Transcendental Curves In The Leibnizian Calculus

DOWNLOAD

Download Transcendental Curves In The Leibnizian Calculus PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Transcendental Curves In The Leibnizian Calculus book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Transcendental Curves In The Leibnizian Calculus

DOWNLOAD
Author : Viktor Blasjo
language : en
Publisher: Academic Press
Release Date : 2017-04-22

Transcendental Curves In The Leibnizian Calculus written by Viktor Blasjo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-22 with Mathematics categories.

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

DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2016

Transcendental Curves In The Leibnizian Calculus written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

The Tangled Origins Of The Leibnizian Calculus

DOWNLOAD
Author : Richard C. Brown
language : en
Publisher: World Scientific
Release Date : 2012

The Tangled Origins Of The Leibnizian Calculus written by Richard C. Brown and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

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 Oxford Handbook Of Leibniz

DOWNLOAD
Author : Maria Rosa Antognazza
language : en
Publisher: Oxford University Press
Release Date : 2018-10-01

The Oxford Handbook Of Leibniz written by Maria Rosa Antognazza and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-01 with Philosophy categories.

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.

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

DOWNLOAD
Author : Richard C Brown
language : en
Publisher: World Scientific
Release Date : 2012-03-23

Tangled Origins Of The Leibnizian Calculus The A Case Study Of A Mathematical Revolution written by Richard C Brown and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-23 with Mathematics categories.

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 S Correspondence In Science Technology And Medicine 1676 1701

DOWNLOAD
Author : James O'Hara
language : en
Publisher: BRILL
Release Date : 2024-07-29

Leibniz S Correspondence In Science Technology And Medicine 1676 1701 written by James O'Hara and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-29 with Science categories.

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.

The Impossibility Of Squaring The Circle In The 17th Century

DOWNLOAD
Author : Davide Crippa
language : en
Publisher: Springer
Release Date : 2019-03-06

The Impossibility Of Squaring The Circle In The 17th Century written by Davide Crippa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-06 with Mathematics categories.

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 History Of Mathematics A Source Based Approach Volume 2

DOWNLOAD
Author : June Barrow-Green
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-23

The History Of Mathematics A Source Based Approach Volume 2 written by June Barrow-Green and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-23 with Mathematics categories.

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.

Traditions Of Analysis And Synthesis

DOWNLOAD
Author : William R. Newman
language : en
Publisher: Springer Nature
Release Date : 2024-12-23

Traditions Of Analysis And Synthesis written by William R. Newman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Science categories.

This open access book provides a fresh perspective on analysis and synthesis across several areas of inquiry. The two operations form a primary basis of modern laboratory science, ranging from the spectrographic analysis used in practically every scientific discipline today, to the naming of entire disciplines, such as synthetic organic chemistry. Despite their acknowledged significance, however, the history of analysis, synthesis, and their relations over the longue durée is poorly understood. Several volumes have been devoted to the history of analysis and synthesis in the sense that premodern mathematicians and philosophers used the terms, but very little work has been done on the tradition of material decomposition and recomposition and its relationship to mathematics and philosophy. The present volume brings together scholars in the history of medicine, mathematics, philosophy, chemistry, and alchemy to explore the ways in which these multiple disciplines understood and used analysis and synthesis as experimental, justificatory, and conceptual tools.

Leibniz And The Structure Of Sciences

DOWNLOAD
Author : Vincenzo De Risi
language : en
Publisher: Springer Nature
Release Date : 2020-01-01

Leibniz And The Structure Of Sciences written by Vincenzo De Risi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Science categories.

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.