[ 442 ] 
fine of CB; whence, by equality, half the fine of 
BCH is to the fine of DH as the fine of CHB 
the fine of CD : but as the fine of CHB to the fine 
of CD, fo, in the triangle CHD, IS l ' ie f ns ° J? r „ 
to the fine of HD : confequently, the fine o DCH 
is equal to half the fine ot BCH. Hence, the d > 
ference of the angles BCH, DCH being given, 
thofe angles are given, and the arc C H I is g ■ v c " y 
P ° Moreover, in the triangle BCH, the bafe BH 
being bifeded by the arc CD, the fine of the angb 
C H D is to the fine of the given angle C B D, as 
the line of the given angle H C D to the line o 
i P ( ' n • therefore, the angle CHB is 
Sven r'in fo much, that in the triangle CBH all the 
“fhe Berthe fines of the angles BCH DCH 
is to the difference of their fines, as the tangent of ha 
the fum of thofe angles to the tangent of half tb = 
difference; therefore, the tangent ot half tl ) e f “ n , , f 
BCH, DCH is three tunes the tangent oi halt 
B< In D (Fig. 6.) the ifofceles triangle ABC, let the 
angle B A C be equal to the fphencal angle > 
and let AE be perpendicular to BC ; al.o, » 
taken equal to C B, join A F: t ten r n the tan- 
three times EB ; and as E F to E b, fo is the = ta _ 
gent of the angle E AF to the tangent of t A B , 
gut EAB is equal to half the fpherieal angle 
therefore, the angle EAF is equal to hal. the lum 
the fphencal angles BC U, o'- ri , i«nrH 
the angle C A F equal to the fphencal angle D C H 
Here, AF is to CF as the fine of the angle ACF 
