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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.
...MoreReview Jesper Lützen (2020) Review of "The Impossibility of Squaring the Circle in the 17th Century: A Debate Among Gregory, Huygens and Leibniz". Historia Mathematica (pp. 99-103).
Review Adam Fix (2019) Review of "The Impossibility of Squaring the Circle in the 17th Century: A Debate Among Gregory, Huygens and Leibniz". British Journal for the History of Science (pp. 709-711).
Article
Scriba, Christoph J.;
(1983)
Gregory's converging double sequence: A new look at the controversy between Huygens and Gregory over the “analytical” quadrature of the circle
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Article
Lützen, Jesper;
(2014)
Seventeenth Century Arguments for the Impossibility of the Indefinite and the Definite Circle Quadrature
(/isis/citation/CBB001550679/)
Article
Sun, Xiao-li;
(2006)
Leibniz and the debate of inventor's right of calculus
(/isis/citation/CBB000780273/)
Chapter
Probst, Siegmund;
(2008)
Neues über Leibniz' Abhandlung zur Kreisquadratur
(/isis/citation/CBB000950169/)
Book
Beeley, Philip;
Scriba, Christoph J.;
(2014)
The Correspondence of John Wallis, Volume IV, 1672-April 1675
(/isis/citation/CBB001552098/)
Article
Bellhouse, David R;
(2014)
The Deification of Newton in 1711
(/isis/citation/CBB001420038/)
Book
Wallis, John;
Beeley, Philip;
Scriba, Christoph J.;
(2014)
The Correspondence of John Wallis. Volume IV, (1672-April 1675)
(/isis/citation/CBB001510022/)
Article
Peiffer, Jeanne;
(2006)
Jacob Bernoulli, maître et rival de son frère Johann
(/isis/citation/CBB001021364/)
Article
Charlotte Wahl;
(2014)
Between Cosmopolitanism and Nationalism. the Role of Expatriates in the Dissemination of Leibniz’s Differential Calculus
(/isis/citation/CBB567158444/)
Article
Ferraro, Giovanni;
(2002)
Convergence and Formal Manipulation of Series from the Origins of Calculus to About 1730
(/isis/citation/CBB000200185/)
Book
Grabiner, Judith V.;
(2010)
A Historian Looks Back: The Calculus as Algebra and Selected Writings
(/isis/citation/CBB001033182/)
Article
Marc Parmentier;
(2015)
Leibniz et le virtuel
(/isis/citation/CBB764317706/)
Article
Martínez-Torregrosa, Joaquín;
López-Gay, Rafael;
Gras-Martí, Albert;
(2006)
Mathematics in Physics Education: Scanning Historical Evolution of the Differential to Find a More Appropriate Model for Teaching Differential Calculus in Physics
(/isis/citation/CBB000671077/)
Thesis
Scott J. Hyslop;
(2015)
The Mathematics of Collision and the Collision of Mathematics in the 17th Century
(/isis/citation/CBB929391854/)
Book
Wardhaugh, Benjamin;
(2012)
The History of the History of Mathematics: Case Studies for the Seventeenth, Eighteenth, and Nineteenth Centuries
(/isis/citation/CBB001251196/)
Book
Davide Gullotto;
(2023)
La Repubblica dei Matematici. Storia dell’analisi matematica nell’età di Euler e Leibniz
(/isis/citation/CBB269641386/)
Article
Michael Raugh;
Siegmund Probst;
(2019)
The Leibniz Catenary and Approximation of e — an Analysis of His Unpublished Calculations
(/isis/citation/CBB083430421/)
Book
Cirino, Raffaele;
(2006)
Dal movimento alla forza: Leibniz, l'infinitesimo tra logica e metafisica
(/isis/citation/CBB000953010/)
Article
Parmentier, Marc;
(2001)
Démonstration et infiniment petits dans la Quadratura arithmetica de Leibniz
(/isis/citation/CBB000770921/)
Article
Blåsjö, Viktor;
(2012)
The Rectification of Quadratures as a Central Foundational Problem for the Early Leibnizian Calculus
(/isis/citation/CBB001251213/)
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