# 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

## Download Transcendental Curves in the Leibnizian Calculus in PDF, Epub and Kindle

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 : Viktor Blasjo
- Publisher : Academic Press
- Release Date : 2017-04-20
- ISBN : 012813237X

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

### The Oxford Handbook of Leibniz

- Author : Maria Rosa Antognazza
- Publisher : Oxford University Press
- Release Date : 2018-10-01
- ISBN : 9780190913649

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,

### The Tangled Origins of the Leibnizian Calculus

- 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

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

### Leibniz and the Structure of Sciences

- Author : Vincenzo De Risi
- Publisher : Springer Nature
- Release Date : 2020-01-01
- ISBN : 9783030255725

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

### The History of Continua

- Author : Stewart Shapiro,Geoffrey Hellman
- Publisher : Oxford University Press, USA
- Release Date : 2021
- ISBN : 9780198809647

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.

### Historical Scientific Instruments in Contemporary Education

- Author : Anonim
- Publisher : BRILL
- Release Date : 2021-11-15
- ISBN : 9789004499676

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 Impossibility of Squaring the Circle in the 17th Century

- Author : Davide Crippa
- Publisher : Springer
- Release Date : 2019-03-06
- ISBN : 9783030016388

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

### Leibniz and the Invention of Mathematical Transcendence

- Author : Michel Serfati
- 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

### Anachronisms in the History of Mathematics

- Author : Niccol- Guicciardini
- Publisher : Cambridge University Press
- Release Date : 2021-07-22
- ISBN : 9781108834964

Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.

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

- Author : June Barrow-Green,Jeremy Gray,Robin Wilson
- 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.

### Research in History and Philosophy of Mathematics

- Author : Maria Zack,Dirk Schlimm
- 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

### L’Hôpital's Analyse des infiniments petits

- Author : Robert E Bradley,Salvatore J. Petrilli,C. Edward Sandifer
- Publisher : Birkhäuser
- Release Date : 2015-07-20
- ISBN : 9783319171159

This monograph is an annotated translation of what is considered to be the world’s first calculus textbook, originally published in French in 1696. That anonymously published textbook on differential calculus was based on lectures given to the Marquis de l’Hôpital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulli’s lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulli’s notes, in Latin, to

### The Best Writing on Mathematics 2017

- Author : Mircea Pitici
- Publisher : Princeton University Press
- Release Date : 2017-10-31
- ISBN : 9781400888559

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