The Impossibility of Squaring the Circle in the 17th Century: A Debate among Gregory, Huygens and Leibniz
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F19%3A00507016" target="_blank" >RIV/67985955:_____/19:00507016 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
The Impossibility of Squaring the Circle in the 17th Century: A Debate among Gregory, Huygens and Leibniz
Original language 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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.
Czech name
—
Czech description
—
Classification
Type
B - Specialist book
CEP classification
—
OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
ISBN
978-3-030-01637-1
Number of pages
184
Publisher name
Birkhäuser
Place of publication
Cham
UT code for WoS book
—