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The Impossibility of Squaring the Circle in the 17th Century

2019-03-06 Mathematics
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Release : 2019-03-06
Genre : Mathematics
Kind : eBook
Book Rating : 382/5 ( reviews)

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Book Synopsis The Impossibility of Squaring the Circle in the 17th Century by : Davide Crippa

Download or read book The Impossibility of Squaring the Circle in the 17th Century written by Davide Crippa. This book was released on 2019-03-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.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.

Squaring the Circle

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 990/5 ( reviews)

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Book Synopsis Squaring the Circle by : Douglas M. Jesseph

Download or read book Squaring the Circle written by Douglas M. Jesseph. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: PrefaceList of AbbreviationsChapter One: The Mathematical Career of the Monster of MalmesburyChapter Two: The Reform of Mathematics and of the UniversitiesIdeological Origins of the DisputeChapter Three: De Corpore and the Mathematics of MaterialismChapter Four: Disputed FoundationsHobbes vs. Wallis on the Philosophy of MathematicsChapter Five: The "Modern Analytics" and the Nature of DemonstrationChapter Six: The Demise of Hobbesian GeometryChapter Seven: The Religion, Rhetoric, and Politics of Mr. Hobbes and Dr. WallisChapter Eight: Persistence in ErrorWhy Was Hobbes So Resolutely Wrong?Appendix: Selections from Hobbes's Mathematical WritingsReferencesIndex Copyright © Libri GmbH. All rights reserved.

Leibniz in His World

2024-11-12 Biography & Autobiography
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Release : 2024-11-12
Genre : Biography & Autobiography
Kind : eBook
Book Rating : 745/5 ( reviews)

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Book Synopsis Leibniz in His World by : Audrey Borowski

Download or read book Leibniz in His World written by Audrey Borowski. This book was released on 2024-11-12. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping intellectual biography that restores the Enlightenment polymath to the intellectual, scientific, and courtly worlds that shaped his early life and thought Described by Voltaire as “perhaps a man of the most universal learning in Europe,” Gottfried Wilhelm Leibniz (1646–1716) is often portrayed as a rationalist and philosopher who was wholly detached from the worldly concerns of his fellow men. Leibniz in His World provides a groundbreaking reassessment of Leibniz, telling the story of his trials and tribulations as an aspiring scientist and courtier navigating the learned and courtly circles of early modern Europe and the Republic of Letters. Drawing on extensive correspondence by Leibniz and many leading figures of the age, Audrey Borowski paints a nuanced portrait of Leibniz in the 1670s, during his “Paris sojourn” as a young diplomat and in Germany at the court of Duke Johann Friedrich of Hanover. She challenges the image of Leibniz as an isolated genius, revealing instead a man of multiple identities whose thought was shaped by a deep engagement with the social and intellectual milieus of his time. Borowski shows us Leibniz as he was known to his contemporaries, enabling us to rediscover him as an enigmatic young man who was complex and all too human. An exhilarating work of scholarship, Leibniz in His World demonstrates how this uncommon intellect, torn between his ideals and the necessity to work for absolutist states, struggled to make a name for himself during his formative years.

Leibniz on Binary

2022-10-25 Mathematics
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Release : 2022-10-25
Genre : Mathematics
Kind : eBook
Book Rating : 126/5 ( reviews)

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Book Synopsis Leibniz on Binary by : Lloyd Strickland

Download or read book Leibniz on Binary written by Lloyd Strickland. This book was released on 2022-10-25. Available in PDF, EPUB and Kindle. Book excerpt: The first collection of Leibniz’s key writings on the binary system, newly translated, with many previously unpublished in any language. The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today’s digital computing. This book offers the first collection of Leibniz’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz’s original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz’s mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz’s development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.

Leibniz’s Correspondence in Science, Technology and Medicine (1676 –1701)

2024-08-01 Science
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Release : 2024-08-01
Genre : Science
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Book Rating : 36X/5 ( reviews)

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Book Synopsis Leibniz’s Correspondence in Science, Technology and Medicine (1676 –1701) by : James O'Hara

Download or read book Leibniz’s Correspondence in Science, Technology and Medicine (1676 –1701) written by James O'Hara. This book was released on 2024-08-01. Available in PDF, EPUB and Kindle. Book excerpt: Leibniz’s correspondence from his years spent in Paris (1672-1676) reflects his growth to mathematical maturity whereas that from the years 1676-1701 reveals his growth to maturity in science, technology and medicine in the course of which more than 2000 letters were exchanged with more than 200 correspondents. The remaining years until his death in 1716 witnessed above all the appearance of his major philosophical works. The focus of the present work is Leibniz's middle period and the core themes and core texts from his multilingual correspondence are presented in English from the following subject areas: mathematics, natural philosophy, physics (and cosmology), power technology (including mining and transport), engineering and engineering science, projects (scientific, technological and economic projects), alchemy and chemistry, geology, biology and medicine.

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