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this conic, and having its vertex at the focus ; the cyclic planes 
of this latter cone will pass respectively through the two right 
lines in which the planes of the two sections meet the directive 
plane. 
‘© 5, Hence, through a right line, situated in a directive 
plane, draw two planes cutting the surface in two conics; a 
cone passing through these two curves intersects that directive 
plane in a certain conic : now let a cone be described, passing 
through this conic, and having its vertex at the focus; this 
latter cone will be one of revolution, and its principal plane 
will pass through the right line assumed in the directive plane. 
** 6, Hence, a cone enveloping the surface intersects a di- 
rective plane in a certain conic; a cone passing through this 
conic, and having its vertex at the focus, is one of revolution ; 
and its principal plane passes through the right line in which 
the plane of contact of the enveloping cone meets the direc- 
tive plane. 
«<7. A plane curve is traced on the surface, and through it 
a cone is described, having its vertex at the pole of a directive 
plane; this cone cuts the directive plane in a certain conic : 
now let a second cone be described, passing through this conic, 
and having its vertex at the focus ; the latter cone is one of re- 
volution, and its principal plane passes through the right line 
in which the plane of the original curve intersects the directive 
plane. 
_ 8, Ifa cone be described, having its vertex at the focus, 
and passing through a plane section of the surface, the cyclic 
planes of this cone will pass respectively through the two 
right lines in which the plane of the section meets the two 
directive planes ; and the directive axis of the cone will there- 
fore be the right line drawn from its vertex to the point where 
the directrix is cut by the plane of the section. 
“9. Hence, any plane passing through the directrix inter- 
sects the surface in acurve such that the cone passing through 
it, and having its vertex at the focus, is one of revolution ; 
