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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.
Rezensionen / Stimmen
"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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
3 s/w Abbildungen, 29 farbige Abbildungen
7 schwarz-weiße und 24 farbige Abbildungen, Bibliographie
Maße
Höhe: 240 mm
Breite: 168 mm
Dicke: 11 mm
Gewicht
ISBN-13
978-3-030-01637-1 (9783030016371)
DOI
10.1007/978-3-030-01638-8
Schweitzer Klassifikation
FM.-Introduction.- James Gregory and the Impossibility of Squaring the Central Conic Sections.- Leibniz's Arithmetical Quadrature of the Circle.- Conclusion.-BM.
