EAN: 9783030016371

FRONTIERS IN THE HISTORY OF SCIENCE THE IMPOS...

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unpublished treatise on the arithmetical quadrature of the circle.The author shows how the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.

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