90 
SUPPLEMENTUM THEOEIAE COMBINATIONIS OBSERVATIONUM 
III, IV, V, VII ad hunc finem combinare liceat; attamem levis attentio docet, 
duas sufficere, alteram ex illis, alteram ex his, quum reliquae in his atque priori 
bus aequationibus conditionalibus iam contentae esse debeant. Aequatio itaque 
conditionalis sexta nobis erit 
log sin[v—(T067) — logsin(^( 5 ) —— 0"067) 
—(— log sin(i/ 14 )—v( 17 )— 0"640) — log sin (+) —v(°^ —0"640) 
+log sin(vO B ) —y( 5 ) —0^107) — logsin(y( 17 )— y( 16 )— 0"107) = 0 
atque septima 
log sin [v ( 2 l — v ^ — 0"419) — log sin (u*' 12 -* — i/ 11 ) — 0"419) 
—J— log sin •—0"640) — log sin—v® —0"640) 
+ log sin (y0 3 ) — + 1 ) — 0"4 3 2) — log sin [v^—y( 15 ) — 0"4 3 2) = 0 
quibus respondent aequationes complexus (13) 
-|-25 = -f- 4,31 (0) — 153,88(2) +149,57 (3) + 39,11 (4) —79,64(5) 
+ 40,53(6) + 31,90(l4)+275,39(16)— 307,29(17) 
— 3 = + 4,31(0) — 24,16(1) + 19,85(2) + 36,1 1 (11) — 28,59(12) 
— 7,52(13)+ 31,90(14)+ 29,06(15)— 60,96(17) 
Quodsi iam singulis directionibus eandem certitudinem tribuimus, statuendo 
= p№ etc. = 1, correlataque septem aequationum conditionalium, eo 
ordine, quem hic sequuti sumus, per A, B, C, D, E, F, G denotamus, horum 
determinatio petenda erit ex aequationibus sequentibus: 
— 1,368 = + 6 A— 2B— 2 C— 2D + 184,7 2F— 19,85 G 
+ 1,773 = — 2A+6J3 + 2 C+2jE— 153,88i^— 20,69 G 
+ 1,042 = —2A+2J5+6 C—2X>—2.E+ 181,00 J 7 '—j— 108,40 G 
— 0,81 3 = — 2 A — 2 C + 6D+2.E—462,51 JP—60,96 G 
— 0,750 == + 2 jB — 2 C + 2D + 6E— 307,29 .F— 133,65 G 
+ 25 = + 184,72A— 153,8815+181,00 C— 462,5lD — 307,29^ 
+ 224868.F+16694,1 G 
— 3 =— 19,85A— 20,6915+ 108,40 C— 60,96D — 133,65E 
+ 16694,1 F+ 8752,39 G 
Hinc deducimus per eliminationem