BOOK OF MATHEMATICAL PROBLEMS. 



sented by LA, LB, LC will have a resultant along LO and equal 

 to twice LO. 



1217. Three parallel forces act at the angular points of a 

 triangle ABC, and are to each other as b + c : c + a : a + b', 

 prove that their resultant passes through the centre of the in- 

 scribed circle of the triangle whose angular points bisect the 

 sides of the former. . 



1218. The position of a point P such that forces acting along 

 PA, PB, PC, and equal to IP A, mPB, nPC respectively, are in 

 equililrium, is given by the equations 



areal coordinates being used. 



1219. "Forces act along the sides of a triangle ABC and are 

 proportional to the sides ; AA', BB', CO' are the bisectors of the 

 angles ; prove that if the forces be turned in the same direction 

 about A', B', C' respectively, through an angle 



A- 



-i i . . 



tan ^_ cot -- cot -- cot 



there will be equilibrium. 



1220. A system of forces whose components are (JT lt Y^, 

 (X a , F a ) ... act at the points (x } , y^), (# 2 , ?/ 2 ) ... and are equiva- 

 lent to a single couple; prove that if each force be turned about 

 its point of application through an angle there will be equili- 

 brium, if 



= 



1221. If L } M, N be the sums of the moments of a given 

 system of forces about three rectangular axes, and X, Y, Z the 

 sums of the components along these axes, then will 



LX+MY+NZ 



be independent of the particular system of axes. 



