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CHAPTER III.-EARLIEST STAGES OF HARMONICS...... 105
Sect. 3. Correction of the Civil Year (Julian Calendar).
117
CHAPTER II.-PRELUDE TO THE INDUCTIVE EPOCH OF
CHAPTER III.-INDUCTIVE EPOCH OF HIPPARCHUS.
Sect. 1. Establishment of the Theory of Epicyles and Eccentrics...
PAGE
145
Sect. 2. Estimate of the Value of the Theory of Eccentrics and Epicycles. 151
Sect. 3. Discovery of the Precession of the Equinoxes...
CHAPTER IV.-SEQUEL TO THE INDUCTIVE EPOCH OF
HIPPARCHUS.
155
Sect. 1. Researches which verified the Theory.
Sect. 2. Researches which did not verify the Theory..
157
159
Sect. 3. Methods of Observation of the Greek Astronomers.
161
Sect. 4. Period from Hipparchus to Ptolemy....
Sect. 5. Measures of the Earth...
166
169
Sect. 6. Ptolemy's Discovery of Evection..
170
Sect. 7. Conclusion of the History of Greek Astronomy.
Sect. 8. Arabian Astronomy..
175
176
BOOK IV.
HISTORY OF PHYSICAL SCIENCE IN THE MIDDLE
AGES.
Introduction..
CHAPTER I.-ON THE INDISTINCTNESS OF IDEAS OF THE
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197
199
201
202
204
205
4. Greek Commentators of Plato and Others..
5. Arabian Commentators of Aristotle...
207
208
CHAPTER III.-OF THE MYSTICISM OF THE MIDDLE AGES.. 211
1. Neoplatonic Theosophy..
2. Mystical Arithmetic..
3. Astrology..
4. Alchemy.
5. Magic..
CHAPTER IV.-OF THE DOGMATISM OF THE STATIONARY
CHAPTER V.-PROGRESS OF THE ARTS IN THE MIDDLE AGES
1. Art and Science.
2. Arabian Science
3. Experimental Philosophy of the Arabians.
4. Roger Bacon.....
5. Architecture of the Middle Ages..
6. Treatises on Architecture..
BOOK V.
HISTORY OF FORMAL ASTRONOMY AFTER THE
STATIONARY PERIOD.
212
216
218
224
225
228
230
235
236
238
239
242
243
245
246
248
255
CHAPTER I.-PRELUDE TO THE INDUCTIVE EPOCH OF CO-
CHAPTER II.-INDUCTION OF COPERNICUS. THE HELIOCEN-
TRIC THEORY ASSERTED ON FORMAL GROUNDS....... 262
CHAPTER III.-SEQUEL TO COPERNICUS. THE RECEPTION
AND DEVELOPMENT OF THE COPERNICAN THEORY.
Sect. 1. First Reception of the Copernican Theory.
Sect. 2. Diffusion of the Copernican Theory..
269
272
Sect. 3. The Heliocentric Theory confirmed by Facts. Galileo's Astro-
nomical Discoveries..
276
Sect. 4. The Copernican System opposed on Theological Grounds......
Sect. 5. The Heliocentric Theory confirmed on Physical Considerations.
(Prelude to Kepler's Astronomical Discoveries.)..................
280
287
CHAPTER IV.-INDUCTIVE EPOCH OF KEpler.
Sect. 1. Intellectual Character of Kepler.....
290
Sect. 2. Kepler's Discovery of his Third Law.....
293
Sect. 3. Kepler's Discovery of his First and Second Laws. Elliptical
Theory of the Planets..
296
CHAPTER V.-SEQUEL TO THE EPOCH OF KEPLER. RECEPTION,
VERIFICATION, AND EXTENSION OF THE ELLIPTICAL THEORY.
Sect. 1. Application of the Elliptical Theory to the Planets.
66
Sect. 2.
Sect. 3. Causes of the further Progress of Astronomy..
THE MECHANICAL SCIENCES.
BOOK VI.
HISTORY OF MECHANICS, INCLUDING FLUID
Introduction.....
MECHANICS.
CHAPTER I.-PRELUDE TO THE EPOCH OF GALILEO.
302
303
305
311
Sect. 1. Prelude to the Science of Statics.....
312
Sect. 2. Revival of the Scientific Idea of Pressure.-Stevinus.-Equilib-
rium of Oblique Forces.....
316
Sect. 3. Prelude to the Science of Dynamics.-Attempts at the First Law
of Motion.....
319
VOL. I.-2
CHAPTER II.-INDUCTIVE EPOCH OF GALILEO.-DISCOVERY
OF THE LAWS OF MOTION IN SIMPLE CASES.
Sect. 1. Establishment of the First Law of Motion.....
Sect. 2. Formation and Application of the Motion of Accelerating Force.
Laws of Falling Bodies....
Sect. 3. Establishment of the Second Law of Motion.-Curvilinear Mo-
tions.....
Sect. 4. Generalization of the Laws of Equilibrium.-Principle of Virtual
Velocities....
322
324
330
331
Sect. 5. Attempts at the Third Law of Motion.-Notion of Momentum... 334
CHAPTER III.-SEQUEL TO THE EPOCH OF GALILEO.—PE-
RIOD OF VERIFICATION AND DEDUCTION. .... 340
CHAPTER IV.-DISCOVERY OF THE MECHANICAL PRINCIPLES
OF FLUIDS.
Sect. 1. Rediscovery of the Laws of Equilibrium of Fluids..
Sect. 2. Discovery of the Laws of Motion of Fluids. . . . . . .
CHAPTER V.-GENERALIZATION OF THE PRINCIPLES OF
345
348
Sect. 1. Generalization of the Second Law of Motion.-Central Forces... 352
Sect. 2. Generalization of the Third Law of Motion.-Centre of Oscilla-
tion.-Huyghens..
CHAPTER VI.-SEQUEL TO THE GENERALIZATION OF THE
PRINCIPLES OF MECHANICS.
PERIOD OF MATHEMAT-
ICAL DEDUCTION.-ANALYTICAL MECHANICS....
1. Geometrical Mechanics.-Newton, &c. ...
2. Analytical Mechanics.-Euler..
3. Mechanical Problems...
4. D'Alembert's Principle..
5. Motion in Resisting Media.-Ballistics..
6. Constellation of Mathematicians...
7. The Problem of Three Bodies..
8. Mécanique Céleste, &c......
9. Precession.-Motion of Rigid Bodies..
10. Vibrating Strings...
11. Equilibrium of Fluids.-Figure of the Earth.-Tides.
12. Capillary Action....
13. Motion of Fluids...
14. Various General Mechanical Principles..
15. Analytical Generality.-Connection of Statics and Dynamics..
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