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Frontiers in the History of Science

The Impossibility of Squaring the Circle in the 17th Century

A Debate Among Gregory, Huygens and Leibniz

Authors: Crippa, Davide

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  • Delivers an unprecedented perspective on this topic
  • Gives a fresh picture of the mathematics in the 17th Century based on previously unstudied documents
  • Conveys mathematics with minimal technical requirements and thorough explanation so that the narrative can be followed by graduate and undergraduate students in sciences and humanities
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-01638-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-030-01637-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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


Reviews

“This book, we are told, is an “abridged and improved” version of the author’s doctoral dissertation, and, in fact, it does read something like a doctoral dissertation: very scholarly and thorough, replete with copious and often lengthy footnotes … . people with a serious interest in the history of science or mathematics will want a copy of this book on their shelves. Any good university library will as well.” (Mark Hunacek, MAA Reviews, June 03, 2019)

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-01638-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-030-01637-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Impossibility of Squaring the Circle in the 17th Century
Book Subtitle
A Debate Among Gregory, Huygens and Leibniz
Authors
Series Title
Frontiers in the History of Science
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-01638-8
DOI
10.1007/978-3-030-01638-8
Softcover ISBN
978-3-030-01637-1
Series ISSN
2662-2564
Edition Number
1
Number of Pages
VIII, 184
Number of Illustrations
3 b/w illustrations, 29 illustrations in colour
Topics