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CHAPTER VI. 



SEQUEL OF THE GENERALIZATION OF THE PRINCIPLES 

 OF MECHANICS. PERIOD OF MATHEMATICAL DE- 

 DUCTION. ANALYTICAL MECHANICS. 



WE have now finished the history of the dis- 

 covery of Mechanical Principles, strictly so 

 called. The three Laws of Motion, generalized in 

 the manner we have described, contain the mate- 

 rials of the whole structure of Mechanics ; and in 

 the remaining progress of the science, we are led to 

 no new truth which was not implicitly involved in 

 those previously known. It may be thought, there- 

 fore, that the narrative of this progress is of com- 

 paratively small interest. Nor do we maintain that 

 the application and developement of principles is a 

 matter of so much importance to the philosophy of 

 science, as the advance towards and to them. Still, 

 there are many circumstances in the latter stages of 

 the progress of the science of Mechanics, which well 

 deserve notice ; and make a rapid survey of that 

 part of its history indispensable to our purpose. 



The Laws of Motion are expressed in terms of 

 space and number ; the developement of the conse- 

 quences of these laws must, therefore, be performed 

 by means of the reasonings of mathematics; and 

 the science of Mechanics may assume the various 



