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TtETERMINATIOK 
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Let the Hyperbola touch the Circle in the Point L, 
and let their common Tangent be L S ; draw LT pa- 
rallel to M N, fo as to be ordinately applied in the 
per bo la to the Diameter C M. Whence L S touching 
the Hyperbola in L, P T will be to T L as T L to 
T S % and the Angle under T S L equal to that un- 
der T L P, but as the Angle under S C L is equal to 
that under N M L, the fame is equal to the Angle un- 
der T L M ; therefore the Angle under S L C is equal 
to the Angle under M L P. Farther, M L being pro- 
duced to V and V C joined, the Angle under L V C is 
equal to that under S L C, by reafon that L S touches 
the Circle in L ; hence the Angles under L V C and 
under M L P are equal, L P, V C are parallel, and 
Apoll. Conic, lib. i. prop. 37. compared with lib. 7. prop. 23. 
s X M P 
