Full text: Theoria combinationis observationum erroribus minimis obnoxiae

THEORIA COMBIN. OBSERV. ERRORIBUS MINIM. OBNOXIAE. 
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Statuamus itaque efTe (I) 
m° ~ 2i° x -j - ' 33° y 4“ z 4” etc. 4“ £° 
u — 53' y -}- (£' z -f- etc, -J- i' 
u" = (T. * 4- etc. -f i" 
etc. 
Hinc erit indefinite 
' d x -j- >7 (3 y -f- ^ d z -f- etc. 
u° d u° u d u u" d u" 
4—fwT - 4~ q*'? 4- etc. 
i d £2 
53' 
53° 
= “° (dx+ y^dy 4- yo d3 4- etc.) 
d' 
4- u (d y -f* etc.) 4“ u" (dz-j- etc.) -f* etc. 
vnde colligimus (II) 
23° 
y=-y-u° -u 
d° <r 
•> ^ n t ' i " 
¿= fl5 U + gy “ + “ 
etc. 
Supponamus, hinc derxuari formulas fequentes (III) 
w° = 2 
m' = a’ £ 4- 
u" = jr-£ + irii + g 
etc. 
lam e differentiali completo aequationis 
a = £(» — -4)4->7(y —+ — c )4- etc. 4-M 
fubtracta aequatione 
|dQ, — ¿dx4“i;4y4'^4z4- etc. 
£ d£2 — (x — ^4)d£ 4- (y~-®)4^4" ( z — ^)4^4* etc * 
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