ALGEBRA. 21 



and that 



109. Having given 



prove that 



aa* + W -f-cc" + <W 



i . = be ,- 



abed ad 



110. In the equations 



* y 



la) m(nc+la-mb) 

 , in, n are all finite; prove that 



I _ _ m _ n _ 



x (by + cz - ax) ~ y(cz + ax-by) = z(ax + by-cz) 



111. If a, 6, e, x, y, 2 be any abc quantities, and 



( , t f be similarly formed from a,, 6,, r 

 . and so on ; then will 



?.*.!.?.*.! 



a b o m y 9 



i*-i 

 - o&d - Sxyt)"^". 



112. Having given 



v+t 



prove that if x, y be unequal, 



9 sm-y 

 r^7"STfixy 



