114] 
steiner’s extension of malfatti’s problem. 
81 
and from the mode of formation of these equations it is obvious that the separators 
have a line in common. 
The equations of the determinators being x = 0, y = 0, z = 0, the equations of the 
tactors are 
V33^r— V©y = 0, V©# —Va.z = 0, Vay-V<ï3æ = 0 ; 
and if ax + fiy + yz + 8w = 0 be the equation of the tactor touching 
x = 0, V©# — Va.z = 0 and Vay —V23« = 0, 
the conditions of contact are 
= j(Va23 - 3^)0 Va - /3 V33) + 7 (© V33 - V©)j 2 , 
= j(Va© - (K) (« va - 7 v©) + vod - jp va>j 2 , 
whence 
(Vaaa - ?§) va« - (Vaaa - 3^) V23/3 + (© vas - jp va) 7 , 
(Va© - ® ) va«+ (3^ v© - j va) /3 - (Va© - ©) 7 , 
c/3 2 4- by 2 — 2f/3<y + — 8 2 = 0, 
and putting for a moment 
fi = va© - © - A va© (Va© - é\ 
v=vas - 3^ - n/2 vaaa (Vaas - 3^); 
after some reductions, and observing that the ratios only of the quantities a, /3, 7, 8 
are material, we obtain 
C. II. 
11