$o8 Mr. Atwood’s Disquisition on 
APPENDIX. 
Note to the Investigation, Pages 232, 233. 
y/sine O x sine P = 
^ sec. f F x sec. S 
This is investigated in Ihe following manner : 
Let R be put to denote a right angle, the other notation be- 
ing the same as in page 232 ; 
Then the angle DWP=}F + P; also DWP=R-S 
wherefore ^F+P = R — S and P = R — i F — S, 
and, since 0 = 2R — F — P, it follows that 0 = R — F -f- S ; 
consequently sin. P = cos. j- F -j- S 
sin. O 
and 
cos. * F 
sin. O x sin. P = cos. J F-j-Sx cos. \ F — S 
or because cos. 1 S 
= cos. 1 J- F x cos. 1 S — sin. 1 -!- F x sin.* $ 
1 — sin. 1 S 
sin. O x sin. P = cos. 1 \ F x 1 — sin. 1 S — sin. 1 |F x sin. 1 S 
or sin. Ox sin. P= cos/^-F-— sin/S 
sec. 4 | F x sec. 1 S ~ „ 
sec. 1 i F x sec. 1 S X COS - T ^ 
or 
sin. O x sin. P 
sin. 1 S 
sec. 1 S — sec. 1 \ F x tang. 5, S 
sec. 1 4 F x sec. 1 S 
or 
1 4- tang. 1 S — 1 4- tang. 1 4 F X tang. 1 S 
sec. 1 \ F X sec. 1 S 
. • r» 1 — tang. 1 |F x tang. 1 S 
sin. O x sm. P — ^t-j. f x sec. 1 s 
Finally, ^sin. O x sin. P 
V 1 — tang. 1 \ F X tang. 1 S 
sec. t F x sec. S 
