114] 
STEINER S EXTENSION OF MALFATTl’s PROBLEM. 
73 
§ 6. 
The system of equations 
(/+ 20 VI) + V& (F + Z ) +/XZ - Vfo VITF 2 VlTZ 2 = 0, 
(g + 20 V23) + Vi3(F + X) + (/FX - Vca Vf +F 2 Vf+X 2 = o, 
(h + 20 V©) + V® (X + F) + hXY - Jab VI+X 2 Vl+T 2 = 0, 
where 
0 = ^(Vli3© + jpVl + ®V©+^V®), 
on which depends the solution of Steiner’s extension of Malfatti’s problem, is at once 
seen to belong to the class of equations treated of in the preceding section, and 
we have <£ = 0, .9 = 0. The equations at the conclusion of the preceding section 
become 
{V£3C + gh+20 (g Vt£ + h VH) + 4 0 2 V2M} V(2T+ h VIS + 20 V330D} g + {VST© + 9 h \ £ 
- a[(/+ 20 VI) | + Vg^ +m-~ s/(g + d Mj(h+0Vf) V-J3^{(VI- 20/)f-fy +Vl£}=0, 
v&c 
((/+ 20 VI) ? + VI, +/?)■ - be Kf - ?)’ + /) = o, 
which may also be written 
(V330D + Jp) (£ + £) + (- a VI + g M + /i VJ3 + 20 V2M) (i? + 20£) 
- A ■/(<, + o VS) (A + 0 V©) V«1 ((VI - 20/) ? -/,+vi?)= o, 
l/(?+D + ' / S(’> + - 6« f(? - №+v‘) = o. 
Hence observing that 
? +0VS=L(VS® + JF)(VIS + ^); A+oVffi = i(Vj3ffl+.f)(VS@ + ffi); 
- a VI + h -JM+g V® + 20 VSffi = 0(V8© + f), 
and putting for a moment 
\= R + C) (V&23 + ?§) V23&, 
V(g + 0 V23) (A + 0 V(2D) Va3C = (Vl3® + jp) 
and therefore