
Transcendental Curves in the Leibnizian Calculus
Description
Key Features
- 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
Readership
PhD students and tenured mathematicians and historians of mathematics with an interest in the early history of calculus and geometry. Leibniz scholars will naturally be most attracted to the content
Table of Contents
Chapter 1: Preliminary matters
- Abstract
- 1.1 Purpose and scope of the present work
- 1.2 Previous scholarship related to the present work
- 1.3 What is new in the present work
- 1.4 Conventions adopted in this work
- 1.5 Some key terms
Chapter 2: Introduction
- Abstract
- 2.1 The problem of transcendental curves
- 2.2 Fundamental conflict between analytic and construction-based paradigms
- 2.3 Implications of this story for the general historiography of the period
Chapter 3: The classical basis of 17th-century philosophy of mathematics
- Abstract
- 3.1 Introduction
- 3.2 Greek geometry
- 3.3 17th-century philosophy of geometry
Chapter 4: Mathematical context
- Abstract
- 4.1 Introduction
- 4.2 The early calculus according to Leibniz
- 4.3 Transcendental curves in the early work of Huygens
- 4.4 Johann Bernoulli’s lectures on the calculus
Chapter 5: Transcendental curves by curve tracing
- Abstract
- 5.1 Introduction
- 5.2 The tractrix
- 5.3 Johann Bernoulli’s generalised tractrix
- 5.4 Leibniz’s construction by tractional motion of any curve given by dy/dx
- 5.5 Jacob Bernoulli’s tractional method
- 5.6 Johann Bernoulli’s crawling curves
Chapter 6: Transcendental curves analytically: exponentials and power series
- Abstract
- 6.1 Introduction
- 6.2 The problem with power series
- 6.3 Exponentials
Chapter 7: Transcendental curves by the reduction of quadratures
- Abstract
- 7.1 Introduction
- 7.2 Computational reduction of quadratures
- 7.3 The rectification of quadratures
Chapter 8: Transcendental curves in physics
- Abstract
- 8.1 Introduction
- 8.2 The elastica
- 8.3 The paracentric isochrone
- 8.4 The brachistochrone
- 8.5 Forces and tangents
Chapter 9: A view from the 18th century
- Abstract
- 9.1 Introduction
- 9.2 The epistemological miracle of analytical methods
- 9.3 Euler’s analytical calculus
- 9.4 Lagrange’s analytical calculus
- 9.5 Lagrange’s analytical mechanics
Chapter 10: Concluding overview
- Abstract
Product details
- No. of pages: 282
- Language: English
- Copyright: © Academic Press 2017
- Published: April 20, 2017
- Imprint: Academic Press
- Paperback ISBN: 9780128132371
- eBook ISBN: 9780128132982
About the Author
Viktor Blasjo
Affiliations and Expertise
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