Tangled Origins Of The Leibnizian Calculus The A Case Study Of A Mathematical Revolution
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| Author | : Richard C Brown |
| Publisher | : World Scientific |
| Total Pages | : 333 |
| Release | : 2012-03-23 |
| Genre | : Mathematics |
| ISBN | : 9814401617 |
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.
| Author | : Richard C. Brown |
| Publisher | : World Scientific |
| Total Pages | : 333 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814390801 |
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."
| Author | : James O'Hara |
| Publisher | : BRILL |
| Total Pages | : 1091 |
| Release | : 2024-08-01 |
| Genre | : Science |
| ISBN | : 900468736X |
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.
| Author | : Viktor Blasjo |
| Publisher | : Academic Press |
| Total Pages | : 284 |
| Release | : 2017-04-22 |
| Genre | : Mathematics |
| ISBN | : 0128132981 |
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
| Author | : Jeff Lambert |
| Publisher | : Rowman & Littlefield |
| Total Pages | : 209 |
| Release | : 2024-08-15 |
| Genre | : Philosophy |
| ISBN | : 1666925926 |
Monadological Intimacy: The Relational Operation of Folds in Leibniz and Deleuze analyzes and explains G.W. Leibniz’s theories of folds and relations to claim there is a common operation of inclusion inherent to both theories, an operation that produces a uniquely monadic form of intimacy. Utilizing key insights from Gilles Deleuze’s The Fold: Leibniz and the Baroque, Jeff Lambert considers the role of what is “virtual” and “ideal” for Leibniz in his theory of relations. However, Deleuze’s interpretation is not without flaws, and this book proposes an understanding of the operations of inclusion that is quite different from the view given by Deleuze in The Fold. Specifically, Lambert contends that relational inclusion has four primary “orders” that coincide with the four types of relations found across Leibniz’s oeuvre: complexion, comparison, congruence, and concurrence. Throughout each order of relations, different forms of interconnection play out through an intimate and immediate representation of the universe. Monadological Intimacy argues that the intimate and immediate representation of the universe within each monad utilizes the same operation of inclusion at work in how Leibniz describes the ideal continuum in each distinct fold of motion.
| Author | : Peter Rowlands |
| Publisher | : World Scientific |
| Total Pages | : 311 |
| Release | : 2017-08-07 |
| Genre | : Science |
| ISBN | : 1786343320 |
This book looks at how Newton's theories can be linked to modern day problems and solutions in physics. Newton created an abstract system of theorizing which has been applied to all aspects of the physical world, however he had difficulties in persuading his contemporaries of its unique merits. A detailed study of Newton's writings, published and unpublished, suggests that he had an almost archetypally powerful mode of thinking guaranteed to produce 'correct' results even in areas of physics where systematic study only began long after his time. Newton and Modern Physics investigates this phenomenon, looking at examples of where Newton's principles have relevance to modern day thinking — the study of Newton's work in both seventeenth century and present-day contexts helps to enhance our understanding of both.
| Author | : Peter Rowlands |
| Publisher | : World Scientific |
| Total Pages | : 322 |
| Release | : 2017-11-10 |
| Genre | : Science |
| ISBN | : 1786344041 |
Unique among celebrated scientists, Newton was equally gifted at theoretical physics, experimental physics and pure mathematics. He was also exceptional in another, less well-recognised sense. No one has come near to equalling his extraordinary analytical power.Analytically-derived truths are controversial because such truths can only be established by extended experimental verification or by their success in generating further truths by systematic development. While Newton's optics was ultimately established by the first method and his theory of gravity by the second, much of his work on other subjects, though equally powerful and innovative, has never been totally established as part of this analytical context. This book discusses why the innovations matter today and why they were, and sometimes still are, controversial.
| Author | : Thanu Padmanabhan |
| Publisher | : Springer |
| Total Pages | : 286 |
| Release | : 2019-04-23 |
| Genre | : Science |
| ISBN | : 303017509X |
This lucid and captivating book takes the reader back to the early history of all the sciences, starting from antiquity and ending roughly at the time of Newton — covering the period which can legitimately be called the “dawn” of the sciences. Each of the 24 chapters focuses on a particular and significant development in the evolution of science, and is connected in a coherent way to the others to yield a smooth, continuous narrative. The at-a-glance diagrams showing the “When” and “Where” give a brief summary of what was happening at the time, thereby providing the broader context of the scientific events highlighted in that chapter. Embellished with colourful photographs and illustrations, and “boxed” highlights scattered throughout the text, this book is a must-read for everyone interested in the history of science, and how it shaped our world today.
| Author | : Penelope J. Corfield |
| Publisher | : Yale University Press |
| Total Pages | : 501 |
| Release | : 2022-02-08 |
| Genre | : History |
| ISBN | : 0300253575 |
A comprehensive history of the Georgians, comparing past views of these exciting, turbulent, and controversial times with our attitudes today The Georgian era is often seen as a time of innovations. It saw the end of monarchical absolutism, global exploration and settlements overseas, the world's first industrial revolution, deep transformations in religious and cultural life, and Britain's role in the international trade in enslaved Africans. But how were these changes perceived by people at the time? And how do their viewpoints compare with attitudes today? In this wide-ranging history, Penelope J. Corfield explores every aspect of Georgian life--politics and empire, culture and society, love and violence, religion and science, industry and towns. People's responses at the time were often divided. Pessimists saw loss and decline, while optimists saw improvements and light. Out of such tensions came the Georgian culture of both experiment and resistance. Corfield emphasizes those elements of deep continuity that persisted even within major changes, and shows how new developments were challenged if their human consequences proved dire.
| Author | : Richard C. Brown |
| Publisher | : World Scientific |
| Total Pages | : 333 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814390798 |
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.
