C 47S J 
PROBLEM I. 
If the twolegSy ab and bc, of the fpherical tri- 
angle ABC right-angled at b^ are given, to 
find the hypotenufe ac, the leg bc, being ^ 
frnall in coinparifon of ac. 
Let AB=a, BC=/?j andfiiippofeAc— + ^ being a near 
approximation to ac, and <^the fmall arc to be added to 
AB to make it equal to= ac ; then cof. AC=cof. ab x cof. bc ; 
that is, according to our notation, a - az — a x l^—ah 
Whence z =• 
I — ab 
A 
X vf. f=cot. a X vf. |6— cot.a X vf. f. 
EXAMPLE. 
Let AB be 75° o' and bc 2.0° o', and the computation, 
will be as follows : 
Cotangent ab. 9.4280 
Verfed fine bc 8,7804 
4* nearly 55' 33" fine 8.2084 
Corredlion -7 from tab. iv. Nautical Almanac. 
Therefore 55 26 andAC = 75° 55' 26". 
By this problem, the dillance of the Sun may be found 
from a planet whofe latitude and difference of longitude 
are known. 
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