26 
CAROL. FRIDERIC. GAUSS 
inultitudoque ipfarum £, »7, £ etc. multitudini indeterminatarum 
x, y, z etc. aequalis, puta rc. Per eliminationem itaque elici 
poterit aequatio talis *) 
x = J-\-[ctci]£-\-[ct0]7i + lciy]g-h etc. 
in qua fubfiitiiendo pro £ etc. valores earum ex III, aequa 
tio identica prodire debet. Quare itatuendo 
a [aa] -\- b [ci&] -f- c [ a y] -f- etc. — ct -j 
a [aci] b' [a(5]-j- c' [uy] -f- etc. = ct | (IV) 
a" [ ct ct ] 4* b" [ ct /3 J + c"[ ay] -f- etc. zs ct' etc. ; 
neceiTario erit indefinite 
ct v -}- et v 4~ a" v" -f- etc. =r x — A (V ) 
Haec aequatio docet, inter fyftemata valorura coeificientium x, x,' 
x" etc. certo etiam referendos efle hos x — a, x' — a', x — a etc., 
nec non, pro fyfiemate quocunque, fieri debere indefinite 
( x — ct) v -{- ( x — ct ) v + ( x — a") v" -f- etc. — A — k 
quae aequatio implicat fequentes 
( k — ct) a -f- ( x — ct ) a + (x" — a") a" -f- etc. — o 
(x — ct)h -j- (x — ct )b' -j- (x" — a')h" -f- etc, — o 
( x — ct) c -f (x —• ct'> c + ( x" — ct") c" -f etc. — o etc. 
Multiplicando has aequationes refp. per [a a], [ct/3j, [ay] etc., 
et addendo, obtinemus propter (IV) 
( x — ct) a -f- ( X— ct ) a + C k'— a') ct' -j- etc. — o 
fine quod idem eil 
xk x x x x -f- etc. ~ ctct -\- ct'ct 4~ ct"ct" -f- etc. 
4~ {x — ct) 2 4“ (x—ct') 2 -j- (x'— ct") 2 -f - etc. 
vnde patet, aggregatum xx x x -j~ x x' -j- etc. valorem mini 
mum obtinere, ii ilaluatur x~a, x' = a\ x" ~ ct' etc. Q. E. I. 
*) Ratio, cur ad denotandos cocfficientes e tali eliminatione prodeun 
tes, bos poliiiimum characteres elegerimus, infra elucebit.