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The impossibility of squaring the circle in the 17th century : a debate among Gregory, Huygens and Leibniz
- 作者： Crippa, Davide, author.
- 其他作者：
- 其他題名：
- Frontiers in the history of science.
- 出版： Cham : Springer International Publishing :Imprint: Birkhauser
- 叢書名： Frontiers in the history of science,
- 主題： Gregory, James, 1638-1675. , Huygens, Christiaan, 1629-1695. , Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. , Mathematics--Philosophy--History--17th century. , History of Mathematical Sciences.
- ISBN： 9783030016388 (electronic bk.) 、 9783030016371 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: FM -- Introduction -- James Gregory and the Impossibility of Squaring the Central Conic Sections -- Leibniz's Arithmetical Quadrature of the Circle -- Conclusion -- BM.
- 摘要註: 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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise De quadratura arithmetica. 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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讀者標籤：
- 系統號： 005466586 | 機讀編目格式
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