I 473 ’] 
in vrh^t follows, for. brevity fake, the arc is exprefled 
by a Greek letter; its fine by the capital chara6ter; and 
the cofine by the fmall italic chara6ter of the fame letter. 
In this notation, the two theorems will fiand thus, 
fin. oi+^-A + aB-Ax\{. jS, and co{. oi+^=a^AB-ax Yl,j3, 
COROLLARY I. 
Since the tangent is equal to the fine divided by the 
cofine, we fliall have 
_ ~n A + flB AXvf. ^ A B A , 
Tang. a-(-p= — — — ' "jx vf. p nearly, 
‘ a — AB — a X vl, p a a ^ 7 
COROLLARY II. 
If we change the fign of /5, we fiiall have fin, oc~$ 
= A-aB - A X y{. CoL oi ~ (3 = AB-a X And 
tang. a-/3 = ---^+-ix vf. /?. . 
By the help of thefe theorems, knowing nearly What 
any quantity in a fpherical triangle is, we may find its- 
corre61ion, thus : if we have to find the cofine of an arc, 
which arc we know is nearly equal to a whofe cofine is a. 
Suppofe the arc to be - (3, and its cofine a-^c. Then a+(^= 
€of. + AB-^?x vf. /?, Therefore, b = ~'^jxyqt{.^. 
R r r 2 The 
