50 Trans. Acad. Sci. of St. Louis. 
inscribed in the cone and tangent to the plane Z,Z,; F, and 
F, are the foci * of the section cut from the cone by the plane 
04 don 8, 8, OF; CFs C Ds CPD 
Let 
a == half the angle at the vertex of the cone. 
8 =the angle which the plane 7,7, makes 
with the axis of the cone. 
6, ==the angle CSF’. 
== the angle C,SF’,. 
Then 
BPP ASSELSIK ) 
ee. Fe aes 
ae PG, get) ) 
a SEC, = 90°+ (2 — 6,) 
In the triangle SF, C,, 
sin 6, 
er eee 
cos (B+0,) Oe. oe 
whence 
sin @, =sin a cos (8 + 6,) 
=sin a (cos 8 cos #,—sin f sin 0,) 
and 
___ sin @ cos B 
= i, on aoe C1) 
Similarly, in the triangle SF,C,, 
sin @, 
fe ee 
cos (2—0,) O,S ~~ °"% 
whence 
sin 7, sin a cos (?— 6,) 
sg = sin a (cos 8 cos 0, + sin f sin 6,) 
sin a cos 2 
ian (= fan waep “ 
_* Salmon, “Conic Sections,” 6th Ed., Sec. 367, 
