( 3 54 ) 
i.e. at the Diftance B b. Draw A R, AN, RN, 
ar, an, rn, a R and n R. 
By the fourth Corollary the Figures A RN and 
am are fimilar, and confequently the Line A N is 
to the Line a n as A R or B R is to a r or b r, i. e. as 
the Radius is to the Sine complement of the Diftance 
B b. But A N is the Chord of the Arch A H N of 
the great Circle BAN equal to the Tranflation of the 
Point A, or double the Inclination of the Specula, 
and an is the Chord of the Arch a b n of a great Cir- 
cle, meafuring the Angle a R by which the Point 
a appears removed by the two Reflections, to an Eye 
placed in the Center R. Therefore the Tranflation, 
or apparent Change of Place of the Point a is mea- 
fured by an Arch of a great Circle, whofe Chord is 
to the Chord of the Arch A H N (equal to double 
the Inclination of the Specula) as the Sine comple- 
ment of its Diftance from the great Circle BAN is to 
the Radius. 
From any Point C of the Circumference OB C 
draw the Chords C M and C m, to the fame Side of 
the Point C, and equal to the Chords A N and an 
refpectively, draw the Radius R M, and from R and 
m draw RQ_ and m P, both perpendicular to C M, 
and cutting it in Q. and P. R Q. is the Sine comple- 
ment, and CM double the Sine of half the Angle 
M R C, or A R N, or of the Angle of Inclination of 
the Specula. The little Arch Mm will reprefent the 
Difference of the apparent Tranflations of the ObjeCts 
in A and a ; and if it be very fmall, may be looked 
on as a ftrait Line, and the little mix’d Triangle 
M m P as a rectilinear one, which will be fimilar 
to RMQ,, becaufe RM is perpendicular to M m and 
RQ. 
