ins 



MID. 



Let the co-ordinates of A axes be a-, , ?/ 



those of B, a? t , t y f , r f ; and tlmso of (7, a? t , y s , ~ ? ; thru, l.y 



t'.G, the co-ordinates a:, #, ~ "1 tin- cvntiv <>!' gravil 

 three equal part x ; at .1. //, C7res]' 



By wliat we have just proved, these are also the co-cnl 

 oi tl ity of the triangle ABC. 



It may be remarked that in Art. CG the co-ordinates may 

 be rectangular or oblique. 



(4) To find the centre of gravity of a pyramid on a 

 far base. 



Let ABC be the base, D the vertex; bisect AC&tE', j. .in 

 BE, DE\ take EF=\EB, then F is the centre of gravity 

 of ABC. Join FD; draw ab, be, ca parallel to AB, BC, CA 



respectively, and let DF meet the plane ale at/; join /// 

 and produce it to meet DE at e. Then, by similar triangles, 

 oe = ec; also 



VL SL 



BF ~ 



but EF=\BF, therefore ef 

 therefore f is the centre of gravity of the triangle ale; and 



