Isaac Newton on Mathematical Certainty and Method
Published:
2009
Online ISBN:
9780262258869
Print ISBN:
9780262013178
Contents
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8.1 Barrow 8.1 Barrow
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8.1.1 Barrow as Newton’s Mentor 8.1.1 Barrow as Newton’s Mentor
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8.1.2 Generation of Magnitudes by Motion 8.1.2 Generation of Magnitudes by Motion
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8.1.3 Symptomata of Curves Deduced from their Generation 8.1.3 Symptomata of Curves Deduced from their Generation
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8.1.4 Subtangents ex calculo 8.1.4 Subtangents ex calculo
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8.1.5 Problem Reduction 8.1.5 Problem Reduction
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8.1.6 Transmutation of Areas 8.1.6 Transmutation of Areas
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8.1.7 Apagogical Proofs 8.1.7 Apagogical Proofs
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8.2 Preliminaries to the Method of Fluxions 8.2 Preliminaries to the Method of Fluxions
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8.2.1 An Analytical Art 8.2.1 An Analytical Art
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8.2.2 Basic Definitions 8.2.2 Basic Definitions
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8.2.3 Notation 8.2.3 Notation
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8.2.4 Problem Reduction 8.2.4 Problem Reduction
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8.2.5 The Role of the Fundamental Theorem 8.2.5 The Role of the Fundamental Theorem
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8.2.6 Proofs of the Fundamental Theorem 8.2.6 Proofs of the Fundamental Theorem
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8.3 The Direct Method of Fluxions 8.3 The Direct Method of Fluxions
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8.3.1 Problem 1 in De Methodis 8.3.1 Problem 1 in De Methodis
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8.3.2 Fluxions of Polynomial Equations in De Methodis 8.3.2 Fluxions of Polynomial Equations in De Methodis
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8.3.3 Fluxions of Complex Fractions and Surd Quantities in De Methodis 8.3.3 Fluxions of Complex Fractions and Surd Quantities in De Methodis
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8.3.4 Fluxions of Nongeometrical Equations in De Methodis 8.3.4 Fluxions of Nongeometrical Equations in De Methodis
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8.3.5 Demonstration of the Direct Method in De Methodis 8.3.5 Demonstration of the Direct Method in De Methodis
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8.3.6 Determination of Tangents in De Methodis 8.3.6 Determination of Tangents in De Methodis
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Determination of tangents: The method Determination of tangents: The method
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Determination of tangents: An example Determination of tangents: An example
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8.4 The Inverse Method of Fluxions 8.4 The Inverse Method of Fluxions
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8.4.1 Problem 2 8.4.1 Problem 2
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8.4.2 Method 1: Squaring of Curves by Series Expansions 8.4.2 Method 1: Squaring of Curves by Series Expansions
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8.4.3 Method 2: Squaring of Curves by Means of Finite Equations 8.4.3 Method 2: Squaring of Curves by Means of Finite Equations
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8.4.4 Method 3: Squaring of Curves by Comparison with Conic Sections 8.4.4 Method 3: Squaring of Curves by Comparison with Conic Sections
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8.4.5 The Analytical Quadrature of the Cissoid 8.4.5 The Analytical Quadrature of the Cissoid
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8.5 The Inverse Method in De Quadratura 8.5 The Inverse Method in De Quadratura
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8.5.1 Toward De Quadratura 8.5.1 Toward De Quadratura
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8.5.2 Theorems in De Quadratura 8.5.2 Theorems in De Quadratura
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8.5.3 The Style of De Quadratura 8.5.3 The Style of De Quadratura
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8.6 Methodus Differentialis 8.6 Methodus Differentialis
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8.7 A Question of Style 8.7 A Question of Style
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Chapter
8 The Analytical Method of Fluxions
Get access
Pages
168–212
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Published:September 2009
Cite
Guicciardini, Niccolò, 'The Analytical Method of Fluxions', Isaac Newton on Mathematical Certainty and Method (Cambridge, MA , 2009; online edn, MIT Press Scholarship Online, 22 Aug. 2013), https://doi.org/10.7551/mitpress/9780262013178.003.0008, accessed 2 June 2024.
Abstract
This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the techniques of the direct method to be perfected, as presented in his treatise De Methodis. After making his De Methodis treatise, he also sought to develop his inverse method algorithm, while also creating a better conceptual foundation to the direct method. The chapter notes that Newton continued in improving the two methods until he composed the De Quadratura, a work which explains the most advanced refinement of his method of fluxions.
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