STEINER’S EXTENSION OF MALFATTl’S PROBLEM. 
273 
+ 
/ — „ , IT f ^ — £^ + h^\ f / 
(j(i+g-h)“-^+°+*+®'’ 2th ) Vf (* “ 
+ 2\/K\/ 1— j\/ 1— ja/ 1 — j\/— Jom; = 0, 
values which might be somewhat simplified by writing y;, co instead of 
2\/i-j\/‘-j'\/>-3'/^“’- 
And it may be also remarked, that the coefficients as well of these formulae as of 
those which follow may be elegantly expressed in terms of the parts of a triangle 
having f, g, h for its sides. 
The equations of the separators are found by taking the differences two and two 
of the equations of the resultors (this requires to be verified a posteriori) ; thus sub- 
tracting the third equation from the second the result contains a constant factor, 
j^jj-^^jj5^{4f¥h»-J(f>-(g_h)=)((g+h)’-P)}, 
equivalent to 
h)2)gh 
Rejecting the factor in question and forming the analogous two equations, the equa- 
tions of the separators are 
g-h f 
1 
h f 
h 
);s = 0 
f vnv 
jy^+ 
VBV 
a/CV 
^ (\ 
i, h-f 
^ {\ 
-!>+ 
h f 
\z = 0 
VUV h 
g 
■v/BV 
s/€\' 
‘“jJ 
^ (i - 
fl 
w 
^ (] 
1 
\z = 0 ; 
' v /33 
V J. 
h 
v'CV 
‘ jJ 
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 ^=0, 3 /= 0 , ^=0, the equations of the 
tactors are 
\/Cj/=0, \/€^x—\/^z=0, \/B^=0 ; 
and if ax-\-^y-\-yz-{-lw — Q be the equation of the tactor touching 
x=0, \/<£,x—s/^z=0 and \/3S^=0, 
the conditions of contact are 
2 N 2 
