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Tables of Contents for Exploring the Limits of Preclassical Mechanics
Chapter/Section Title
Page #
Page Count
Introduction
1
8
Concept and Inference: Descartes and Beeckman on the Fall of Bodies
9
62
Introduction
9
3
The Medieval Tradition
12
12
Proportions
12
3
The ``Moments'' of Motion and the Quantification of Motion by Proportions
15
2
The Configuration of Qualities and Motions
17
5
``Impetus'' as the Cause of Motion and of Acceleration
22
2
Descartes' Proof of the Law of Fall
24
14
Descartes' Initial Document (1618)
25
4
Beeckman's Note in his Journal (1618)
29
3
Descartes' Diary Note (1618)
32
1
Descartes' Letters to Mersenne (1629-1631)
33
3
Later References to the Original Proof
36
2
The Law of Fall Derived within the Context of the Theory of Gravity
38
8
Beeckman's Commentary on Descartes' Initial Document
38
2
Descartes' Alternative ``Law of Free Fall'' in his Initial Document
40
3
Descartes' Revised ``Law of Fall''
43
3
The Conceptual and Deductive Structure of Descartes' Proof of the Law of Fall
46
25
Conceptualization as a Condition for the Proof
47
1
Conceptualization of Free Fall in Classical Mechanics
47
1
Conceptualization of Free Fall in Descartes' Proof
47
2
Geometrical Representation of Free Fall
49
1
Meaning of the Figure in Classical Mechanics
50
1
Meaning of the Figure in Descartes' Proof
50
1
Deductive Structure of the Proof
51
1
The Structure of the Proof in Classical Mechanics
51
2
The Structure of Descartes' Proof
53
4
The Internal Contradiction in Descartes' Argument
57
1
Functional Interpretation of the Geometrical Representation
58
2
Descartes' Erroneous Abstraction of a General Rule
60
2
Generalization of Descartes' Deductive Argument
62
2
The Source of the Contradiction
64
2
The Beeckman-Descartes Dialogue Revisited
66
5
Conservation and Contrariety: The Logical Foundations of Cartesian Physics
71
64
Introduction
71
1
Principles of Conservation and Conservation Laws
72
9
The Foundational Function of Conservation Laws
72
5
Descartes' Conservation Laws
77
4
The Logic of Contraries and its Application in Physics
81
13
Contrariety and Contradiction
82
3
The Logic of Contraries
85
3
Aristotle's Physics of Contraries
88
2
Contraries in 17th Century Logic and Physics
90
2
Descartes' Physics of Contraries
92
2
Descartes' Derivation of the Rules of Impact
94
14
The Means of Representation
94
2
Contrary Predicates and Opposing Modes
96
4
The Rules of Impact
100
2
The Opposition between Determinations
102
2
Double Opposition: Determination vs Determination and Motion vs Rest
104
1
Double Opposition: Determination vs Determination and Swiftness vs Slowness
105
1
Analysis of Difficulties
105
3
Determination
108
22
The Argument of the Dioptrics
112
1
Reflection
113
4
Refraction
117
3
Criticisms of the Dioptrics
120
1
Pierre Fermat
121
3
Thomas Hobbes
124
3
Oblique Impact
127
3
Conclusion
130
5
Proofs and Paradoxes: Free Fall and Projectile Motion in Galileo's Physics
135
144
Introduction
135
6
Free Fall and Projectile Motion in De Motu
141
17
The Laws of the Motion of Fall
141
6
Acceleration as an Accidental Characteristic of Fall
147
5
The Trajectory of Projectile Motion
152
4
Summary
156
2
Free Fall and Projectile Motion in Galileo's Manuscripts between ca. 1592 and ca. 1604
158
22
The Discovery of the Form of the Trajectory and of the Characteristics of Acceleration in Free Fall
159
6
Attempts at a Deductive Treatment of Acceleration around 1604
165
1
Derivation of the Law of Fall from a Principle of Acceleration
165
10
Derivation of the Double Distance Rule
175
4
Summary
179
1
Free Fall in Galileo's Manuscripts after ca. 1604
180
28
The Discovery of the Proportionality between the Degree of Velocity and Time
180
2
Double Distance Rule
182
6
A Reexamination of the Law of Fall
188
9
Other Approaches to the Derivation of the Law of Fall and Further Paradoxes
197
1
The Proportion Proof
198
2
The Mirandum Paradox
200
2
The Hollow Paradox as an Argument for Galileo's Principle
202
3
The Inclined Plane Proof
205
2
Summary
207
1
Projectile Motion in Galileo's Manuscripts after ca. 1604
208
28
The Size of the Trajectory for Horizontal Projection
209
7
Contradictions in the Analysis of Oblique Projection
216
1
Oblique Projection and Inclined Plane: Folio 175v
216
4
Oblique Projection and Uniform Horizontal Motion: Folio 171v
220
3
The Search for a Composition Rule for Impetuses
223
1
Scalar Addition of Impetuses: Folio 90r
224
3
Vertical Height and Compounded Impetus: Folio 80v
227
2
Vectorial Composition of Scalar Impetus: Folio 91 v
229
3
Compounded Impetus and Distance Traversed
232
3
Summary
235
1
The Laws of Free Fall and Projectile Motion in Galileo's Published Works
236
17
A Failed Revision of the Derivation of the Law of Fall
237
1
A New Proof Technique
238
4
Derivation of the Law of Fall
242
2
Refutation of Space Proportionality by the New Proof Technique
244
3
The Problematical Role of the Area in the New Proof Technique
247
4
Oblique Projection as a Gap in the Discorsi
251
2
Summary
253
1
Preclassical Limits to Galileo's Mechanics
253
21
The Aristotelian Concept of Velocity and the Configuration of Qualities in Galileo's Published Works
254
1
Traditional Foundations of Galileo's Derivation of the Law of Fall
254
2
The Unsolved Mirandum Paradox
256
2
The Rules of Kinematics in the Discorsi
258
3
Impetus as Cause of Motion in Galileo's Published Works
261
1
Horizontal Projection and Horizontal Plane
261
2
The Paradoxes of Oblique Projection in the Discorsi
263
3
The Role of Causes and Contrariety in Galileo's Understanding of Projectile Motion
266
3
The De Motu Theory of Motion in Media in the Discorsi
269
1
Did Galileo Renounce Causal Explanation of Acceleration in the Discorsi?
270
3
Summary
273
1
Descartes' Critique Revisited
274
5
Epilogue
279
8
First Example: Conceptualization of Free Fall
280
1
Second Example: Composition of Motions
281
3
Third Example: Conceptualization of Projectile Motion
284
3
Documents
287
96
A Note on Sources, Translations, and Figures
287
1
Documents to Chapter 1. Concept and Inference
288
15
Descartes' Initial Document (1618)
288
2
Beeckman's Note in his Journal (1618)
290
3
Descartes' Diary Note (1618)
293
1
Descartes' Reasoning on the Compression of Water in Containers (Nov./Dec. 1618)
294
1
Descartes: From a Letter to Mersenne (Nov. 13, 1629)
294
2
Descartes: From a Letter to Mersenne (Dec. 18, 1629)
296
1
Descartes: From a Letter to Mersenne (Oct./Nov. 1631)
297
1
Descartes: From a Letter to Mersenne (Aug. 14, 1634)
298
1
Descartes: Note on Acceleration in a Vacuum (from the Excerpta Anatomica, 1635 or later)
299
1
Descartes: From a Letter to de Beaune (April 30, 1639)
300
1
Descartes: From a Letter to Mersenne (March 11, 1640)
300
1
Descartes: From a Letter to Mersenne (June 11, 1640)
301
1
Kenelm Digby: On Acceleration in Natural Motion (1644)
301
2
Documents to Chapter 2: Conservation and Contrariety
303
47
Leibniz on Measurement by Congruence and Equipollence: From a Letter to de I'Hospital (Jan. 15, 1696)
303
2
Descartes: Principles of Philosophy, Bk. II §§36-53
305
7
Descartes: From a Letter to Clerselier (Feb. 17, 1645)
312
2
Descartes: From Chapter 2 of the Dioptrics (1637)
314
6
Fermat: From a Letter to Mersenne (April or May, 1637)
320
1
Descartes: From a Letter to Mersenne for Fermat, (Oct. 5, 1637)
321
1
Fermat: From a Letter to Mersenne for Descartes (Nov. 1637)
322
6
Descartes: From a Letter to Mydorge (March 1, 1638)
328
2
Hobbes: From the Optical Manuscript of 1640 (Tractatus opticus II)
330
3
From Mersenne's Ballistica
333
1
Descartes: From a Letter to Mersenne for Hobbes (Jan. 21, 1641)
334
1
Hobbes: From a Letter to Mersenne for Descartes (Feb. 7, 1641)
335
3
Descartes: From a Letter to Mersenne for Hobbes (March 4, 1641)
338
2
Hobbes: From a Letter to Mersenne for Descartes (March 30, 1641)
340
4
Descartes: From a Letter to Mersenne for Hobbes (April 21, 1641)
344
1
Descartes: From a Letter to Mersenne for Bourdin (July 29, 1640)
345
1
Descartes: From a Letter to Mersenne (Aug. 30, 1640)
346
1
Descartes: From a Letter to Mersenne (Dec. 3, 1640)
347
1
Descartes: From a Letter to Mersenne (April 26, 1643)
347
3
Documents to Chapter 3. Proofs and Paradoxes
350
27
Descartes' Critique of Galileo (from a Letter to Mersenne Oct. 11, 1638)
350
1
Galileo: From Folio 151r
351
1
Guidobaldo and Galileo's Experiment
352
2
Paolo Sarpi: From the Notebook for 1592
354
1
Galileo: From a Letter to Sarpi (Oct. 16, 1604)
354
2
Galileo: From Folio 147r
356
2
Galileo: from Folio 182 (182bv and 182ar)
358
2
Galileo: Folio 128
360
1
Galileo: From Folio 163v
361
1
Galileo: Folio 85v
362
1
Galileo: From Folio 179v
362
1
Galileo's Mirandum Fragment: From Folio 164v
363
1
Galileo: From a Letter to de' Medici (Feb. 11, 1609)
363
1
Galileo: Folio 152r
364
2
Galileo: Folio 91v
366
1
Galileo: Folio 87v
367
1
Galileo: Folio 90r
368
3
Galileo: Folio 80r
371
1
Galileo: Discorsi, Third Day: Naturally Accelerated Motion (1638)
372
3
Galileo: Discorsi, Third Day: Naturally Accelerated Motion (1638)
375
1
Galileo: Addendum on Projectile Motion for a Revised Edition of the Discorsi
376
1
Documents for the Epilogue
377
6
Descartes: From a Letter to Huygens (Feb. 18, 1643)
377
1
Clerselier: From a Letter to Fermat (May 13, 1662)
378
1
Pierre Silvain Regis, Law of Reflection (1691)
379
1
Cavalieri: From Lo Speccio Ustorio (1632)
380
3
Bibliography
383
22
Index
405
5
Index locorum
410