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The impossibility of squaring the ci...

Crippa, Davide.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The impossibility of squaring the circle in the 17th centuryby Davide Crippa.
其他題名:	a debate among Gregory, Huygens and Leibniz /
作者:	Crippa, Davide.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	viii, 184 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	MathematicsPhilosophy17th century.
電子資源:	https://doi.org/10.1007/978-3-030-01638-8
ISBN:	9783030016388$q(electronic bk.)

The impossibility of squaring the circle in the 17th centurya 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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise De quadratura arithmetica.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$q(electronic bk.)

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

853842
Gregory, James,
1638-1675.Subjects--Topical Terms:

853845
Mathematics
--Philosophy--17th century.

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

Dewey Class. No.: 510

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