( m ) 
R (X to C M, and the Angles it (Land P right An- 
gles. The Line C P may be taken as equal to 
C -My and M P as the Difference of the Lines C M and 
Cm. Therefore the little Arch M m is to the Line 
M P nearly as R M to R CL: But C M (i. e. AN) 
was to C m (/. e. an) as BR to b r , and the Dif- 
ference M P of CM and C m to the Difference B D 
of B R and b r as CM to BR. Therefore M m , the 
Difference of the apparent Tranflations, is to B D, 
the verfed Sine of the Diftance B b y or to an Arch 
equal to it, in the compound Ratio of R M the Ra- 
dius to R CL Sine complement of the Angle of 
Inclination of the Specula, and C M double the 
Sine of the fame to BR the Radius, i. e. as C M 
to R CL. 
The Obfervation may be corrected by one eafy 
Operation in Trigonometry, as will appear from the 
firft Part of this Corollary, viz. by taking the half of 
the Angle obferved, and then finding another Angle, 
whofe Sine is to the Sine of that half, as the Sine 
complement of the Diftance Bb is to the Radius: 
This Angle doubled, will be the true Diftance of the 
Objefts. But as this Operation, though eafy, will 
require the nfe of Figures, I rather chofe the Method 
of Approximation, becaufe by that the Obferver, re- 
taining in his Memory the Proportions of the Sines of 
a few particular Arches to the Radius, may eafily efti- 
mate the Correftion without Figures, when the Angle 
is not great, and by a Line of artificial Numbers and 
Sines, may always determine it with greater Exaftnefs 
than will ever be necelfary. 
When the Angle obferved is very near 180 Degrees, 
the Correction may be omitted ; for then it will be 
eafy 
