?1 



c 

 1 



2 



3 

 4 

 5 

 6 



= 50 =r 

 (r -f-x -f-xx)" 



1 



I -+X +-XX 



i-t-2X-^-5xx-H ;x'-+x* 



I -H 3 X -»- <Jxx -f- 7 x' -+• 6 x* -^- 3 x' -^- X* 



1-H4X-HICXX— l6x^-Hl9X^-Hi6x'-»-lcx*-H4x'-«-X* 

 I -+-5X +-i5XX-3cx^-+-45x*H-5 1 x'H-45x'-(-3cx^-f-etc. 



I-H6x*-2lXX-f-5<^ xVpcX*-^-!^ 6x'-f-l4l X'-l-I26x -HClC. 



etc. cic. 



Kx LiUimo cafu, 4110 n — 6, patet igitur efTe 



ay=i- i^,y=:6- {iy=.i; (iy=5c- (5y=9c- 



{iy=i^6; (ty=i^i; {',y = i:6; (iy = 9c; 



{iy=}c-{s^y=2:; {^y=i6- (a)^^,. 



5. -. Vt nunc invertigomus quomodo lii cliaraflcrcs 

 ex triiiomio orti pcr firailcs charaflcrcs e\ binomio ortos ex- 

 primi queant; poteftalcm propofilam fub forma binoini.ili 

 rfpracrcntemus hoc niodo: fi -|- x ( 1 -|- x)]", cuius evohilio 

 ergo pracbebit Jianc pror^rcffjonem : 



i-+-(i)^^('H-a^)-+-(E)'xx(i-f-x)=-f-("3)'x'(H x)^ 

 -h(")^x'(i-f-x)'^-elc. 

 cui.is tcr.niinus gcncralis hanc habcbit forinam : (-' ^x"* 

 (n x)'. 



5. 8. Coiifjdcrt mus nunc jno cvolutionr piopofita 

 potcftatem ipfius x (piamcuncjuc x", eiuscpu; coclVicicns 

 eft (-^)', cuius valoicni invcftigcmus. Jlunc in fincm 

 fX fingulis mcmbris binomiahbus modo invcnlis (lcjnonii 

 debet potcftas x*^, quatcnus cp id in in iis contiiiclur. For- 



