( ijo ) 
'D ET ERM I NATION. - 
I T is evident, that this conic Sedion, may either 
cut the Circle in two Points, touch it in one Point, 
or fall wholly without it. Therefore let the Se- 
ction touch the Circle in the Point I, and let I L touch 
both the Sedion and the Circle in the lame point I. 
Then GL being joined, the Angle under IGL on ac- 
count of the conic Sedion is a right one ^ lb that 
F G L is one continued right Line, and IF is to I L as 
FGtoGI; as likewife, M being the Center of the 
Circle, M I to I L, or F H to H I, as F G to twice 
G I, becaule M I is to I F as G I to twice G I. Hence 
by Permutation F H is to F G as H I to twice G I ; that 
is, as the Sine of the Angle of Incidence to twice the 
Sine of the rehaded Angle. 
* De la Hire Conic, lib. 8, prop. 23. 
Moreover 
