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Transcendental Curves In The Leibnizian Calculus

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Transcendental Curves in the Leibnizian Calculus

Transcendental Curves in the Leibnizian Calculus Book
Author : Viktor Blasjo
Publisher : Academic Press
Release : 2017-04-22
ISBN : 0128132981
Language : En, Es, Fr & De

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Book Description :

Transcendental Curves in the Leibnizian Calculus analyzes the mathematical and philosophical conflict between Euclidean and Cartesian mathematics. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. Brings to light this underlying and often implicit complex of concerns that permeate early calculus Evaluates the technical conception and mathematical construction of the geometrical method Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus Provides a beautifully written work of outstanding original scholarship

Transcendental Curves in the Leibnizian Calculus

Transcendental Curves in the Leibnizian Calculus Book
Author : Anonim
Publisher : Unknown
Release : 2016
ISBN : 0987650XXX
Language : En, Es, Fr & De

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The Oxford Handbook of Leibniz

The Oxford Handbook of Leibniz Book
Author : Maria Rosa Antognazza
Publisher : Oxford University Press
Release : 2018-10-01
ISBN : 0190913649
Language : En, Es, Fr & De

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Book Description :

The extraordinary breadth and depth of Leibniz's intellectual vision commands ever increasing attention. As more texts gradually emerge from seemingly bottomless archives, new facets of his contribution to an astonishing variety of fields come to light. This volume provides a uniquely comprehensive, systematic, and up-to-date appraisal of Leibniz's thought thematically organized around its diverse but interrelated aspects. Discussion of his philosophical system naturally takes place of pride. A cluster of original essays revisit his logic, metaphysics, epistemology, philosophy of nature, moral and political philosophy, and philosophy of religion. The scope of the volume, however, goes beyond that of a philosophical collection to embrace all the main features of Leibniz's thought and activity. Contributions are offered on Leibniz as a mathematician (including not only his calculus but also determinant theory, symmetric functions, the dyadic, the analysis situs, probability and statistics); on Leibniz as a scientist (physics and also optics, cosmology, geology, physiology, medicine, and chemistry); on his technical innovations (the calculating machine and the technology of mining, as well as other discoveries); on his work as an 'intelligencer' and cultural networker, as jurist, historian, editor of sources and librarian; on his views on Europe's political future, religious toleration, and ecclesiastical reunification; on his proposals for political, administrative, economic, and social reform. In so doing, the volume serves as a unique cross-disciplinary point of contact for the many domains to which Leibniz contributed. By assembling leading specialists on all these topics, it offers the most rounded picture of Leibniz's endeavors currently available.

Jacob Hermann and the Diffusion of the Leibnizian Calculus in Italy

Jacob Hermann and the Diffusion of the Leibnizian Calculus in Italy Book
Author : Silvia Mazzone,Clara Silvia Roero
Publisher : Olschki
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Infinitesimal Differences

Infinitesimal Differences Book
Author : Ursula Goldenbaum,Douglas Jesseph
Publisher : Walter de Gruyter
Release : 2008-11-03
ISBN : 3110211866
Language : En, Es, Fr & De

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Book Description :

The development of the calculus during the 17th century was successful in mathematical practice, but raised questions about the nature of infinitesimals: were they real or rather fictitious? This collection of essays, by scholars from Canada, the US, Germany, Japan and Switzerland, gives a comprehensive study of the controversies over the nature and status of the infinitesimal. Aside from Leibniz, the scholars considered are Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. The collection also contains newly discovered marginalia of Leibniz to the writings of Hobbes.

Newton and Leibniz

Newton and Leibniz Book
Author : Margaret E. Baron,H. J. M. Bos
Publisher : Unknown
Release : 1974
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Arts Mathematics Newton and Leibniz

Arts Mathematics  Newton and Leibniz Book
Author : Open University
Publisher : Unknown
Release : 1974
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Equivalence and Priority

Equivalence and Priority Book
Author : Domenico Bertoloni Meli,Gottfried Wilhelm Freiherr von Leibniz,Research Fellow Domenico Bertoloni Meli
Publisher : Oxford University Press, USA
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Leibniz's dispute with Newton over the physico-mathematical theories expounded in the Principia Mathematica (1687) have long been identified as a crucial episode in the history of science. Bertolini Meli here examines several hitherto unpublished manuscripts in Leibniz's hand illustrating his first reading of and reaction to Newton's Principia. Six of the most important manuscripts are here presented for the first time. Contrary to Leibniz's own claims, this new evidence shows that he had studied Newton's masterpiece before publishing An Essay on the Causes of Celestial Motions. This article, representing his response to Newton, also included in English translation. Meli analyzes the important implications of this episode on a variety of themes ranging from priority claims to the mathematization of nature in the 17th century. Besides providing a careful study of Leibniz's style and strategy, the author examines how our perception of Newton's achievement is affected and the reception of the rival theories by the mathematical community around 1700. This unique work will interest all historians of science and philosophy.

Bulletin

Bulletin Book
Author : Institute of Mathematics and Its Applications
Publisher : Unknown
Release : 1985
ISBN : 0987650XXX
Language : En, Es, Fr & De

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The New Encyclopaedia Britannica

The New Encyclopaedia Britannica Book
Author : Anonim
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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The Mind of Leibniz

The Mind of Leibniz Book
Author : Kurt von S. Kynell
Publisher : Unknown
Release : 2003
ISBN : 9780773468931
Language : En, Es, Fr & De

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Book Description :

This volume attempts to resolve the century old dispute between Newton and Leibniz over the discovery of the calculus, and also explores both the mind and the life long research of Gottfried Wilhelm von Leibniz, documenting his phenomenal mathematical and philosophical research, as well as the apparent nature and possible origins of genius and human intelligence.

Mathematics and Mathematicians

Mathematics and Mathematicians Book
Author : Pierre Dedron,Jean Itard
Publisher : Unknown
Release : 1978
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Scripta Mathematica

Scripta Mathematica Book
Author : Anonim
Publisher : Unknown
Release : 1961
ISBN : 0987650XXX
Language : En, Es, Fr & De

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The Impossibility of Squaring the Circle in the 17th Century

The Impossibility of Squaring the Circle in the 17th Century Book
Author : Davide Crippa
Publisher : Springer
Release : 2019-03-06
ISBN : 3030016382
Language : En, Es, Fr & De

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Book 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.

History of Science History of mathematics

History of Science  History of mathematics Book
Author : Rajbir Singh
Publisher : Unknown
Release : 1994
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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The New Encyclopaedia Britannica Macropaedia

The New Encyclopaedia Britannica  Macropaedia Book
Author : Anonim
Publisher : Unknown
Release : 1995
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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The New Encyclopaedia Britannica Macropaedia Knowledge in depth

The New Encyclopaedia Britannica  Macropaedia   Knowledge in depth Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Leibniz and Adam

Leibniz and Adam Book
Author : Marcelo Dascal,Elhanan Yakira
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Families of Curves and the Origins of Partial Differentiation

Families of Curves and the Origins of Partial Differentiation Book
Author : S.B. Engelsman
Publisher : Elsevier
Release : 2000-04-01
ISBN : 9780080872049
Language : En, Es, Fr & De

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Book Description :

This book provides a detailed description of the main episodes in the emergence of partial differentiation during the period 1690-1740. It argues that the development of this concept - to a considerable degree of perfection - took place almost exclusively in problems concerning families of curves. Thus, the book shows the origins of the ideas and techniques which paved the way for the sudden introduction of partial differential equations in 1750. The main methodological characteristic of the book is its emphasis on a full understanding of the motives, problems and goals of the mathematicians of that time.

Nieuw Archief Voor Wiskunde

Nieuw Archief Voor Wiskunde Book
Author : Anonim
Publisher : Unknown
Release : 1996
ISBN : 0987650XXX
Language : En, Es, Fr & De

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