[ 9i3 ] 
Rad.* : fin. AB x fin. BC (cof. lat. x cof. decl. .©) 
• ; verf. f. ABC : verf. f. AC —— verf. f. A F j 
And, in like manner, in the triangle A B D, 
Rad. q : cof. lat. x cof. decl. © : : verf. f. A B D 
: verf. f. A D — verf. f. A F j 
Confequently, 
Rad. q : cof.lat. x cof.decl. © : : verf.fi ABD — verf.f. ABC 
; verf. f. A D — verf. f. A C. 
But 4 rad. x verf. f. ABD — verf. f. A ifC is = 
„ ABD + ABC ABD — ABC 
lin. 7 x lin - o " “ a 
2 2 
Therefore, 
Rad. q : cof. lat. x cof. decl. © : : fin. 
ABD + ABC 
x f in> £22 — £22 *. J. rad. x verf.f. AD — verl.f. AC. 
And this is the fir ft operation in the treatife, thefe re- 
, , - ABD + ABC 
marks concern. For in the redtangie, the iin. 2 
x the fin. A 13 D — A B 9.^ the firfl fide, when the obfer- 
vations are both made on the fame fide of noon, and 
the fecond fide of this re&angle, when one obferva- 
tion is before noon, and tne othei after, ia the fine 
of the diftance of the middle time between the ob- 
fervations from noon, and the other fide is the fine 
of half the diftance between the obfervations. ^ And 
in the new tables one column exhibits the aiithme- 
tical complement of the logarithmic fine of half the 
elapfed time, and the next, the logarithm or twice 
the fine of the middle tim e. 
But moreover, t rad. x veri. 1 . A U veil. l. /i C 
AD + AC . AD - AC 
being equal to fin. 
x fin. 
the 
operation may be exprefied more commodioufty thus, 
r - ‘ Rad. 
