18 CONTENTS. 



CHAPTER II. INDUCTIVE EPOCH OF GALILEO. DISCOVERY 



OF THE LAWS OF MOTION IN SlMPLE CASES. 



PACK 



Sect. I . Establishment of the First Law of Motion 822 



Sect. 2. Formation and Application of the Motion of Accelerating Force. 



Laws of Falling Bodies 324 



Sect. 3. Establishment of the Second Law of Motion. Curvilinear Mo- 

 tions 330 



Sect. 4. Generalization of the Laws of Equilibrium. Principle of Virtual 



Velocities 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. Eediscovery of the Laws of Equilibrium of Fluids 345 



Sect. 2. Discovery of the Laws of Motion of Fluids 348 



CHAPTER V. GENERALIZATION OF THE PRINCIPLES OF 



MECHANICS. 



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 350 



CHAPTER VI. SEQUEL TO THE GENERALIZATION OF THE 

 PRINCIPLES OF MECHANICS. PERIOD OF MATHEMAT- 

 ICAL DEDUCTION. ANALYTICAL MECHANICS 362 



1. Geometrical Mechanics. Newton, &c 363 



2. Analytical Mechanics. Euler 3G3 



3. Mechanical Problems 364 



4. D' Alembert's Principle 365 



5. Motion in Resisting Media. Ballistics 365 



6. Constellation of Mathematicians 366 



7. The Problem of Three Bodies 367 



8. Mecanique Celeste, &c 371 



9. Precession. Motion of Rigid Bodies 374 



10. Vibrating Strings 375 



11. Equilibrium of Fluids. Figure of the Earth. Tides 376 



12. Capillary Action 377 



13. Motion of Fluids 378 



14. Various General Mechanical Principles 380 



15. Analytical Generality. Connection of Statics and Dynamics 381 



