| Description |
1 online resource (xv, 345 pages) : illustrations (some color) |
| Series |
History of mechanism and machine science, 1875-3426 ; volume 46 |
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History of mechanism and machine science ; v. 46. 1875-3426
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| Contents |
Intro -- Preface -- Contents -- 1 Philosophers, Mathematics and Motion -- 1.1 Motion Does Not Exist -- 1.2 Mathematics and the Idealist Tradition in Greek Philosophy -- 1.3 Mathematics and Motion -- 1.4 Aristotle Refutes Zeno -- 1.5 Zeno's Trick: Motion Is Interpreted as a Super-Task -- 1.6 The Neo-platonist Ontological Hierarchy -- 1.7 The Postulates 1 Through 3 in Neo-platonism: Proclus Solution -- 1.8 Zeuthen's Thesis -- 2 Motion Beyond the Elements -- 2.1 The Euclidean Construction Game -- 2.2 The Incompleteness of the Euclidean Construction Game -- 2.3 Archytas of Tarente |
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2.4 A Solution from Plato's Academy -- 2.5 Menaechmus and Conic Sections -- 2.6 A Remarkable Application and Heron's Solution -- 2.7 The Doubling of the Cube: Eratosthenes' Instrument -- 2.8 The Neusis-Construction and the Conchoids -- 2.9 Diocles' Cissoid -- 3 General Considerations and Kinematical Aspects of Motion -- 3.1 Pappus' Classification -- 3.2 Composition of Different Uniform Motions: The Quadratrix -- 3.3 Time-Dependent Kinematical Aspects of Motion -- 3.4 Composition of Uniform Motions and Paradoxes of Motion in Mechanical Problems |
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3.5 A Remark on Methodology and a Theorem by Archimedes on Uniform Motion -- 3.6 Archimedes: Motion in Geometry -- 4 Kinematical Models in Astronomy -- 4.1 Plato and Astronomy -- 4.2 The Model in Plato's Timaeus -- 4.3 Eudoxus' Models -- 4.4 Apollonius' Epicycle Model -- 4.5 Hipparchus' Theory of the Motion of the Sun (About 150 BCE) -- 4.6 Ptolemy' Contributions -- 4.7 Ptolemy's Contributions Continued -- 4.8 Astronomy in the Islamic World: The Tusi-Couple -- 5 The Birth of Instantaneous Velocity -- 5.1 Introduction -- 5.2 Velocity Distributions in Space and Time |
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5.3 The Average Velocity of a Rotating Radius -- 5.4 The Average Velocity of a Rotating Disc -- 5.5 Bradwardine: Towards Instantaneous Velocity -- 5.6 Dumbleton and the Merton Theorem -- 5.7 Giovanni Casali and Nicole Oresme -- 5.8 Acceleration: Euler and Newton's Second Law -- 6 The Parallelogram of Instantaneous Velocities -- 6.1 Introduction -- 6.2 Gilles Personne de Roberval: The Tangent as the Line of Instantaneous Advance -- 6.3 Isaac Newton on Tangents -- 6.4 D'Alembert on the Parallelogram of Instantaneous Velocities -- 6.5 A Philosophical Aside and Kant on the Parallelogram of Velocities |
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7 Napier, Fermat, Descartes -- 7.1 Introduction -- 7.2 John Napier's Kinematical Definition of the Logarithm and Torricelli's 'Logarithmica' -- 7.3 Pierre de Fermat and Motion in His Introduction to Plane and Solid Loci -- 7.4 René Descartes -- 7.5 Descartes' Ambitions and His New Compasses -- 7.6 Algebra Comes In -- 7.7 Pappus' Problem -- 7.8 An Example: The Turning Ruler and Moving Curve Procedure -- 7.9 Descartes' Solution of Pappus' 5-Line Problem -- 7.10 The Use of Strings -- 7.11 The Final Results -- 8 De Witt, van Schooten, Newton and Huygens -- 8.1 Frans van Schooten Junior |
| Summary |
This book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed October 5, 2023) |
| Subject |
Kinematics -- History
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Kinematics
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| Genre/Form |
History
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| Form |
Electronic book
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| ISBN |
9783031398728 |
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3031398726 |
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