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CHAPTER III.-SEQUEL TO COPERNICUS. THE RECEPTION
AND DEVELOPMENT OF THE COPERNICAN THEORY.
PAGE
Sect. 1. First Reception of the Copernican Theory..
269
Sect. 2. Diffusion of the Copernican Theory...........
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
64
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.
Sect. 1. Prelude to the Science of Statics......
302
303
305
311
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. L-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.......
CHAPTER IV.-DISCOVERY OF THE MECHANICAL PRINCIPLES
OF FLUIDS.
340
Sect. 1. Rediscovery of the Laws of Equilibrium of Fluids..
Sect. 2. Discovery of the Laws of Motion of Fluids....
345
348
CHAPTER V.-GENERALIZATION OF THE PRINCIPLES OF
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
356
PRINCIPLES OF MECHANICS.
PERIOD OF MATHEMAT-
ICAL DEDUCTION.-ANALYTICAL MECHANICS..
362
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..
363
364
365
366
367
371
374
375
376
377
378
380
15. Analytical Generality.-Connection of Statics and Dynamics.
381
BOOK VII.
HISTORY OF PHYSICAL ASTRONOMY.
CHAPTER I.-PRELUDE TO THE INDUCTIVE EPOCH OF NEW-
TON
CHAPTER II.-THE INDUCTIVE EPOCH OF NEWTON.-DIS- COVERY OF THE UNIVERSAL GRAVITATION OF Matter, ACCORDING TO THE LAW OF THE INVERSE SQUARE OF THE DISTANCE....
1. Sun's Force on Different Planets....
2. Force in Different Points of an Orbit.
3. Moon's Gravity to the Earth.....
4. Mutual Attraction of all the Celestial Bodies..
CHAPTER III.-SEQUEL TO THE EPOCH OF NEWton.— RECEPTION OF THE NEWTONIAN THEORY.
Sect. 1. General Remarks....
Sect. 2. Reception of the Newtonian Theory in England..
CHAPTER IV.-SEQUEL TO THE EPOCH OF NEWTON, CONTINUED.
VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY.
Sect. 1. Division of the Subject .....
Sect. 2. Application of the Newtonian Theory to the Moon.....
Sect. 3.
and Earth..
Sect. 4. Application of the Newtonian Theory to Secular Inequalities....
385
399
400
402
406
411
414
416
420
421
429
433
434
Planets, Satellites,
438
444
Sect. 8. Confirmation of the Newtonian Theory by Experiments on At-
traction.
456
Sect. 9. Application of the Newtonian Theory to the Tides..
CHAPTER V.-DISCOVERIES ADDED TO THE NEWTONIAN THEORY.
457
Sect. 1. Tables of Astronomical Refraction......
Sect. 2. Discovery of the Velocity of Light.-Römer..
462
463
20
Sect. 3. Discovery of Aberration.-Bradley
Sect. 4. Discovery of Nutation....
464
465
Sect. 5. Discovery of the Laws of Double Stars.-The Two Herschels.... 467
CHAPTER VI.-THE INSTRUMENTS AND AIDS OF ASTRONOMY
DURING THE NEWTONIAN PERIOD.
470
476
478
479
480
481
BOOK II.-THE PHYSICAL SCIENCES IN ANCIENT GREECE.
Plato's Timæus and Republic..
Hero of Alexandria.
Introduction..
BOOK III.-THE GREEK ASTRONOMY.
497
501
503
BOOK IV.-PHYSICAL SCIENCE IN THE MIDDLE AGES.
Did Francis Bacon reject the Copernican Doctrine?..
Kepler persecuted......
530
532