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The impossibility of squaring the ci...

Crippa, Davide.

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The impossibility of squaring the circle in the 17th century = a debate among Gregory, Huygens and Leibniz /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The impossibility of squaring the circle in the 17th century/ by Davide Crippa.
Reminder of title:	a debate among Gregory, Huygens and Leibniz /
Author:	Crippa, Davide.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	viii, 184 p. :ill., digital ;24 cm.
[NT 15003449]:	FM -- Introduction -- James Gregory and the Impossibility of Squaring the Central Conic Sections -- Leibniz's Arithmetical Quadrature of the Circle -- Conclusion -- BM.
Contained By:	Springer eBooks
Subject:	Mathematics - Philosophy - 17th century. -
Online resource:	https://doi.org/10.1007/978-3-030-01638-8
ISBN:	9783030016388

The impossibility of squaring the circle in the 17th century = a debate among Gregory, Huygens and Leibniz /
Crippa, Davide.

The impossibility of squaring the circle in the 17th centurya debate among Gregory, Huygens and Leibniz /[electronic resource] :by Davide Crippa. - Cham :Springer International Publishing :2019. - viii, 184 p. :ill., digital ;24 cm. - Frontiers in the history of science,2662-2564. - Frontiers in the history of science..

FM -- Introduction -- James Gregory and the Impossibility of Squaring the Central Conic Sections -- Leibniz's Arithmetical Quadrature of the Circle -- Conclusion -- BM.

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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise De quadratura arithmetica. 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.

ISBN: 9783030016388

Standard No.: 10.1007/978-3-030-01638-8doiSubjects--Personal Names:

3453955
Gregory, James,
1638-1675.Subjects--Topical Terms:

928825
Mathematics
--Philosophy--17th century.

LC Class. No.: QA8.4 / .C757 2019

Dewey Class. No.: 510

The impossibility of squaring the circle in the 17th century = a debate among Gregory, Huygens and Leibniz /
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505 0 $a FM -- Introduction -- James Gregory and the Impossibility of Squaring the Central Conic Sections -- Leibniz's Arithmetical Quadrature of the Circle -- Conclusion -- BM.
520 $a 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 De quadratura arithmetica. 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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