56 
CAROL. FRIDERIC. GAUSS 
IV Haud abiimili modo inuenitur valor medius producti 
qc° y° £°7]° 
= y 4 'Eah a fi /j, 4 Ijactb'¡jl x l£<ibct $ -j- yu 4 2a/3 b'ct 
Sed habetur 
2 ct ctb' $ — 2 « a . 21 (o — a ctb {3 
2 « b a (5' — 2 a b . 2 a (3 -—2 « £ & /3 
S«/3fcV = Hafi^bu — ^afibet 
vnde valor ille medius fit, propter 26/3=ri, 2a/3=:o # 
2 b ct = o, 
= (^ 4 — 3>tx 4 )2:«&^3-h ^ 4 CA+2«&.2ce/3) 
V. Quum prorfus eodem modo valor medius producti 
x° z° £° fiat 
= (^ 4 — 3Ai 4 )2acc«y-J- // 4 (i-|-2ac.2rty) 
et iic porro, additio yalorem medium producti x° (x° £° -f-y° q° 
4" z ° 4~ etc.) fuppeditat 
= (*> 4 — 3At 4 )2(«^C«c£ + ^/3 + cy-f etc ) ) -4- (¿> + 0// 4 
4-/a 4 (2cra.2ccci 4-2a6.2ce/34~ 2flc.2ct<y -f- etc.) 
~{v* —{aarctet-\-b (o\-cy + etc.)) -f (g -j. 2 )^4 
VI. Prorfus eodem modo valor medius producti y° 7j° (x° 
4" s ° £° 4“ etc » ) eruitur 
= (> 4 — 5/4 4 )2(6/3 (ac« 4-6/34“ cy + etc.)) -f ( ? 4- o 
dein valor medius producti z° <T° ( x° -|- y° jj° z o e t c .) 
= C^ 4 — 3.A* 4 )2(cv i («a 4-fej34-«yf : 'etc.)) o) ^4 
et hc porro. Hinc per additionem prodit v\alor medius quadrati 
(x°? 0 4-y°il 0 4- *°S° 4- etc, ) 2 
= (>' 4 -3/4 4 ;2iCacc4-^/3>4-cy4-eit) , ' i )4-Cf’p4-2'p) i u 4 
VII. Omnibus tandem rite collectis eruitur 
N ~ (7t~2§)v* 4- (TfTt — 7t~ Z7t§ 4- 4p 4- gg)p* + 
(y 4 — 3 /¿ 4 ) S((«a4-ij34-cy4- etc.) 2 )