STEINER’S EXTENSION OF MALFATTl’S PROBLEM. 
265 
equation will be linear, and it is easily seen that the value is i')^. 
Hence 
{ 2 |M/v|+(^<'+*')^+ 2 ^}^— U^=^^g 2 " )^— 
And we may assume 
2/Ai/|+ (^+j'>+2^— U=^^{ (a|+/3;5+70 -l-^(?+0 } j 
subject to its being shown that 
4|^‘'l+2(|a-+i')?7+4^=^^^|^A+^^ (a|+/3;?+yQ— (i+D j 
gives a constant value for A. The comparison of coefficients gives 
2f4, + 2{' = /3 
4=4'{(A+i).-(A-^)s}. 
the first and third of which give 
4(1-H=^(a+x)(7-«)5 
which will be identical with the second, if 
which follows at once from the equation 
1 +!«■<? 
V= • 
Forming next the two equations 
A+A=(;:^(f‘+')^ 
A-x=(; 4 p{(f‘+'')’'- 2 / 3 ) 
these will be equivalent to a single equation if 
(fA + 1/) = { (^ + 1^) 7 — 2/3 } ^ 
e. if 
(^.+t/)4/3"+7^) — 4(fA4-v)/37— 40v— l)/3^ 
2 M 2 
In fact 
