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The Impossibility of Squaring the Circle in the 17th Century: A Debate among Gregory, Huygens and Leibniz
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SYSNO ASEP 0507016 Document Type B - Monograph R&D Document Type Monograph Title The Impossibility of Squaring the Circle in the 17th Century: A Debate among Gregory, Huygens and Leibniz Author(s) Crippa, Davide (FLU-F) ORCID, RID, SAI Issue data Cham: Birkhäuser, 2019 ISBN 978-3-030-01637-1 Series Frontiers in the history of science Number of pages 184 s. Publication form Print - P Language eng - English Country CH - Switzerland Keywords quadrature of the circle ; infinitesimal analysis ; Leibniz ; impossibility ; geometry Subject RIV AA - Philosophy ; Religion OECD category Philosophy, History and Philosophy of science and technology Institutional support FLU-F - RVO:67985955 Annotation This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle. The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics. Workplace Institute of Philosophy Contact Chlumská Simona, chlumska@flu.cas.cz ; Tichá Zuzana, asep@flu.cas.cz Tel: 221 183 360 Year of Publishing 2020
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