Full text: [Wahrscheinlichkeitsrechnung und Geometrie] (4. Band)

89 
ERRORIBUS MINIMIS OBNOXIAE. 
Triangulum VII. 
Hauselberg 
Wulfsode . 
Wilsede . . 
34° 25' 46"7 52 
109 38 36,566 
35 55 37,227 
Aderunt itaque septem aequationes conditionales secundi generis (aequationes 
primi generis manifesto cessant), quas ut eruamus, computandi sunt ante omnia 
excessus sphaeroidici septem triangulorum. Ad hunc finem requiritur cognitio 
magnitudinis absolutae saltem unius lateris: latus inter puncta Wilsede et Wulf 
sode est 22877,94 metrorum. Hinc prodeunt excessus sphaeroidici triangulorum 
I... 0"202; II... 2"442; III... T'257; IV... l"919; V...T957; VI... 0"321; 
VII... T'295. 
lam si directiones eo ordine, quo supra allatae indicibusque distinctae sunt, 
per t/°), v( l \ v^\ etc. designantur, trianguli I anguli fiunt 
u(3)__ v 00 „(s)_ v (*), 360° + iV)—f>< 10 ) 
adeoque aequatio conditionalis prima 
— v (2)_j_^(3) — ^(4)_j_^(s)_j_^(7) — v (io)_|_i 79 o 59 ' 59 " 798 _ o 
Perinde triangula reliqua sex alias suppeditant; sed levis attentio docebit, has 
septem aequationes non esse independentes, sed secundam identicam cum summa 
primae, quartae et sextae; néc non summam tertiae et quintae identicam cum 
summa quartae et septimae: quapropter secundam et quintam negligemus. Loco 
remanentium aequationum conditionalium in forma finita, adscribimus aequatio 
nes correspondentes e complexu (13), dum pro characteribus g, g'etc. his (0), 
(l), (2) etc. utimur: 
-1"368 = — (2) + (3)- (4)+ (5)+ (7) — (10) 
+ 1,773 = -(l) + (2)- (7)+ (9) —(11) + (12) 
+ 1,042 = _(0) + (2)— (7)+ (8) + (14)— (17) 
— 0,813 = — (5) + (6)— (8)+ (10) — (16) + (17) 
— 0.750 = — (8) + (9)— (11) + (13) — (15) + (17) 
Aequationes conditionales tertii generis octo e triangulorum systemate peti 
possent, quum tum terna quatuor triangulorum I, II, IV, VI, tum terna ex his 
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