48 DISSERTATION SECOND. [partis. 



already seen, by the mathematical discoveries of two of 

 the greatest men who have ever enlightened the world. A 

 slight sketch of the improvements which the theory of 

 mechanics owes to Newton has been just given ; those 

 which it owes to Leibnitz, though not equally important, 

 nor equally numerous, are far too conspicuous to be pas- 

 sed over in silence. So far as concerns general princi- 

 ples they are reduced to three, — the argument of the suffi- 

 cient reason, — the law of continuity, — and the measurement 

 of the force of moving bodies by the square of their veloci- 

 ties \ which last, being a proposition that is true or false ac- 

 cording to the light in which it is viewed, I have supposed it 

 placed in that which is most favourable. 



With regard to the first of these, — the principle of the 

 sufficient reason, — according to which, nothing exists in any 

 state without a reason determining it to be in that state 

 rather than in any other, — though it be true that this pro- 

 position was first distinctly and generally announced by the 

 philosopher just named, yet is it certain that, long before his 

 time, it had been employed by others in laying the founda- 

 tions of science. Archimedes and Galileo had both made 

 use of it, and perhaps there never was any attempt to place 

 the elementary truths of science on a solid foundation in 

 which this principle had not been employed. We have an 

 example of its application in the proof usually given, that a 

 body in motion cannot change the direction of its motion, 

 abstraction being made from all other bodies, and from all 

 external action ; for it is evident, that no reason exists to 

 determine the change of motion to be in one direction more 

 than another, and we therefore conclude that no such change 

 can possibly take place. Many other instances might be 

 produced where the same principle appears as an axiom of 

 the clearest and most undeniable evidence. Wherever, in- 

 deed, we can pronounce it with certainty that the conditions 



