Transcendental Curves In The Leibnizian Calculus

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Transcendental Curves in the Leibnizian Calculus

Author : Viktor Blasjo
Publisher : Academic Press
ISBN 13 : 0128132981
Total Pages : 284 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Transcendental Curves in the Leibnizian Calculus by : Viktor Blasjo

Download or read book Transcendental Curves in the Leibnizian Calculus written by Viktor Blasjo and published by Academic Press. This book was released on 2017-04-22 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. 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

Author :
Publisher :
ISBN 13 :
Total Pages : 253 pages
Book Rating : 4.:/5 (946 download)

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Book Synopsis Transcendental Curves in the Leibnizian Calculus by :

Download or read book Transcendental Curves in the Leibnizian Calculus written by and published by . This book was released on 2016 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Certain Class of Transcendental Curves

Author : Florence Eliza Allen
Publisher :
ISBN 13 :
Total Pages : 4 pages
Book Rating : 4.:/5 (122 download)

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Book Synopsis A Certain Class of Transcendental Curves by : Florence Eliza Allen

Download or read book A Certain Class of Transcendental Curves written by Florence Eliza Allen and published by . This book was released on 1914 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Families of Curves and the Origins of Partial Differentiation

Author : S.B. Engelsman
Publisher : Elsevier
ISBN 13 : 0080872042
Total Pages : 249 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Families of Curves and the Origins of Partial Differentiation by : S.B. Engelsman

Download or read book Families of Curves and the Origins of Partial Differentiation written by S.B. Engelsman and published by Elsevier. This book was released on 2000-04-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Integral Calculus On the Integration of the Powers of Transcendental Functions

Author : James Ballantyne
Publisher : Legare Street Press
ISBN 13 : 9781019585559
Total Pages : 0 pages
Book Rating : 4.5/5 (855 download)

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Book Synopsis The Integral Calculus On the Integration of the Powers of Transcendental Functions by : James Ballantyne

Download or read book The Integral Calculus On the Integration of the Powers of Transcendental Functions written by James Ballantyne and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This detailed mathematical text provides an in-depth exploration of the integral calculus, including new methods and theorems and their application in the calculation of Bernoullian numbers and the rectification of the logarithmic curve. Written by James Ballantyne, this book is a valuable resource for mathematicians and students of calculus. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Singular Points Peculiar to Transcendental Curves

Author : Jesse Pawling (3d)
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (697 download)

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Book Synopsis Singular Points Peculiar to Transcendental Curves by : Jesse Pawling (3d)

Download or read book Singular Points Peculiar to Transcendental Curves written by Jesse Pawling (3d) and published by . This book was released on 1893 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Calculus

Author : Ron Larson
Publisher :
ISBN 13 : 9780669393491
Total Pages : 1316 pages
Book Rating : 4.3/5 (934 download)

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Book Synopsis Calculus by : Ron Larson

Download or read book Calculus written by Ron Larson and published by . This book was released on 1995 with total page 1316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Infinitesimal Differences

Author : Ursula Goldenbaum
Publisher : Walter de Gruyter
ISBN 13 : 3110211866
Total Pages : 337 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Infinitesimal Differences by : Ursula Goldenbaum

Download or read book Infinitesimal Differences written by Ursula Goldenbaum and published by Walter de Gruyter. This book was released on 2008-11-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.

Higher Plane Algebraic and Transcendental Curves (with)

Author : Helen Smith Rogers
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis Higher Plane Algebraic and Transcendental Curves (with) by : Helen Smith Rogers

Download or read book Higher Plane Algebraic and Transcendental Curves (with) written by Helen Smith Rogers and published by . This book was released on 1959 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Oxford Handbook of Leibniz

Author : Maria Rosa Antognazza
Publisher : Oxford University Press
ISBN 13 : 0190913649
Total Pages : 928 pages
Book Rating : 4.1/5 (99 download)

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Book Synopsis The Oxford Handbook of Leibniz by : Maria Rosa Antognazza

Download or read book The Oxford Handbook of Leibniz written by Maria Rosa Antognazza and published by Oxford University Press. This book was released on 2018-10-01 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Impossibility of Squaring the Circle in the 17th Century

Author : Davide Crippa
Publisher : Springer
ISBN 13 : 3030016382
Total Pages : 184 pages
Book Rating : 4.0/5 (3 download)

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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 and published by Springer. This book was released on 2019-03-06 with total page 184 pages. 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.

The Tangled Origins of the Leibnizian Calculus

Author : Richard C. Brown
Publisher : World Scientific
ISBN 13 : 9814390798
Total Pages : 333 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis The Tangled Origins of the Leibnizian Calculus by : Richard C. Brown

Download or read book The Tangled Origins of the Leibnizian Calculus written by Richard C. Brown and published by World Scientific. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.

Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution

Author : Richard C Brown
Publisher : World Scientific
ISBN 13 : 9814401617
Total Pages : 333 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution by : Richard C Brown

Download or read book Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution written by Richard C Brown and published by World Scientific. This book was released on 2012-03-23 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known “calculi” Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.

Leibniz and the Structure of Sciences

Author : Vincenzo De Risi
Publisher : Springer Nature
ISBN 13 : 3030255727
Total Pages : 304 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Leibniz and the Structure of Sciences by : Vincenzo De Risi

Download or read book Leibniz and the Structure of Sciences written by Vincenzo De Risi and published by Springer Nature. This book was released on 2020-01-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Leibniz

Author : Maria Rosa Antognazza
Publisher : Cambridge University Press
ISBN 13 : 1316154742
Total Pages : 668 pages
Book Rating : 4.3/5 (161 download)

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Book Synopsis Leibniz by : Maria Rosa Antognazza

Download or read book Leibniz written by Maria Rosa Antognazza and published by Cambridge University Press. This book was released on 2008-10-06 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of all the thinkers of the century of genius that inaugurated modern philosophy, none lived an intellectual life more rich and varied than Gottfried Wilhelm Leibniz (1646–1716). Maria Rosa Antognazza's pioneering biography provides a unified portrait of this unique thinker and the world from which he came. At the centre of the huge range of Leibniz's apparently miscellaneous endeavours, Antognazza reveals a single master project lending unity to his extraordinarily multifaceted life's work. Throughout the vicissitudes of his long life, Leibniz tenaciously pursued the dream of a systematic reform and advancement of all the sciences. As well as tracing the threads of continuity that bound these theoretical and practical activities to this all-embracing plan, this illuminating study also traces these threads back into the intellectual traditions of the Holy Roman Empire in which Leibniz lived and throughout the broader intellectual networks that linked him to patrons in countries as distant as Russia and to correspondents as far afield as China.

A Book of Curves

Author : Edward Harrington Lockwood
Publisher : Cambridge University Press
ISBN 13 : 9781001224114
Total Pages : 290 pages
Book Rating : 4.2/5 (241 download)

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Book Synopsis A Book of Curves by : Edward Harrington Lockwood

Download or read book A Book of Curves written by Edward Harrington Lockwood and published by Cambridge University Press. This book was released on 1967 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.

The Richness of the History of Mathematics

Author : Karine Chemla
Publisher : Springer Nature
ISBN 13 : 3031408551
Total Pages : 702 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis The Richness of the History of Mathematics by : Karine Chemla

Download or read book The Richness of the History of Mathematics written by Karine Chemla and published by Springer Nature. This book was released on 2023-11-27 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.