Infinitesimal Differences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Infinitesimal Differences write by Ursula Goldenbaum. This book was released on 2008-11-03. Infinitesimal Differences available in PDF, EPUB and Kindle. The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics write by John L. Bell. This book was released on 2019-09-09. The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics available in PDF, EPUB and Kindle. This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Elements of the Differential and Integral Calculus
Elements of the Differential and Integral Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of the Differential and Integral Calculus write by Catherinus Putnam Buckingham. This book was released on 1880. Elements of the Differential and Integral Calculus available in PDF, EPUB and Kindle.
A Primer of Infinitesimal Analysis
A Primer of Infinitesimal Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Primer of Infinitesimal Analysis write by John L. Bell. This book was released on 2008-04-07. A Primer of Infinitesimal Analysis available in PDF, EPUB and Kindle. A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Elements of the Mathematical Theory of Limits
Elements of the Mathematical Theory of Limits - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of the Mathematical Theory of Limits write by John Gaston Leathem. This book was released on 1925. Elements of the Mathematical Theory of Limits available in PDF, EPUB and Kindle.
