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 : 282 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 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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.

Families of Curves and the Origins of Partial Differentiation

Author : S.B. Engelsman
Publisher : Elsevier
ISBN 13 : 9780080872049
Total Pages : 237 pages
Book Rating : 4.8/5 (72 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 237 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.

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.

The Tangled Origins of the Leibnizian Calculus

Author : Richard C. Brown
Publisher : World Scientific
ISBN 13 : 9814390801
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: 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 OC calculiOCO 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."

The Tangled Origins of the Leibnizian Calculus

Author : Richard C Brown
Publisher : World Scientific
ISBN 13 : 9814401617
Total Pages : 332 pages
Book Rating : 4.8/5 (144 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 2012-03-23 with total page 332 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. Contents:Evolution or Revolution in MathematicsIssues in Seventeenth Century MathematicsIsaac Barrow: A Foil to LeibnizA Young Central European PolymathFirst Steps in MathematicsThe Creation of CalculusLogicThe Universal CharacteristicThe Baroque Cultural ContextEpilogueSome Concluding Remarks on Mathematical ChangeAppendices:A: A Transmutation Theorem of LeibnizB: Leibniz's Series Quadrature of a ConicC: Syllogistic LogicD: The Vis Viva DisputeE: Some Applications of Curves and Neusis in Greek GeometryF: InfinitesimalsA Note on the Author Readership: Advanced undergraduate students, graduate students and researchers in mathematics, history of mathematics or history of science. Keywords:Leibniz;Calculus;Geometry;17th Century MathematicsKey Features:The thoroughness and comprehensiveness of the treatment of this book are based on recent researchTechnical details of the mathematics are carefully dealt with instead of just being summarized for the general readerNo other work on the development of calculus includes a description and analysis of the Baroque/Renaissance atmosphere of fascination with symbols, emblems, Real Characters and philosophical languages which motivated both Leibniz's mathematics and his search for the Universal Characteristic

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.

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.

Anachronisms in the History of Mathematics

Author : Niccol- Guicciardini
Publisher : Cambridge University Press
ISBN 13 : 1108834965
Total Pages : 393 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Anachronisms in the History of Mathematics by : Niccol- Guicciardini

Download or read book Anachronisms in the History of Mathematics written by Niccol- Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.

Historical Scientific Instruments in Contemporary Education

Author :
Publisher : BRILL
ISBN 13 : 9004499679
Total Pages : 324 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis Historical Scientific Instruments in Contemporary Education by :

Download or read book Historical Scientific Instruments in Contemporary Education written by and published by BRILL. This book was released on 2021-11-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: When science’s “black boxes” are pried open, its workings become accessible. Like time-travellers into history but grounded in today’s cultures, learners interact directly with authentic instruments and replicas. Chapters describe educational experiences sparked through collaborations interrelating museum, school and university.

The History of Continua

Author : Stewart Shapiro
Publisher : Oxford University Press, USA
ISBN 13 : 0198809646
Total Pages : 593 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis The History of Continua by : Stewart Shapiro

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press, USA. This book was released on 2021 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

The History of Mathematics: A Source-Based Approach, Volume 2

Author : June Barrow-Green
Publisher : American Mathematical Society
ISBN 13 : 1470472996
Total Pages : 703 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The History of Mathematics: A Source-Based Approach, Volume 2 by : June Barrow-Green

Download or read book The History of Mathematics: A Source-Based Approach, Volume 2 written by June Barrow-Green and published by American Mathematical Society. This book was released on 2022-12-23 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Representation and Productive Ambiguity in Mathematics and the Sciences

Author : Emily R. Grosholz
Publisher : Clarendon Press
ISBN 13 : 0191538515
Total Pages : 330 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Representation and Productive Ambiguity in Mathematics and the Sciences by : Emily R. Grosholz

Download or read book Representation and Productive Ambiguity in Mathematics and the Sciences written by Emily R. Grosholz and published by Clarendon Press. This book was released on 2007-08-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian 'analysis' - the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience. Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable for mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are sublty altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.

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.

A History of Kinematics from Zeno to Einstein

Author : Teun Koetsier
Publisher : Springer Nature
ISBN 13 : 3031398726
Total Pages : 354 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis A History of Kinematics from Zeno to Einstein by : Teun Koetsier

Download or read book A History of Kinematics from Zeno to Einstein written by Teun Koetsier and published by Springer Nature. This book was released on 2023-10-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.

Research in History and Philosophy of Mathematics

Author : Maria Zack
Publisher : Springer Nature
ISBN 13 : 3030312984
Total Pages : 180 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Research in History and Philosophy of Mathematics by : Maria Zack

Download or read book Research in History and Philosophy of Mathematics written by Maria Zack and published by Springer Nature. This book was released on 2020-01-02 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era. The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy of mathematics, including Fred Sommers’s creation of Traditional Formal Logic and Alexander Grothendieck’s work as a starting point for discussing analogies between commutative algebra and algebraic geometry. Continuing the focus on the philosophy of mathematics, the next selections discuss the mathematization of biology and address the study of numerical cognition. The volume then moves to discussing various aspects of mathematics education, including Charles Davies’s early book on the teaching of mathematics and the use of Gaussian Lemniscates in the classroom. A collection of papers on the history of mathematics in the nineteenth century closes out the volume, presenting a discussion of Gauss’s “Allgemeine Theorie des Erdmagnetismus” and a comparison of the geometric works of Desargues and La Hire. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.