Transcendental Curves in the Leibnizian Calculus
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- Author : Viktor Blasjo
- Publisher : Academic Press
- Release : 22 April 2017
- ISBN : 9780128132982
- Page : 282 pages
- Rating : 4.5/5 from 103 voters
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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
- Author : Viktor Blasjo
- Publisher : Academic Press
- Release Date : 2017-04-22
- ISBN : 9780128132982
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
Transcendental Curves in the Leibnizian Calculus

- Author : Anonim
- Publisher : Unknown
- Release Date : 2016
- ISBN : OCLC:946978463
The Oxford Handbook of Leibniz
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- Publisher : Oxford University Press
- Release Date : 2018-10-01
- ISBN : 9780190913649
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- Author : Richard C. Brown
- Publisher : World Scientific
- Release Date : 2012
- ISBN : 9789814390804
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
The Tangled Origins of the Leibnizian Calculus
- Author : Richard C Brown
- Publisher : World Scientific
- Release Date : 2012-03-23
- ISBN : 9789814401616
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- Author : Vincenzo De Risi
- Publisher : Springer Nature
- Release Date : 2020-01-01
- ISBN : 9783030255725
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- Publisher : Oxford University Press, USA
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- Publisher : Springer
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- ISBN : 9783030016388
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- Publisher : Cambridge University Press
- Release Date : 2021-07-22
- ISBN : 9781108834964
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- Publisher : Franz Steiner Verlag Wiesbaden GmbH
- Release Date : 2018
- ISBN : 3515120823
The invention of mathematical transcendence in the seventeenth century is linked to Leibniz, who always claimed it to be his own creation. However, Descartes had created a completely new symbolic frame in which one considers plane curves, which was a real upheaval. Leibniz initially appreciated this Cartesian frame. Although, as we see in the book, during his research he was confronted with inexpressible contexts he then called 'transcendent'. The development of a concept of mathematical transcendence is at the core
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- Publisher : American Mathematical Society
- Release Date : 2022-05-26
- ISBN : 9781470443825
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.
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- Publisher : Springer Nature
- Release Date : 2020-01-02
- ISBN : 9783030312985
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
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- Author : Mircea Pitici
- Publisher : Princeton University Press
- Release Date : 2017-11-14
- ISBN : 9780691178639
The year's finest mathematics writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics
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- Publisher : Unknown
- Release Date : 2022-01-06
- ISBN : 9781108420303
A collection of cutting-edge scholarship on the close interaction of philosophy with science at the birth of the modern age.