Redefining Geometrical Exactness
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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. He then 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.
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.
Between Tradition And Innovation
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Author : Ad J. Meskens
language : en
Publisher: BRILL
Release Date : 2021-03-29
Between Tradition And Innovation written by Ad J. Meskens and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-29 with Education categories.
This book offers an analysis of the ground breaking mathematical work of Gregorio a San Vicente and his student and shows that the Flemish Jesuit Mathematics School had profound influence on mathematics in the seventeenth century.
Geometry From A Differentiable Viewpoint
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Author : John McCleary
language : en
Publisher: Cambridge University Press
Release Date : 2013
Geometry From A Differentiable Viewpoint written by John McCleary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
From Logic To Practice
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Author : Gabriele Lolli
language : en
Publisher: Springer
Release Date : 2014-11-28
From Logic To Practice written by Gabriele Lolli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Philosophy categories.
This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
The Geometry Of An Art
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Author : Kirsti Andersen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-23
The Geometry Of An Art written by Kirsti Andersen 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 2008-11-23 with Mathematics categories.
This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.
The Oxford Handbook Of Descartes And Cartesianism
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Author : Steven Nadler
language : en
Publisher: Oxford University Press, USA
Release Date : 2019-04-25
The Oxford Handbook Of Descartes And Cartesianism written by Steven Nadler and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-25 with Philosophy, French categories.
The Oxford Handbook of Descartes and Cartesianism comprises fifty specially written chapters on Rene Descartes (1596-1650) and Cartesianism, the dominant paradigm for philosophy and science in the seventeenth century, written by an international group of leading scholars of early modern philosophy. The first part focuses on the various aspects of Descartes's biography (including his background, intellectual contexts, writings, and correspondence) and philosophy, with chapters on his epistemology, method, metaphysics, physics, mathematics, moral philosophy, political thought, medical thought, and aesthetics. The chapters of the second part are devoted to the defense, development and modification of Descartes's ideas by later generations of Cartesian philosophers in France, the Netherlands, Italy, and elsewhere. The third and final part considers the opposition to Cartesian philosophy by other philosophers, as well as by civil, ecclesiastic, and academic authorities. This handbook provides an extensive overview of Cartesianism - its doctrines, its legacies and its fortunes - in the period based on the latest research.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date :
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Transcendental Curves In The Leibnizian Calculus
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Author : Viktor Blasjo
language : en
Publisher: Academic Press
Release Date : 2017-04-22
Transcendental Curves In The Leibnizian Calculus written by Viktor Blasjo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-22 with Mathematics categories.
Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. Brings to light this underlying and often implicit complex of concerns that permeate early calculus Evaluates the technical conception and mathematical construction of the geometrical method Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus Provides a beautifully written work of outstanding original scholarship
