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Philip Beeley - One of the best experts on this subject based on the ideXlab platform.
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physical arguments and moral inducements John Wallis on questions of antiquarianism and natural philosophy
Notes and Records, 2018Co-Authors: Philip BeeleyAbstract:In his posthumously published work Chartham News (1669), the antiquary William Somner tentatively sought to link the discovery of fossilized remains near Canterbury to the prehistoric existence of an isthmus connecting Britain and France, before calling on natural philosophers to pursue his explanation further. This call was eventually heeded by the Oxford mathematician John Wallis, but only after more than thirty years had elapsed. The arrival in England of a catalogue of questions concerning the geology of the Channel led to the republication of Chartham News in the Philosophical Transactions , prompting Wallis to develop a physical explanation based on his intimate knowledge of the Kent coastline. Unbeknown to Wallis at the time, that catalogue had been sent by G. W. Leibniz, who had in turn received it from G. D. Schmidt, the former Resident of Brunswick-Luneburg in Sweden. Wallis9s explanation, based on the principle of establishing physical causes both for the rupturing of the isthmus and for the origin of fossils, placed him in a camp opposed by Newtonian authors such as John Harris at a time when the priority dispute over the discovery of the calculus led to the severing of his ties with the German mathematician and philosopher Leibniz.
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Historiographical Change and Editorial Practice: The Origins of the Edition of the Correspondence of John Wallis (1616–1703)
Trends in the History of Science, 2018Co-Authors: Philip BeeleyAbstract:The edition of the correspondence of John Wallis (1616–1703) has had a relatively long and varied history, being conceived originally by Christoph J. Scriba as a small companion volume of those letters of the great Oxford mathematician that had not already appeared elsewhere, in publications such as the Correspondence of Isaac Newton or the Œuvres completes de Christiaan Huygens. In this chapter, the author charts the evolution of the Wallis Edition from those initial plans through to the major critical edition that is now in progress. Drawing on Scriba’s own letters and papers, he argues that the history of the Wallis Edition mirrors changes that have taken place in the nature and outlook of the history of mathematics itself; changes on which Scriba reflected intensely during his lifetime and to which he contributed both through his writings and his historiographical practice.
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historiographical change and editorial practice the origins of the edition of the correspondence of John Wallis 1616 1703
2018Co-Authors: Philip BeeleyAbstract:The edition of the correspondence of John Wallis (1616–1703) has had a relatively long and varied history, being conceived originally by Christoph J. Scriba as a small companion volume of those letters of the great Oxford mathematician that had not already appeared elsewhere, in publications such as the Correspondence of Isaac Newton or the Œuvres completes de Christiaan Huygens. In this chapter, the author charts the evolution of the Wallis Edition from those initial plans through to the major critical edition that is now in progress. Drawing on Scriba’s own letters and papers, he argues that the history of the Wallis Edition mirrors changes that have taken place in the nature and outlook of the history of mathematics itself; changes on which Scriba reflected intensely during his lifetime and to which he contributed both through his writings and his historiographical practice.
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Correspondence of John Wallis
2012Co-Authors: Philip Beeley, Christoph J. ScribaAbstract:Introduction Editorial principles and abbreviations Correspondence Biographies of correspondents List of manuscripts Bibliography List of letters Index: persons and subjects Errata
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CHAPTER 23 – John Wallis (1616–1703): Mathematician and Divine*
Mathematics and the Divine, 2005Co-Authors: Philip BeeleyAbstract:This chapter focuses on the Wallis' defence of the Trinity. Wallis' strategy in upholding the orthodox Anglican doctrine in the light of Socinian attacks was to retain the fundamental inexplicability of the Trinity as a matter of faith and at the same time to show that it was not inconsistent with reason—a strategy not unlike that adopted by Leibniz on the same topic. In this respect, Wallis distinguishes the question of the possibility of the Trinity from that of its truth, which, as he emphasizes, are to be approached from different ways, an aspect from natural reason, the other from revelation: “there is nothing in natural reason why it should be thought Impossible; but whether or not it be so, depends only upon revelation”. Wallis' cautious approach using the method of analogy avoided the implication of tritheism that could be found in the writings of Sherlock and which thus played into the hands of the Socinians Wallis, who nevertheless defended Sherlock, confined his discourse to a single point: that there is no impossibility in the Trinity. And this he saw as being sufficient for his purpose, namely to defeat the antitrinitarian arguments while at the same time retaining the essential mystery of the Christian doctrine.
Peter Hauge - One of the best experts on this subject based on the ideXlab platform.
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John Wallis writings on music edited by david cram and benjamin wardhaugh farnham burlington vt ashgate 2014 xiii 239 pp 65 00 hardback isbn 978 0 7546 68701
The Eighteenth Century, 2015Co-Authors: Peter HaugeAbstract:John Wallis: writings on music, edited by David Cram and Benjamin Wardhaugh, Farnham & Burlington, VT, Ashgate, 2014, xiii + 239 pp., £65.00 (hardback), ISBN 978-0-7546-68701Slowly but surely the important series, Music Theory in Britain, 1500-1700: Critical Editions published by Ashgate, is expanding with new volumes. So far, most of those which have appeared are concerned with the more esoteric and nerdy aspects of music theory. It is indeed thought provoking how much seventeenth century English music theorists and natural philosophers wrote on music and how few of the writers have been the objects of study among musicologists today. The series is seminal for an entirely new interpretation of the position of music theory in early modern English intellectual circles. Looking at the present volumes of the series published so far, it is obvious that there seems to have been a close and influential discussion between professional musicians and natural philosophers; however, also the music connoisseur played a vital role asking inquisitive questions. From a musicological point view, some of the most complex writings, truly demanding a profound knowledge of early modern mathematics, are those concerned with temperament and tuning for instance. The present critical edition comprising the main musical writings of John Wallis (1616-1703) is one of those volumes that the modern reader may find hard to get through.John Wallis, mathematician and for 54 years Savilian Professor of Geometry in Oxford, was ordained in 1640 becoming a doctor in divinity and elected royal chaplain in 1660. He was elected a fellow of the Royal Society in 1661 and published frequently in the Society's journal Philosophical Transactions on a wide range of subjects including hearing, theology, logic, mathematics, grammar and ancient music theory - many of the topics in fact required by the job description as Savilian professor, as the editors of the present volume note. Apparently, it was not until the beginning of the 1660s that Wallis began to show a greater interest in music when the violist, teacher and music theorist John Birchensha presented his musical ideas to the Royal Society. The secretary of the Society, who thought that Birchensha'sideas might be of interest to Wallis, wrote to him about these ideas. Wallis was indeed interested and wrote a treatise on the mathematics of music and musical tuning. The treatise, here edited as Chapter 1, sets the basis for Wallis's later writings on music, in particular the coincidence theory of consonance. Wallis was also fascinated by the syntonic diatonic scale (Ptolemaic scale) which, contrary to the "medieval" Pythagorean scale which was most often mentioned and explained in contemporary music theoretical treatises, included not only pure octaves, fifths and fourths but also thirds and hence sixths. Though the tuning was nearly impossible to use in practice since it advocated two distinct sizes of the whole tone, it nevertheless drew some attention, especially from natural philosophers and musical connoisseurs. Musicians still argued in favour of the Pythagorean tuning though it certainly was not used in practice. There was, as Wallis mentions, a discrepancy between music theory and music practice and he was simply trying to describe in theory what musicians did in practice. As the editors argue (6-7),Walliswasmostlikelyinspiredbyothercontemporary natural philosophers such as Johannes Kepler, Marin Mersenne and Rene Descartes who all seem to have based their ideas regarding the Ptolemaic scale on Gioseffo Zarlino's famous Le Istitutioni harmoniche first printed in 1558.In 1677, Wallis became aware of the discussions concerning the sympathetic vibrations of strings and nodes of vibration. He wrote a letter on the matter to the Royal Society which was subsequently published in the Philosophical Transactions as a " New Musical Discovery" (Chapter 2 in the present edition). The article was, with a few revisions, later published in a Latin version in 1693. …
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John Wallis: writings on music, edited by David Cram and Benjamin Wardhaugh, Farnham & Burlington, VT, Ashgate, 2014, xiii + 239 pp., £65.00 (hardback), ISBN 978-0-7546-68701
The Seventeenth Century, 2015Co-Authors: Peter HaugeAbstract:John Wallis: writings on music, edited by David Cram and Benjamin Wardhaugh, Farnham & Burlington, VT, Ashgate, 2014, xiii + 239 pp., £65.00 (hardback), ISBN 978-0-7546-68701Slowly but surely the important series, Music Theory in Britain, 1500-1700: Critical Editions published by Ashgate, is expanding with new volumes. So far, most of those which have appeared are concerned with the more esoteric and nerdy aspects of music theory. It is indeed thought provoking how much seventeenth century English music theorists and natural philosophers wrote on music and how few of the writers have been the objects of study among musicologists today. The series is seminal for an entirely new interpretation of the position of music theory in early modern English intellectual circles. Looking at the present volumes of the series published so far, it is obvious that there seems to have been a close and influential discussion between professional musicians and natural philosophers; however, also the music connoisseur played a vital role asking inquisitive questions. From a musicological point view, some of the most complex writings, truly demanding a profound knowledge of early modern mathematics, are those concerned with temperament and tuning for instance. The present critical edition comprising the main musical writings of John Wallis (1616-1703) is one of those volumes that the modern reader may find hard to get through.John Wallis, mathematician and for 54 years Savilian Professor of Geometry in Oxford, was ordained in 1640 becoming a doctor in divinity and elected royal chaplain in 1660. He was elected a fellow of the Royal Society in 1661 and published frequently in the Society's journal Philosophical Transactions on a wide range of subjects including hearing, theology, logic, mathematics, grammar and ancient music theory - many of the topics in fact required by the job description as Savilian professor, as the editors of the present volume note. Apparently, it was not until the beginning of the 1660s that Wallis began to show a greater interest in music when the violist, teacher and music theorist John Birchensha presented his musical ideas to the Royal Society. The secretary of the Society, who thought that Birchensha'sideas might be of interest to Wallis, wrote to him about these ideas. Wallis was indeed interested and wrote a treatise on the mathematics of music and musical tuning. The treatise, here edited as Chapter 1, sets the basis for Wallis's later writings on music, in particular the coincidence theory of consonance. Wallis was also fascinated by the syntonic diatonic scale (Ptolemaic scale) which, contrary to the "medieval" Pythagorean scale which was most often mentioned and explained in contemporary music theoretical treatises, included not only pure octaves, fifths and fourths but also thirds and hence sixths. Though the tuning was nearly impossible to use in practice since it advocated two distinct sizes of the whole tone, it nevertheless drew some attention, especially from natural philosophers and musical connoisseurs. Musicians still argued in favour of the Pythagorean tuning though it certainly was not used in practice. There was, as Wallis mentions, a discrepancy between music theory and music practice and he was simply trying to describe in theory what musicians did in practice. As the editors argue (6-7),Walliswasmostlikelyinspiredbyothercontemporary natural philosophers such as Johannes Kepler, Marin Mersenne and Rene Descartes who all seem to have based their ideas regarding the Ptolemaic scale on Gioseffo Zarlino's famous Le Istitutioni harmoniche first printed in 1558.In 1677, Wallis became aware of the discussions concerning the sympathetic vibrations of strings and nodes of vibration. He wrote a letter on the matter to the Royal Society which was subsequently published in the Philosophical Transactions as a " New Musical Discovery" (Chapter 2 in the present edition). The article was, with a few revisions, later published in a Latin version in 1693. …
William Poole - One of the best experts on this subject based on the ideXlab platform.
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the correspondence of John Wallis 1616 1703 volume iv 1672 april 1675 edited by philip beeley and christoph j scriba
Bshm Bulletin: Journal of The British Society for The History of Mathematics, 2015Co-Authors: William PooleAbstract:Three prior volumes in this edition of the correspondence of the mathematician John Wallis (1616–1703) have appeared to date, covering the years 1641–59, 1660–68, and 1668–71 respectively, and now ...
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The Correspondence of John Wallis (1616–1703) Volume IV (1672–April 1675), edited by Philip Beeley and Christoph J Scriba
BSHM Bulletin: Journal of the British Society for the History of Mathematics, 2015Co-Authors: William PooleAbstract:Three prior volumes in this edition of the correspondence of the mathematician John Wallis (1616–1703) have appeared to date, covering the years 1641–59, 1660–68, and 1668–71 respectively, and now ...
W. Viereck - One of the best experts on this subject based on the ideXlab platform.
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Wallis, John (1616–1703)
Encyclopedia of Language & Linguistics, 2006Co-Authors: W. ViereckAbstract:A remarkable scholar, John Wallis (1616–1703) excelled in many fields. His most influential work in language studies was his Grammatica linguae Anglicanae (1653), in which he adopted a modern approach. He was the first to disclose the structure of English by detaching himself from the system of Latin.
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Wallis John 1616 1703
Encyclopedia of Language & Linguistics (Second Edition), 2006Co-Authors: W. ViereckAbstract:A remarkable scholar, John Wallis (1616–1703) excelled in many fields. His most influential work in language studies was his Grammatica linguae Anglicanae (1653), in which he adopted a modern approach. He was the first to disclose the structure of English by detaching himself from the system of Latin.
Gabriela Lucheze De Oliveira Lopes - One of the best experts on this subject based on the ideXlab platform.
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indicacoes de abordagens para o ensino de integral a partir da obra arithmetica infinitorum de John Wallis
VII CONGRESSO INTERNACIONAL DE ENSINO DE MATEMÁTICA - 2017, 2017Co-Authors: Gabriela Lucheze De Oliveira Lopes, Iran Abreu MendesAbstract:Neste artigo, apresentamos algumas das ideias e metodos emergentes da obra Arithmetica Infinitorum de John Wallis datada de 1656, com a finalidade de apontar seu potencial pedagogico, que possa subsidiar o ensino de conceitos matematicos numa perspectiva de melhorar o entendimento sobre as ideias matematicas nos estudantes de Cursos de Formacao Inicial de Professores de Matematica. Ao levar uma obra historica em Matematica para discussao em sala de aula, ganhamos a possibilidade de enriquecer as aulas, discutindo com os estudantes aspectos sociais e culturais que sobressairam desse estudo, estabelecendo assim uma integralizacao da Matematica aos contextos social e cultural de um periodo historico. Apoiados neste pensamento, nos exibimos nossas sugestoes e encaminhamentos didaticos para o ensino de Integrais a partir do nosso exame desta obra. Nesta dinâmica, os futuros educadores matematicos, possivelmente, desenvolverao um espirito investigador em conteudos relacionados ao ensino e aprendizagem de Matematica. Este artigo originou-se de nossa tese de doutorado que teve como objetivo examinar de que forma as ideias de John Wallis, emergentes na obra Arithmetica Infinitorum, datada de 1656, apresentou inovacoes que podem contribuir para o encaminhamento conceitual e didatico de nocoes basicas da componente curricular de Calculo Diferencial e Integral, no curso de Licenciatura em Matematica. Para esta tese, realizamos um trabalho que partiu de nossa elaboracao de uma versao para o portugues da traducao em lingua inglesa, The Arithmetic of Infinitesimals, de Jaqueline Stedall datada de 2004, recorrendo, em algumas ocasioes, ao original em latim.
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a criatividade matematica de John Wallis na obra arithmetica infinitorum contribuicoes para ensino de calculo diferencial e integral na licenciatura em matematica
2017Co-Authors: Gabriela Lucheze De Oliveira LopesAbstract:A pesquisa que originou este texto de tese de doutorado teve como objetivo examinar de que forma as ideias de John Wallis, emergentes na obra Arithmetica Infinitorum, datada de 1656, apresentou inovacoes que podem contribuir para o encaminhamento conceitual e didatico de nocoes basicas da componente curricular de Calculo Diferencial e Integral, no curso de Licenciatura em Matematica. Nesse sentido, avaliamos o potencial pedagogico da referida obra para subsidiar o ensino de conceitos matematicos, em particular as nocoes de integrais, com vistas ao melhoramento do entendimento dos estudantes acerca dessas ideias matematicas, tratadas nos Cursos de Formacao de Professores de Matematica. Por admitirmos que os alunos necessitam ampliar o numero de trajetorias que levam ao desenvolvimento de uma ideia Matematica e que, neste trabalho, nos propusemos a responder a seguinte questao: como a exploracao didatica do exercicio criativo de um matematico na historia pode contribuir na abordagem pedagogica para o ensino de conteudos de Calculo e Analise na Licenciatura em Matematica? Para tal, apoiamo-nos em principios de criatividade elaborados por Mihaly Csikszentmihalyi, que propos um modelo para criatividade que leva em consideracao o contexto social e cultural. Por considerarmos fundamental a explicacao do ciclo do pensamento referente a invencao matematica, associamos a esses principios os processos do Pensamento Matematico Avancado, proposto por Tommy Dreyfus, de modo que destacamos como esses processos se conectam com as nocoes de criatividade. Assim, formulamos um modelo para examinarmos a obra Arithmetica Infinitorum, indicando seus potenciais pedagogicos para subsidiar o ensino de conceitos matematicos baseado em um carater investigativo. De maneira que foi possivel estabelecermos uma proposta de conexao entre conhecimento matematico desenvolvido historicamente por diferentes matematicos e seus potenciais conceituais epistemologicos, com a possibilidade de ser implementada na acao do professor de Matematica formador de professores de Matematica, com vistas a desenvolver competencias e habilidades para uma futura atuacao do professor em formacao.
