q56 



unde substiiutis in formulis generalibus pro z qi s inventis valori- 

 bus a, af, a" ^ a"' prodibit terminus generalis 



^z= 1 + 7 C-=~) + 12 C-Y-^) + 6 (:Li^J) ~ ,,3 



et summatorius 



.^e + re^ 12(1-) -4-6 ©:::.:ii(:^-i)!. 



4) ^rf numéros biquadratos. 



^. 2 4. Pro horum numerorum progressione differentiae ita 

 se habent : 



b'zzzdB 16'''— 110 



rf'rizSôg irf''' = 302 

 e' zn-àl { I etc. 

 etc. i 



b'" =18 4 

 c"' =: 1 8 



etc. 



6"'ir:24| etc. 

 etc. 



«=z 1 



6::^= 16 



c =: 8 1 



J :=:: 2 5 6 



cr:c 625 



f^z 12 9 6 

 etc. 



quibus valoribus rite substitutis terminus generalis elicitur sequenti 

 modo expressus : 



^::^l^l5C-=i)^.50C-:^)-^60('i^)-^24('^J):rz;z* 



terminus vero summatorius ita : 



.= (!)+ 15(1)4- 50(1)+ 60(1) -H 24(1), 



quae expressio reducitur ad hanc formani : 



, 6n« -+- iSn' -4- lOït' — n 



^' — 30 ■ ' 



sive per factores ad hanc : 



^ n(n -)- 1) 1,2 )1 -H 1) (3n- -u 3n — 1) 



31) 



Hinc sequitur si summa 7/ primorum numerorum biquadratorum di- 

 vidatur per summam n numerorum quadratorum , quotientem ex 

 hac divisione natum fore —i • 



