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1 The Predecessors: Descartes, Newton and Leibniz 1
1.1 The Reception of the Legacy of Descartes, Newton and Leibniz 9
1.1.1 Newton Versus Leibniz: Voltaire 12
1.1.2 Newton and Leibniz: Chatelet 14
1.1.3 Descartes, newton and Leibniz: Euler and Chatelet 16
1.2 The Common Basis: Descartes on Motion of Bodies 17
1.3 The Common Basis: The Ancient Prototype in Geometry and Mechanics 21
1.3.1 Euclid, Archimedes, Heron 35
1.3.2 Galileo: A New Science Dealing with an Ancient Subject 28
1.4 The New Prototype: Arithmetization of Mathematics and Mechanics 31
2 Newton and Leibniz on Time, Space and Forces 33
2.1 Newton's Program for Mechanics 40
2.2 Newton and Leibniz on Time, Space, Place and Motion 45
2.2.1 Newton and Leibniz on Time and Space 46
2.2.2 Order and Quantification 50
2.2.3 The Very Beginning of Motion 51
2.2.4 Polygon and Circle: Periodic Motion 53
2.3 Leibniz's Program for Mechanics 55
2.3.1 Early Version 56
2.3.2 Later Version: Living Forces 59
3 Newton and Leibniz on the Foundation of the Calculus 65
3.1 Newton's Concept of Fluents and Fluxions 70
3.1.1 The Arithmetic and Geometric Representation of Quantities 72
3.1.2 One Universal Infinitesimal Quantity 75
3.2 Newton's Algorithm: Method of Fluxions 77
3.3 Leibniz's Foundation of the Calculus 81
3.3.1 Nova Methodus 85
3.3.2 Leibniz's Comments on the Calculus 89
3.4 The Calculus: Development, Criticism and Controversies 92
3.5 Berkeley 98
4 Euler's Program for Mechanics 101
4.1 Euler's Program for Mechanics 110
4.1.1 Geometry and Motion 113
4.1.2 Euler's Program for Mechanics: Mechanica and the Arithmetization ofMechanics 117
4.1.3 Rest and Motion: Internal Principles 123
4.1.4 From Geometrical to Analytical Representation of Mechanics 129
4.1.5 The Relations Between Straight and Curved Lines and Paths 134
4.1.6 The Analytical Representation of Motion 141
4.1.7 External Principles: Forces 145
4.1.8 External Principles: The Increment of Velocity is Independent of Velocity 150
4.1.9 The Proposals of Daniel Bernoulli 153
4.1.10 The Operational Definition of Mass 159
4.2 Extension, Mobility, Steadfastness and Impenetrability 161
4.2.1 Extension and Mobility 162
4.2.2 Uniform Motion: The Division of Time Intervals 166
4.2.3 Inertia or Steadfastness 167
4.2.4 Impenetrability, Inertia and Forces 172
4.2.5 Summary: Euler's Axiomatics 175
4.3 Euler and His Contemporaries 176
4.4 Euler's World Models 187
5 The Foundation of the Calculus 195
5.1 The Arithmetization of the Calculus 198
5.2 Euler's Foundation of the Calculus 202
5.2.1 Calculus Differentialis: Finite and Infinitesimal Increments 207
5.2.2 Infinitesimal, Finite and Infinite Quantities 216
5.2.3 Topological Interpretation 220
5.3 Algorithms 222
5.4 Reconsideration of the Calculus: Robinson 230
6 Euler's Early Relativistic Theory 235
6.1 Euler on Absolute and Relative Motion 241
6.2 Basic Models 243
6.2.1 The Model of Ship and Shore: The Observer in a Cabin on the Ship 245
6.2.2 More than One Observer: The Stadium 246
6.2.3 Euler's Analytical Model of Relative Motion 246
6.2.4 Motion as an Illusion. "Spitzfindigkeiten" 247
6.3 Euler's Relational Theory of Motion 252
6.3.1 The Analysis of Basic Concepts 252
6.3.2 The Introduction of Observers, Zuschauer 255
6.3.3 The Priority of Relative Motion 256
6.3.4 The Invariance of the Equation of Motion 257
6.4 Mach, Einstein and Minkowski 260
6.4.1 Postulated Simultaneity: Newton 261
6.4.2 Experimentally Confirmed Simultaneity: Einstein 263
6.4.3 Minkowski's World of Events 266
7 Euler's Wirksamkeit, Helmholtz's Treatment of Energy Law and Beyond 269
7.1 Helmholtz' Treatment of Newton's Laws 270
7.2 The Interpretation of the Calculus: Kinematics and Dynamics 272
7.3 Helmholtz' Treatment of Leibniz's "Living Forces" 275
7.4 The Extension of a System 277
7.5 Euler's Wirksamkeit 281
8 Euler's Mechanics and Schrodinger's Quantum Mechanics 285
8.1 The Historical Background of the Development of Quantum Mechanics 287
8.2 Planck on Newton and Leibniz 289
8.3 Discrete and Continuous Quantities 290
8.3.1 Discrete and Continuous Variables in the Calculus of Differences 290
8.3.2 Discrete Series of Energies 292
8.4 Schrodinger's Approach: Configurations and States 298
8.4.1 Euler's Mechanics Reconsidered 299
8.4.2 Energy and Configurations 300
8.4.3 Quantization as Selection Problem 304
Summary 311
References 313
Index 325
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| $99.99 | Digital |
| WonderClub |
Gymmy Boy
reviewed Euler as Physicist on March 08, 2013
Euler as Physicist
After reading three of Kragh's books (Cosmology and Controversy [1996], Conceptions of Cosmos [2006] and Higher Speculations [2011]) I decided to read one more - and I am glad I did. Whereas in the earlier mentioned books Kragh delves deeply into science and writes books of 300-400+ pages on just a few topics, Quantum Generations is a much more accessible book. In essence, it's a book about the developments in physical science in the 20th century.
Written in 1997-1999, the book is a little outdated on some topics (such as cosmology), but it gives the reader a comprehensive - and comprehensible! - overview of physics. Each chapter is about 15 pages long and deals with a specific topic, which is a welcome change (in most of his other books, Kragh writes very long and dense chapters of 40+ pages long). Kragh gives detailed explanations about the scientific theories themselves, but also discusses topics such as the militarization of physics after World War II, socio-cultural attitudes towards science, the scientific method as such (and philosophy of science).
The only downside of this book is that some chapters are extremely accessible, and some other chapters - especially towards the end of the book; dealing with high energy physics and grand unification theories - require much more prior knowledge about the respective topics. Kragh could have offered a little bit more background information on topics such as the discovery of new fundamental particles, the development of the weak electromagnetic theory and the gauge field theories of strong interactions. Nevertheless, this was a delightful book to read and helps tremendously to put more basic knowledge of physics in a bigger perspective.
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