14 
114] steiner’s extension of malfatti’s problem. 
and we may assume 
71 
2 f ivÇ + ( f i + v)r ] + 2Ç+ ü = A {(aÇ + @ v + yÇ)-$(!;+ £)}, 
2fiv% + (/a + v) v + 2f - U = ~ {(a£ + /3?? 4- y£) + 8 (£ + 01. 
subject to its being shown that 
éfivÇ+2 (/a + i/)77 + 4£ = ^-y^ j^A + (a| + /3t? + 7 £) - 8 (A (£ + £) 
gives a constant value for A. The comparison of coefficients gives 
4 [iv = ' 
 
A + T) a “ ( A - yj 
*+*-V ( A+ >> 
4 = ^ÏÏA + l) 7 -fA-I)«h 
A 
the first and third of these give 
4(1- fiv) = ( A + y) (7 - a), 
which will be identical with the second, if 
2(l-^Q = _g_ = _ 
/a + v y — a 
which follows at once from the equation 
1 + /¿<p 
v — jT- 
/*-9 
an 
the 
Forming next the two equations 
A + v = 
A (/a -1/) /3 
A-A = 
(/a + v) 8, 
{(j* + v)y-2P}, 
A (fi — v) ft 
these will be equivalent to a single equation if 
(/A + V) 2 S 2 = {(/A + V) 7 - 2/3} 2 + (/A - A») 2 /3 2 , 
that is, if 
(/a + v) 2 8- = (/x + v)• (/3 2 + 7 2 ) — 4 (/a + i>) /?7 — 4 (/ai/ — 1 ) /3 2 ;