356 LAOBAHGE'S PROOF or VIKI 



.viT.-rly, if the equation 



P*+Q0 + fiv+ ...=0 



: every possible indefinitely small di :it of 



the system, it will remain in equilibrium. For, ti 

 imved during these displacements, t 



which act on the system remain in the same condition, an<l 

 . reftflOH why they should produce one, rather than 

 her, of the two displacements, for which a, /9, 7, ... have 

 diti'erent siunis. This is the case of a balance which remains 

 in equilibrium, because there is no reason why it should in- 

 cline to one side rather than the other. 



The principle of virtual velocities beiii thn.s proved f>r 

 commensurable forces, will also hold when the l'rces are in- 

 commensurable; for we know that any proposition which can 

 be proved for commensurable quantities maybe extended by a 

 reductio ad absurdum to incommensurable quantities. 



