Let O B C in the annexed Figure reprefent an infinite 
Sphere, at whofe Center R are placed the two Specula 
inclined to one another in any given Angle,and let their 
common Section coincide with the Diameter O R C. 
Let B A N be the Circumference of a great Circle, to 
the Plane of which the common Section of the Spe- 
cula ORC is perpendicular, and B R its Radius: 
Let b a n be the Circumference of a Circle parallel ro 
BAN, and at the Diilance from it B b : Draw 
b D the Sine, -and b r the Sine complement of the 
Arch B b : B D is the verfed Sine of the fame. Let 
A be a Point of an Objedt placed in the Circufnfe* 
rence of the great Circle BAN, and N the Point in 
which its Image is formed by the two fuccellive Re- 
flexions, as before defcribed ; and let a be a Point of 
another Objedl placed any where in the Circumfe- 
rence of the Parallel b a #, and n its Image 5 and let 
ah n be an Arch of a great Circle paffing through 
the Points a and n. The Point a is at the fame Di- 
ftance from the great Circle BAN, as the Point b , 
e 
