THEORIA COMBIN. OBSERV. ERRORIBUS MINIM. OBNOXIAE.

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mediatae, aequali praecilione gaudentes, puta quarum error me-dius — mV p — m'V p' =z m'\ r p" etc., liue quibus pondus — r tri-buitur, fuppeditauillent

nzo, v ~ o, v" — o etc.

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Problema.

Dejignantibus v, v, <o etc. functiones lineares indetermi .natarum x, y , z etc. fequentes

v = ax-\-by\-cz -}- etc. + l -x

v — ci x -f- b'y -j- c z -f- etc. l' | (I)

d"— ax + b"y -f- c'z + etc. 1" etc. )

ex omnibus fyftematibus coefidentium x, x', x" etc., qui indefi-

nite dant

x v x v' x" v" -J- etc. — x — h

i»

ita vt k fit quantitas^determinata i, e. ab x, y, z etc. independens,eruere id, pro quo x x,+ X K + x x + etc. nancifcatur valorem mi-nimum.

Solutio. Statuamus

a v + a ' v + a> ' v " 4" etc. = £ 1bv + b'v' + b”v" 4-etc. t (II)c V 4" C V 4" c " V ” “1" etC. —• i ) ■etc.: eruntque etiam £, ij, g etc. functiones lineares ipfarum a?,y , z etc., puta

£ r= xSoa 4" y2n6 4" 4“ etc. “H \

y — x~2ab 4~ y ^£bb 4~ z^bc 4~ etc. 4“ 26 f r (HI)

g — x2u c 4- y 2 6 e 4- zScc 4" etc. 4'Sci etc. J

(vbi 2aa denotat aggregatum a aada" a”etc. f ac per-

inde de reliquis).

D '