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1 |
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|a Bl�asj�o, Viktor.
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|a Transcendental curves in the Leibnizian Calculus /
|c Viktor Bl�asj�o.
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| 260 |
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|a San Diego :
|b Academic Press,
|c 2017.
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| 300 |
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|a 1 online resource (284 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a Studies in the History of Mathematical Inquiry
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|a Print version record.
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|a Front Cover; Transcendental Curves in the Leibnizian Calculus; Copyright; Contents ; Acknowledgments ; Chapter 1 Preliminary matters; 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; 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.
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|a Chapter 3 The classical basis of 17th-century philosophy of mathematics3.1. Introduction; 3.2. Greek geometry; 3.3. 17th-century philosophy of geometry; Chapter 4 Mathematical context; 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; 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.
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|a 5.5. Jacob Bernoulli's tractional method5.6. Johann Bernoulli's crawling curves; Chapter 6 Transcendental curves analytically: exponentials and power series; 6.1. Introduction; 6.2. The problem with power series; 6.3. Exponentials; Chapter 7 Transcendental curves by the reduction of quadratures; 7.1. Introduction; 7.2. Computational reduction of quadratures; 7.3. The rectification of quadratures; Chapter 8 Transcendental curves in physics; 8.1. Introduction; 8.2. The elastica; 8.3. The paracentric isochrone; 8.4. The brachistochrone; 8.5. Forces and tangents.
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|a Chapter 9 A view from the 18th century9.1. 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; Notes; References; Index; Back Cover.
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|a Includes bibliographical references and index.
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| 650 |
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|a Curves, Algebraic.
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| 650 |
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6 |
|a Courbes alg�ebriques.
|0 (CaQQLa)201-0005591
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| 650 |
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7 |
|a MATHEMATICS
|x Geometry
|x General.
|2 bisacsh
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| 650 |
|
7 |
|a Curves, Algebraic
|2 fast
|0 (OCoLC)fst00885451
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| 776 |
0 |
8 |
|i Print version:
|a Blasjo, Viktor.
|t Transcendental Curves in the Leibnizian Calculus.
|d San Diego : Elsevier Science, �2017
|z 9780128132371
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| 830 |
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0 |
|a Studies in the History of Mathematical Inquiry.
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| 856 |
4 |
0 |
|u https://sciencedirect.uam.elogim.com/science/book/9780128132371
|z Texto completo
|
