Table of contents for Mechanics from Aristotle to Einstein / Michael J. Crowe.


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1 Mechanics before Galileo                                   1
Introduction: What Is Mechanics? . .................      1
Some Key Questions Dealt with in Mechanics . .......  2
Part I: Mechanics in Antiquity ................... .      3
Aristotle  .......  ..    ...   .. .   .. . .......   3
Aristotle on Place, Motion, and Void  . ............ .  7
Mechanics in Later Antiquity  . .................    11
Part II: Medieval Mechanics  ................... ..      12
The Mertonians, Oresme, and the Mean Speed Theorem  . . 12
Summary .........        ........ .........          19
Part III: Two Major Problems in Early Modern Mechanics .... .  20
The Problem of the Possibility of the Earth's Motion .... .  21
The Problem of the Relativity of Motion . ........... 22
2 Galileo and Terrestrial Mechanics                         29
Chronology of Galileo's Life  ................... ..     29
Introduction ........      ..   ................         31
Does a Falling Body's Weight Influence Its Rate of Fall?  . ....  31
Galileo on Weight and Rate of Fall . ................ 32
Commentary  ...................            .......   36
Galileo on the Motion of Pendula  . .................    37
Commentary  ...................            .......   41
Galileo on Accelerated Motion and Free Fall . ........... 44
Third Day: On Local Motion . ................. 44
Commentary ....... .       ................          45
Third Day: On Naturally Accelerated Motion . ........ 46
Commentary  ...................            .......   62
Galileo, the Law of Inertia, and Projectile Motion . ......... 65
Galileo on Inertial Motion  ................... ...        68
Commentary ................... .......                75
Galileo's Mathematical Treatment of Projectile Motion ....... 76
Galileo on Projectile Motion  ................... ..       76
Fourth Day: On the Motion of Projectiles . .......... 76
Commentary ........       ..........       .......    77
Projectile Motion in General ................... .. 78
Galileo on the Maximum Range of a Projectile . .......... 81
Commentary .................              ........ 82
Conclusion ................... ........... 82
3 From Galileo to Newton                                     85
Introduction ...................            ........ . 85
William  Gilbert (1544-1603) ................... ..        85
Johannes Kepler (1571-1630) . .................. 86
Rene Descartes (1596-1650) ................... . 89
Descartes, Principles of Philosophy, pp. 54-66 ........ 92
Christiaan Huygens (1629-1695) . ................. 100
Huygens and the Law of Centripetal Acceleration ....... 101
Huygens and the Theory of Collisions . ............ 102
Selection from Huygens, On Colliding Bodies ......... 103
Commentary  ...................             .......  105
Huygens: Conclusion ...........         . .  .. ... 107
4 Newton and Mechanics                                      111
Chronology of the Life of Sir Isaac Newton . ............ 111
Introduction ................... .......... 117
Background: The Period before Newton . ............. 118
The Prehistory of Newton's Principia . ............... 120
Newton during the 1660s . ........ . ......... 120
Application of the Law of Centripetal Acceleration to the Moon 123
The Relationships among the Inverse Square Law, Kepler's
Third Law, and the Law of Centripetal Acceleration : . 125
Summary .............           ....     .......     126
Newton from 1670 to 1680, Especially His Correspondence
with  Robert Hooke  ...................        126
Newton, Flamsteed, and the Comet of 1680-1681 ...... 128
Newton from 1684 to 1687 . .................. 129
Newton's Principia ................... ....          130
Isaac Newton, Principia . .................. ... 133
Newton's Preface to the Reader ................... 133
Definition 1 ........     ...... ...........           135
Commentary on Definition 1 . ................. 135
Definition 2 ........      ..... ............          136
Commentary on Definition 2 . ................. 137
Definition 3 ........      ..... ...........           138
Commentary on Definition 3 . ................. 138
Definition 4 .................. ...........            140
Commentary on Definition 4 . ................. 140
Definitions 5-8 ..................        .........    140
Commentary on Definitions 5-8 . ............... 143
Introductory Comment on Newton's Scholium ......... 144
Newton's Scholium to the Definitions . ............... 144
Commentary on Newton's Scholium . ............. 151
Laws of Motion: Law 1 ................... ..... 152
Commentary on Law 1: The Law of Inertia . ......... 152
Laws of Motion: Law 2 . .................. .... 153
Commentary on Law 2: The Force Law . ........... 153
Note on Gravitational versus Inertial Mass . ......... 155
Laws of Motion: Law 3 ........   ...............       156
Commentary on Law 3: Action Equals Reaction ....... 157
Corollaries to the Laws of Motion . ................. 157
Commentary on Newton's Corollaries . ............ 158
Principia, Book I: On the Motion of Bodies . ............ 159
Section 1: The Method of First and Ultimate Ratios . ....... 159
Commentary on Newton's Lemmas . ............. 161
Section 2: The Finding of Centripetal Forces  . ...........  163
Book I Proposition 1 ................... ...... 163
Commentary on Proposition 1 . ................ 164
Corollaries to Proposition 1.1  ................... .  165
Commentary on the Remaining Sections of Book I ......... 166
Principia, Book III: On the System of the World ......... . . 171
Newton's Preface to Book III . .................. . 171
Rules of Philosophizing ................... .... 172
Commentary on Newton's "Rules of Philosophizing" ..... 174
Phenomenon 1 ............          .        .  .   ........ ..176
Commentary on Phenomenon 1 . ............... 177
Phenomena 2-4 ........... . . . .          ........ ..178
Commentary on Phenomenon 4 ................ 180
Phenomena 5-6  ...................          . .. . . .  .  180
Book III Propositions 1-4  ................... ...     181
Commentary on Proposition 4 . ................ 184
Book III Propositions 5-8  ................... ...     184
Commentary on Book III from Phenomenon 1 to Proposition 8 191
Book III Proposition 8 Corollaries .................. 194
Commentary on Newton's Corollaries to Proposition 8 . . . . 196
Book III Propositions 9-13  ................... ..       199
Commentary on Book Ill: Propositions 9-42 . ........ 203
General Scholium  . ..................          .......  204
Commentary on Newton's General Scholium . ........ 208
The Hypothetico-Deductive Method . ................ 209
Introduction. ...................          ....... 209
Preliminary Logical Discussion . ............... 209
Can Either Deduction or Induction Be Claimed as
the Sole Scientific Method?  . .............  210
The Hypothetico-Deductive Method . ............. 210
Huygens and the HD Method . ................ 211
Advantages and Problems of the HD Method . ........ 212
Conclusion  ...........      ....   .. .....  ..    212
Newton and the Hypothetico-Deductive Method . ......... 213
What Is the Methodological Structure of Newton's Principia? . 213
Newton's View of the HD Method . .............. 214
The Methodology of Newton's Principia . ........... 215
Newton's Correspondence with Bentley . .............. 220
Introduction ..........     .....  ..........       220
Letterl  . ..................        ..........     222
Letter II    ................... ..........         225
Letter III    ................... .........         228
Letter IV  ........    ......... .........          229
The Leibniz-Clarke Correspondence . ............... 232
Introduction. ...................          ....... 232
Mr. Leibniz's First Paper  ................... .    233
Dr. Clarke's First Reply  ................... .     234
Mr. Leibniz's Second Paper . ................. 235
Dr. Clarke's Second Reply . .................. 237
Mr. Leibniz's Third Paper . .................. 238
Dr. Clarke's Third Reply  ................... .     239
Newton, Voltaire, and Cartesianism . ................ 240
Some Quotations Concerning Newton . .............. 241
5 Between Newton and Einstein                              245
Introduction  .........   ...  .. .  ....    .... ....  245
Part I: The Eighteenth and Nineteenth Centuries .......... 247
Mechanics in the Seventeenth Century . ........... 247
Mechanics from Newton to Einstein . ............. 248
Heat Theory and the Concept of Energy . .......... 251
Electricity and Magnetism . .................. 253
Light: Particle or Pulse?  ................... .   253
Field Theory  . ..................         .......  254
Part II: The Michelson-Morley Experiment . ............ 255
Mathematical Background . .................. 255
The Michelson-Morley Experiment . ............. 263
The Lorentz-FitzGerald Contraction . ............. 266
6 Einstein and Relativity Theory                          269
Introduction ................ ............              269
Chronology of the Life of Albert Einstein . ............. 270
The Special Theory of Relativity . ................. 274
Introduction  ........   ...   ...   .  : ......   274
Tensions between Newtonian Mechanics and
Maxwellian Electromagnetic Theory .......... 275
Einstein on "Inner Perfection" and "External Confirmation" . . 278
Einstein's Two Postulates and a Derivation of the Special
Theory of Relativity. . .................. 279
Time Dilation  ...................         .......  283
Summary ................... .......... 284
The Twin Paradox ................... .... 285
Four Dimensions ...................           ..... 285
Derivation of the Equation E = mc2 . ............ 286
The General Theory of Relativity . ................. 287
The Three Classic Tests of the General Theory of Relativity . 290
Conclusion  ................... ........           292
Comment on Mach, Planck, and Einstein . ............. 292
Concluding Comment ................... ..... 297
Appendix: Galileo Laboratory                              299
Experiment 1  ................... .........             300
Experiment 2  ................... ......... 301
Experiment 3  ................... ......... 301
Experiment 4  ................... ......... 302
Selected Bibliography                                     305
In General      ...................  ..........       . 305
Galileo ................. .............                 306
Descartes  ................... . ..........             308
Newton ...... .                ..    ...........      . 308
General works ......     ...         .     .  ...   ........ 308



Library of Congress subject headings for this publication: Mechanics, Mechanics Sources, Science History, Physics Histsory