* 
Plane Sections of a Cone of Revolution. 185 
and any radius, CO, (=1), describe an arc. With C as a 
center and a radius CZ, equal to the given eccentricity (less 
than unity) describe another are. A perpendicular to the 
axis of the cone through the point where the second are meets 
the element of the cone intersects the first are at a point A, 
outside the cone. 
Then, from the figure, 
CP = CE cosa=ecosa 
Also 
CP = CO cos ECK = cos HECK 
= cos (a+ DCE) 
Whence 
cos (a + DCH) =e cosa 
DCK = 0 
ECK = 6+a 
Therefore any plane making with the axis of the cone the ' 
same angle as does CH, such for example as X, X, (drawn 
parallel to CA ) will cut from the cone an ellipse of the given 
eccentricity. 
COs a 
with C as a center and any radius, CO, (= 1), describe an 
arc. With C asa centerand a radius, CZ, equal to the given 
1 
For the hyperbolic section [e => 2 bat | Figure 2, 
eccentricity ( greater than unity, but less than CD=— ) 
ass 
describe another arc. A perpendicular to the axis of the 
