C 249 ] 
a. more exa& formula than that of Euler <1 — 
D 
D 
-I'm. P cof. A •+• p' 
§ 3 . By taking </= T _ |in _ p ( . 0 , A , 
D fin. P cof. A D fin. p cof. A D tang. p ... 
: which 
we have d — 13 
i — lin. P col. A lin. A col. p tang. A 
affords an elegant theorem, to find the increafe of the 
apparent diameter of the moon. 
§ 9. I have found others by the following methods. 
Since fin. A : fin. A \-p : : tang. D : tang, d, and fin. A : 
fin. A -\-p — fin. A : : tang. D : tang, d — tang. D : : fin. 
D cof. d: fin. d— D ; but cof. D — cof. d without 
any fenfible error, and fin. D cof. D— i fin. 2 D, and 
fin. A-pp — fin. A — 2 fin. 4. p cof. A-P-lp, we fliall 
have fin. u= * In thc 
fame manner, as 1 before found fin. p'= fin. P fin. A 
and fin. P fin. A: fin. /::tang. D : tang, d, h ence 
fin./' : fin. p — fin./': : fin./' : 2 fin.? ] 1 
fin. 2 D fin. p- 
cof. 
2 2 
~p' cof. /> + // 
2 • 
fin. 2 D:fin.^—D— ____r 
fm. P fin. A 
§ i o. Laftly let L —the diftance of the moon from 
the center of the fphere, / its radius, that of the lphcre 
being =1, we have i:L::fin. P: 1 and L 1: 
tang. D or 1 : / : : fin. P : tang. D — / fin. P ; hence / 
— “jjTpp" being once found, fince fin. A : fin. A-ff/: : 
tang. D : tang. and fin. A -f- / : fin. p : : 1 : fin. P, we 
lhall have fin- A ; fin. p : : tang. D : fin. P tang, d : : / ; 
1 found the logarithm of / — 
/ fin. p 
lin. i\' 
V 01 . LVL 
tang, d 
K k 
9-4343965 
