97 
Prop. 
To determine the lines of curvature of the single-surfaced 
Hyperboloid. 
The equation of the ellipsoid may be changed into that of this 
curve by making c’* negative, by which it becomes 
ab’e—a'cy —B'e'a* = — a’b’c 
By this condition we have also 
The equation of the projection of the lines of curvature is the same 
as in the case of the ellipse, and the quantities a” b” subject to the 
same condition, 
a*y® + b?. ne = ah? 
ea" —b” = f. 
The semiaxes of the directrices are in this case 
Since a’ < a the vertices of the axis 2a’ of the directrices must fall 
within those ef the section of the surface by the plane ay. 
