Redefining Geometrical Exactness
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Redefining Geometrical Exactness
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Author : H. J. M. Bos
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Redefining Geometrical Exactness written by H. J. M. Bos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with History categories.
Until the 17th century, rigor and exactness in mathematics meant geometry and Euclid. Other means of confirming results, such as computation, were considered inferior to the traditional constructions using ruler and compass. In 1637 Descartes introduced what is now called analytical geometry, which made algebraic methods equal to geometry in the methods of mathematics. In this detailed study, Bos explores the origins of what is meant by "rigor" in mathematics, and how that definition evolved to include the use of new geometric and algebraic methods.
Redefining Geometrical Exactness
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Author : Henk J.M. Bos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Redefining Geometrical Exactness written by Henk J.M. Bos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. Hethen analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness.
Redefining Geometrical Exactness
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Author : Henk J M Bos
language : en
Publisher:
Release Date : 2000-12-15
Redefining Geometrical Exactness written by Henk J M Bos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-15 with categories.
Landmark Writings In Western Mathematics 1640 1940
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Author : Ivor Grattan-Guinness
language : en
Publisher: Elsevier
Release Date : 2005-02-11
Landmark Writings In Western Mathematics 1640 1940 written by Ivor Grattan-Guinness and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-11 with Mathematics categories.
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field
Reading Mathematics In Early Modern Europe
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Author : Philip Beeley
language : en
Publisher: Routledge
Release Date : 2020-10-20
Reading Mathematics In Early Modern Europe written by Philip Beeley and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-20 with Literary Criticism categories.
Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers’ marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.
Affects Actions And Passions In Spinoza
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Author : Chantal Jaquet
language : en
Publisher: Edinburgh University Press
Release Date : 2018-01-23
Affects Actions And Passions In Spinoza written by Chantal Jaquet and has been published by Edinburgh University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-23 with Philosophy categories.
Revisiting the generally accepted notion of psycho-physical parallelism in Spinoza, Chantal Jaquet offers a new analysis of the relation between body and mind. Looking at a range of Spinoza's texts, and using an original methodology, she analyses their unity in action through affects, actions and passions.
Literature After Euclid
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Author : Matthew Wickman
language : en
Publisher: University of Pennsylvania Press
Release Date : 2016-02-16
Literature After Euclid written by Matthew Wickman and has been published by University of Pennsylvania Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-16 with History categories.
Literature After Euclid tells the story of the creative adaptation of geometry in Scotland during and after the long eighteenth century. Analyzing the work of Scottish literati, Matthew Wickman challenges how we perceive the Scottish Enlightenment and the modernist ethos that relegated "classical" Enlightenment to the dustbin of history.
Descartes And The Ingenium
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Author : Raphaële Garrod
language : en
Publisher: BRILL
Release Date : 2020-11-23
Descartes And The Ingenium written by Raphaële Garrod and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with History categories.
Descartes and the ‘Ingenium’ tracks the significance of embodied thought (ingenium) in the philosophical trajectory of the founding father of dualism. The first part of the book defines the notion of ingenium in relation to core concepts of Descartes's philosophy, such as memory and enumeration. It focuses on Descartes’s uses of this notion in methodical thinking, mathematics, and medicine. The studies in the second part place the Cartesian ingenium within preceding scholastic and humanist pedagogical and natural-philosophical traditions, and highlight its hitherto ignored social and political significance for Descartes himself as a member of the Republic of Letters. By embedding Descartes' notion of ingenium in contemporaneous medical, pedagogical, but also social and literary discourses, this volume outlines the fundamentally anthropological and ethical underpinnings of Descartes's revolutionary epistemology. Contributors: Igor Agostini, Roger Ariew, Harold J. Cook, Raphaële Garrod, Denis Kambouchner, Alexander Marr, Richard Oosterhoff, David Rabouin, Dennis L. Sepper, and Theo Verbeek.
Isaac Newton On Mathematical Certainty And Method
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Author : Niccolo Guicciardini
language : en
Publisher: MIT Press
Release Date : 2011-08-19
Isaac Newton On Mathematical Certainty And Method written by Niccolo Guicciardini and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-19 with Mathematics categories.
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.
Research In History And Philosophy Of Mathematics
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Author : Maria Zack
language : en
Publisher: Birkhäuser
Release Date : 2015-11-10
Research In History And Philosophy Of Mathematics written by Maria Zack and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-10 with Mathematics categories.
This volume contains thirteen papers that were presented at the 2014 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held on the campus of Brock University in St. Catharines, Ontario, Canada. It contains rigorously reviewed modern scholarship on general topics in the history and philosophy of mathematics, as well as on the meeting’s special topic, Early Scientific Computation. These papers cover subjects such as •Physical tools used by mathematicians in the seventeenth century •The first historical appearance of the game-theoretical concept of mixed-strategy equilibrium •George Washington’s mathematical cyphering books •The development of the Venn diagram •The role of Euler and other mathematicians in the development of algebraic analysis •Arthur Cayley and Alfred Kempe’s influence on Charles Peirce's diagrammatic logic •The influence publishers had on the development of mathematical pedagogy in the nineteenth century •A description of the 1924 International Mathematical Congress held in Toronto, told in the form of a “narrated slide show” Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.