MECHANICS. 63 



of the system is in a horizontal plane at the dis- 

 tance x from the given horizontal plane. 



Take a,., = , and the 



centre of gravity is in a plane parallel to the first of 

 the two vertical planes, and distant from it by the 

 line x'. 



Lastly, take in the intersection of these planes, a point 

 distant from the second vertical plane by a quanti- 



ty of' = Ad"+Bft" + Cc" + 

 A+B+C+D 



This point will be the centre of gravity of the given 

 bodies, as is evident from 110. 



&. The problem in this article may also be resolved 

 by means of this geometrical proposition: If from 

 the centres of gravity of any number of bodies gi- 

 ven in position, lines be drawn to their common 

 centre of gravity, the sum of the products, formed 

 by multiplying each of these lines into the weight 

 of the body from which it is drawn, is a minimum, 

 or is less than if the lines were drawn to any other 

 point. 



This may easily be deduced from the 3d Cor. to the 

 5th Prop, of the 2d Book of the Loci Plani, APOL- 

 LONIUS. See SIMSON'S edition, p. 180. 



115. To find the centre of gravity of a triangular 

 plane, all the points of which are supposed to gravi- 

 tate equally. 



From 



