STEINER’S EXTENSION OF MALFATTl’S PROBLEM. 
271 
we have 
('p_g=_h»+--85-')K=(l+YZ) 
{j^-ghy 
+ 
f^-(g-h)^)[(P-gh)(p_(g--h)^)-2gh(g-h)^-2gh^— j| 
4g^h^(g-h)^(P-gh) 
J2 
K^{K(Y+Z)- 2P-2g^-2h^+4J2} 
=4(1 - J){(f=-(g- hr) [(j'- gh) ((g+h)“-p-^*’ 
4g%ng-h)*(J’-gh) 
J2 
Also, since 
we have 
(f- (g-h)»)+ ((g+h)’-f‘-^^') =4gh 
( P-gh) 
J2 ’ 
(^f-g^-h^+^')K^(l+YZ)H-KMK(Y+Z)-2P-2g^-2h^} 
=4 (1 - i) (f (g- i,)=)2ghj’(i -f:) (1 - ■ 
And the values obtained above give also 
2gh\/ l-jjKVr+Y*s/T+Z’ 
which shows that the relation between Y and Z is verified by the assumed values of 
these quantities, and the other two equations are of course also verified. The solu- 
tion of the problem will be rendered more complete if the equations of the required 
sections and of the auxiliary sections made use of in the geometrical construction are 
expressed in terms of f, g, h, J. 
§7. 
First, to substitute in the equations of the required sections or resultors. Writing 
the first equation in the form 
2~v/ ^ =0, 
the coefficient of .r will be 
or, as it is convenient to write it, 
(l+j)f(-f+S+h)^(l-^){jpg|^-f+g+h-2j}. 
2 N 
MDCCCLII, 
