzes myths reveals neglected aspects of mathematics that can encourage creativity in students and mathematicians.

Book Synopsis The Cult of Pythagoras by : Alberto A. Martinez

Download or read book The Cult of Pythagoras written by Alberto A. Martinez and published by University of Pittsburgh Press. This book was released on 2012-10-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this follow-up to his popular Science Secrets, Alberto A. Martinez discusses various popular myths from the history of mathematics: that Pythagoras proved the hypotenuse theorem, that Archimedes figured out how to test the purity of a gold crown while he was in a bathtub, that the Golden Ratio is in nature and ancient architecture, that the young Galois created group theory the night before the pistol duel that killed him, and more. Some stories are partly true, others are entirely false, but all show the power of invention in history. Pythagoras emerges as a symbol of the urge to conjecture and "fill in the gaps" of history. He has been credited with fundamental discoveries in mathematics and the sciences, yet there is nearly no evidence that he really contributed anything to such fields at all. This book asks: how does history change when we subtract the many small exaggerations and interpolations that writers have added for over two thousand years? The Cult of Pythagoras is also about invention in a positive sense. Most people view mathematical breakthroughs as "discoveries" rather than invention or creativity, believing that mathematics describes a realm of eternal ideas. But mathematicians have disagreed about what is possible and impossible, about what counts as a proof, and even about the results of certain operations. Was there ever invention in the history of concepts such as zero, negative numbers, imaginary numbers, quaternions, infinity, and infinitesimals? Martinez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the actual origins of mathematical concepts. Martinez argues that an accurate history that analyzes myths reveals neglected aspects of mathematics that can encourage creativity in students and mathematicians.