The Impossibility of Squaring the Circle in the 17th Century : A Debate Among Gregory, Huygens and Leibniz Paperback / softback
by Davide Crippa
Part of the Frontiers in the History of Science series
Paperback / softback
Description
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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.
Information
-
Item not Available
- Format:Paperback / softback
- Pages:184 pages, 29 Illustrations, color; 3 Illustrations, black and white; VIII, 184 p. 32 illus., 29 ill
- Publisher:Springer Nature Switzerland AG
- Publication Date:19/03/2019
- Category:
- ISBN:9783030016371
Information
-
Item not Available
- Format:Paperback / softback
- Pages:184 pages, 29 Illustrations, color; 3 Illustrations, black and white; VIII, 184 p. 32 illus., 29 ill
- Publisher:Springer Nature Switzerland AG
- Publication Date:19/03/2019
- Category:
- ISBN:9783030016371
