Thomas Harriot's Doctrine of Triangular Numbers

Thomas Harriot's Doctrine of Triangular Numbers

Author: Janet Beery

Publisher: European Mathematical Society

Published: 2009

Total Pages: 150

ISBN-13: 9783037190593

DOWNLOAD EBOOK

Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.) By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.


Book Synopsis Thomas Harriot's Doctrine of Triangular Numbers by : Janet Beery

Download or read book Thomas Harriot's Doctrine of Triangular Numbers written by Janet Beery and published by European Mathematical Society. This book was released on 2009 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.) By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.


Thomas Harriot: Science and Discovery in the English Renaissance

Thomas Harriot: Science and Discovery in the English Renaissance

Author: Robert Fox

Publisher: Taylor & Francis

Published: 2022-12-29

Total Pages: 185

ISBN-13: 100081114X

DOWNLOAD EBOOK

This volume sheds new light on one of the most remarkable polymaths of the English Renaissance. It offers original perspectives not only on Harriot’s personal achievements in mathematics and natural philosophy but also on the wider realms of exploration, colonial ambition, and philosophical debate in which he earned the attention and respect of contemporaries in and far beyond the socially elevated circles of his two great patrons, first Walter Ralegh and then Henry Percy, the ninth Earl of Northumberland. Harriot’s sixteenth-century world was one of unprecedented expansion in both scientific understanding and the discovery of new lands and peoples. The essays gathered here bring out forcefully the effect of this expanding vision, encapsulated in Harriot’s Briefe and true report of the new found land of Virginia (1588), the first detailed description of America to be published in the English language. In addition to an essay by a recent biographer of Harriot, the volume contains reworked versions of seven Thomas Harriot Lectures, an annual lecture series inaugurated in 1990 in Oriel College, Oxford. It follows two earlier volumes of Harriot Lectures, also edited by Robert Fox, that appeared in 2000 and 2012.


Book Synopsis Thomas Harriot: Science and Discovery in the English Renaissance by : Robert Fox

Download or read book Thomas Harriot: Science and Discovery in the English Renaissance written by Robert Fox and published by Taylor & Francis. This book was released on 2022-12-29 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume sheds new light on one of the most remarkable polymaths of the English Renaissance. It offers original perspectives not only on Harriot’s personal achievements in mathematics and natural philosophy but also on the wider realms of exploration, colonial ambition, and philosophical debate in which he earned the attention and respect of contemporaries in and far beyond the socially elevated circles of his two great patrons, first Walter Ralegh and then Henry Percy, the ninth Earl of Northumberland. Harriot’s sixteenth-century world was one of unprecedented expansion in both scientific understanding and the discovery of new lands and peoples. The essays gathered here bring out forcefully the effect of this expanding vision, encapsulated in Harriot’s Briefe and true report of the new found land of Virginia (1588), the first detailed description of America to be published in the English language. In addition to an essay by a recent biographer of Harriot, the volume contains reworked versions of seven Thomas Harriot Lectures, an annual lecture series inaugurated in 1990 in Oriel College, Oxford. It follows two earlier volumes of Harriot Lectures, also edited by Robert Fox, that appeared in 2000 and 2012.


Thomas Harriot

Thomas Harriot

Author: Robyn Arianrhod

Publisher: Oxford University Press

Published: 2019-04-04

Total Pages: 352

ISBN-13: 0190271876

DOWNLOAD EBOOK

As Robyn Arianrhod shows in this new biography, the most complete to date, Thomas Harriot was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot--whose life was almost exactly contemporaneous to Shakespeare's--took part in the first expedition to colonize Virginia in 1585. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, he was also the first European to acquire a working knowledge of an indigenous language from what is today the US, and to record in detail the local people's way of life. In addition to his groundbreaking navigational, linguistic, and ethnological work, Harriot was the first to use a telescope to map the moon's surface, and, independently of Galileo, recorded the behavior of sunspots and discovered the law of free fall. He preceded Newton in his discovery of the properties of the prism and the nature of the rainbow, to name just two more of his unsung "firsts." Indeed many have argued that Harriot was the best mathematician of his age, and one of the finest experimental scientists of all time. Yet he has remained an elusive figure. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and not long after his death in 1621 had all but been forgotten. In recent decades, many scholars have been intent on restoring Harriot to his rightful place in scientific history, but Arianrhod's biography is the first to pull him fully into the limelight. She has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his scientific and cultural achievements, expertly guiding us through what makes them original and important, and the story behind them. Harriot's papers provide unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, and who achieved the lasting fame that escaped him, Harriot helped lay the foundations of what in Newton's time would become modern physics. Thomas Harriot: A Life in Science puts a human face to scientific inquiry in the Elizabethan and Jacobean worlds, and at long last gives proper due to the life and times of one of history's most remarkable minds.


Book Synopsis Thomas Harriot by : Robyn Arianrhod

Download or read book Thomas Harriot written by Robyn Arianrhod and published by Oxford University Press. This book was released on 2019-04-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Robyn Arianrhod shows in this new biography, the most complete to date, Thomas Harriot was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot--whose life was almost exactly contemporaneous to Shakespeare's--took part in the first expedition to colonize Virginia in 1585. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, he was also the first European to acquire a working knowledge of an indigenous language from what is today the US, and to record in detail the local people's way of life. In addition to his groundbreaking navigational, linguistic, and ethnological work, Harriot was the first to use a telescope to map the moon's surface, and, independently of Galileo, recorded the behavior of sunspots and discovered the law of free fall. He preceded Newton in his discovery of the properties of the prism and the nature of the rainbow, to name just two more of his unsung "firsts." Indeed many have argued that Harriot was the best mathematician of his age, and one of the finest experimental scientists of all time. Yet he has remained an elusive figure. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and not long after his death in 1621 had all but been forgotten. In recent decades, many scholars have been intent on restoring Harriot to his rightful place in scientific history, but Arianrhod's biography is the first to pull him fully into the limelight. She has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his scientific and cultural achievements, expertly guiding us through what makes them original and important, and the story behind them. Harriot's papers provide unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, and who achieved the lasting fame that escaped him, Harriot helped lay the foundations of what in Newton's time would become modern physics. Thomas Harriot: A Life in Science puts a human face to scientific inquiry in the Elizabethan and Jacobean worlds, and at long last gives proper due to the life and times of one of history's most remarkable minds.


Thomas Harriot and His World

Thomas Harriot and His World

Author: Robert Fox

Publisher: Routledge

Published: 2016-12-05

Total Pages: 265

ISBN-13: 1351879197

DOWNLOAD EBOOK

This second volume of papers on Thomas Harriot edited by Professor Robert Fox is based on the annual Harriot lectures delivered at Oriel College, Oxford between 2000 and 2009. It complements the previous volume, published as Thomas Harriot: An Elizabethan Man of Science in 2000. The focus in several of the papers is on Harriot's outstanding achievements as a mathematician; others consider why he has never received the recognition accorded to his great contemporary, Galileo; others again examine his association with his entrepreneurial patron Walter Ralegh and his contributions to the intensely practical world of exploration and seamanship, as exemplified in his voyage to the coast of present-day North Carolina in 1585. The volume adds significantly to our understanding of a true Renaissance man who wrote accomplished Latin, earned the respect of Europe's leading mathematicians and astronomers, and moved easily in circles close to the English court and whose 'Brief and true report of the new found land of Virginia' (1588) was the first detailed description of America to be published in the English language.


Book Synopsis Thomas Harriot and His World by : Robert Fox

Download or read book Thomas Harriot and His World written by Robert Fox and published by Routledge. This book was released on 2016-12-05 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of papers on Thomas Harriot edited by Professor Robert Fox is based on the annual Harriot lectures delivered at Oriel College, Oxford between 2000 and 2009. It complements the previous volume, published as Thomas Harriot: An Elizabethan Man of Science in 2000. The focus in several of the papers is on Harriot's outstanding achievements as a mathematician; others consider why he has never received the recognition accorded to his great contemporary, Galileo; others again examine his association with his entrepreneurial patron Walter Ralegh and his contributions to the intensely practical world of exploration and seamanship, as exemplified in his voyage to the coast of present-day North Carolina in 1585. The volume adds significantly to our understanding of a true Renaissance man who wrote accomplished Latin, earned the respect of Europe's leading mathematicians and astronomers, and moved easily in circles close to the English court and whose 'Brief and true report of the new found land of Virginia' (1588) was the first detailed description of America to be published in the English language.


The Invention of Discovery, 1500–1700

The Invention of Discovery, 1500–1700

Author: Dr James Dougal Fleming

Publisher: Ashgate Publishing, Ltd.

Published: 2013-05-28

Total Pages: 240

ISBN-13: 1409478688

DOWNLOAD EBOOK

The early modern period used to be known as the Age of Discovery. More recently, it has been troped as an age of invention. But was the invention/discovery binary itself invented, or discovered? This volume investigates the possibility that it was invented, through a range of early modern knowledge practices, centered on the emergence of modern natural science. From Bacon to Galileo, from stagecraft to math, from martyrology to romance, contributors to this interdisciplinary collection examine the period's generation of discovery as an absolute and ostensibly neutral standard of knowledge-production. They further investigate the hermeneutic implications for the epistemological authority that tends, in modernity, still to be based on that standard. The Invention of Discovery, 1500–1700 is a set of attempts to think back behind discovery, considered as a decisive trope for modern knowledge.


Book Synopsis The Invention of Discovery, 1500–1700 by : Dr James Dougal Fleming

Download or read book The Invention of Discovery, 1500–1700 written by Dr James Dougal Fleming and published by Ashgate Publishing, Ltd.. This book was released on 2013-05-28 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early modern period used to be known as the Age of Discovery. More recently, it has been troped as an age of invention. But was the invention/discovery binary itself invented, or discovered? This volume investigates the possibility that it was invented, through a range of early modern knowledge practices, centered on the emergence of modern natural science. From Bacon to Galileo, from stagecraft to math, from martyrology to romance, contributors to this interdisciplinary collection examine the period's generation of discovery as an absolute and ostensibly neutral standard of knowledge-production. They further investigate the hermeneutic implications for the epistemological authority that tends, in modernity, still to be based on that standard. The Invention of Discovery, 1500–1700 is a set of attempts to think back behind discovery, considered as a decisive trope for modern knowledge.


The Doctrine of Triangles

The Doctrine of Triangles

Author: Glen Van Brummelen

Publisher: Princeton University Press

Published: 2021-06-08

Total Pages: 390

ISBN-13: 0691179417

DOWNLOAD EBOOK

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.


Book Synopsis The Doctrine of Triangles by : Glen Van Brummelen

Download or read book The Doctrine of Triangles written by Glen Van Brummelen and published by Princeton University Press. This book was released on 2021-06-08 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.


Series and Products in the Development of Mathematics: Volume 1

Series and Products in the Development of Mathematics: Volume 1

Author: Ranjan Roy

Publisher: Cambridge University Press

Published: 2021-03-18

Total Pages:

ISBN-13: 1108573185

DOWNLOAD EBOOK

This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.


Book Synopsis Series and Products in the Development of Mathematics: Volume 1 by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics: Volume 1 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.


Series and Products in the Development of Mathematics

Series and Products in the Development of Mathematics

Author: Ranjan Roy

Publisher: Cambridge University Press

Published: 2021-03-18

Total Pages: 479

ISBN-13: 1108709370

DOWNLOAD EBOOK

Second of two volumes tracing the development of series and products. Second edition adds extensive material from original works.


Book Synopsis Series and Products in the Development of Mathematics by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second of two volumes tracing the development of series and products. Second edition adds extensive material from original works.


Series and Products in the Development of Mathematics: Volume 2

Series and Products in the Development of Mathematics: Volume 2

Author: Ranjan Roy

Publisher: Cambridge University Press

Published: 2021-03-18

Total Pages: 480

ISBN-13: 1108573150

DOWNLOAD EBOOK

This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.


Book Synopsis Series and Products in the Development of Mathematics: Volume 2 by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics: Volume 2 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.


3000 Years of Analysis

3000 Years of Analysis

Author: Thomas Sonar

Publisher: Springer Nature

Published: 2020-12-27

Total Pages: 706

ISBN-13: 303058223X

DOWNLOAD EBOOK

What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.


Book Synopsis 3000 Years of Analysis by : Thomas Sonar

Download or read book 3000 Years of Analysis written by Thomas Sonar and published by Springer Nature. This book was released on 2020-12-27 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.