Book ID: CBB805052525

The Impossibility of Squaring the Circle in the 17th Century: A Debate Among Gregory, Huygens and Leibniz (2019)

unapi

Crippa, Davide (Author)


Birkhäuser


Publication Date: 2019
Physical Details: 192
Language: English

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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.

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Reviewed By

Review 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). unapi

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). unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB805052525/

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Authors & Contributors
Scriba, Christoph J.
Probst, Siegmund
Parmentier, Marc
Beeley, Philip
Davide Gullotto
Raugh, Michael
Concepts
Mathematics
Calculus
Controversies and disputes
Correspondence and corresponding
Geometry
Squaring the circle
Time Periods
17th century
18th century
Early modern
20th century
19th century
Places
England
Germany
Europe
Institutions
Royal Society of London
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