[ 828 ] 
May it here be farther added, that thus all the 
cafes of obi que fpherical triangles may be folved 
without dividing them into rectangular? For when 
two Tides and the angle included, or when two angles 
and the iide between them are given, the two other 
angles or tides may be found by the proportions of 
Napeir and Briggs, whereby the other two angles or 
Tides are found together (*&); the proportions, when 
two Tides with the including angle are given, being 
thefe, 
Cof. 
AC + CB . ^ AC c/3 C B 
cotang. {ACB 
CAB + CBA 
: tang. — — 
& 2 
And 
Sin. 
AC + CB 
2 
r A C cn C B 
iin. 
2 
; ; cotang, i A C B 
CAB co CB A 
: tang. • 
The fecond of thefe has been demonftrated with 
great concifenefs by Dr. Halley, from the principles 
of the ftereographic projection of the fphere (/) j and 
the firft is derived by him from the fecond, but not 
and BC amounted to 37.596411. The logarithmic fine of 
AC cn B C ^ 562468) deducted from half this fum ( 18.79821 1 ) 
2 
leaves 9-235737. This number fought among the logarithmic 
tangents exhibits for its correfpondent fine 9.2294CO, which being 
deduced from the forefaid half fum (18.79211) leaves 9.568805, 
which is the logarithmic fine of 2i° 44' 50Tb equal to half AB. 
(£) Vide Neper. Mirif. Canon. Conltr. pag. penult. 
(/) See Jones’s Synopfis, p.281, 
altogether 
