INDEFINITJM ELWANDO. 171 



m fuccefliue ponantur m — i,m~2.,m-3 - - - coeffi. 



cientes A,B,C, D - - - diuerfos quoque induere de- 



bent valores. In pofterum valores iftos , hac tatione 



indicabo , Yt 



m refpondeat A m , B m , C m - - - - 

 m-T - - - A m ~\ B™, C m ~> - - 

 :*»-a - - - A^S B m - 2 , C m ~* - - 



r - - - A r , B r , C r - - - - - 



"vnde probe notandum, nifi aliud monuerim , expreflio» 

 nes huiusmodi A r , Br, C r - - hic mihi non denotare, 

 Yt alias folent, potentias iftas harum literarum, A,B,C, 

 neque r hic effe exponentem potentiae , fed indicen^ 

 <ex quo , ad quemnam ipfius m -valorem quoduis 

 A,B, C, pertineat , determinatur. 



5) Suppofitis his, cum fit per "hypothefm (x+if 1 

 -zzA m x m -+-B m x m --'-\-C m x m - 2 -hD m x m - 1 - - - erit 

 ( 2 ( ^ -4- 1 ) ) m — 2 m A m x m -hz m B m x m -' -f- 2 m C m * m — 2 

 -f-a m D m r m - J - - -.. Eft vero quoque , (2(x-f-i)) r 

 z=:(( 2^ + 1)4- i) m , vnde necefle eft , st fit (2(^+1))' 

 t=- A%2.x -f- 1 ) m -f- B m (a x -f- 1 f-^C"^ x-t~ 'T^* 



-i-D m (2.v-f if-^. - 



•6) Euoluamus feorfim , potentias ( 2 x -f- 1 ) w , 

 (zx-hi] } m ~\ (2x-\- 1)™— 2 - - - in feries, ac erit 



{2x+i) m ^:2.™A m x m -\-2 m -*B m x m -^n m -*C m x m - 2 -\-'2 m - 3 D m x m ~< - - 

 (2*4- i) m ~ 7 := - - - +2 v ~ , A m -'x m -'+2 m - i B m ~ l x m - 2 -{-2 m - 3 C m ''x m ~* - • 

 ( 2 j+ir-'r _-..--. .+2 m - 3 A m - 2 x m -*~h2 m - z W l - 2 x m - 3 -- 

 (ax-f i) m_I ~ -------- . +2'"-*A m - J x m - 1 - - 



Y a Quodii 





