De aequat. algebricis 



475 



£, . ..n 



(h' n,2/i)=(//(^4-1>+1) 



(//•« + 2 Zt— 1) . . . //'n ,/ „l'-*-i 



2...(2A-<-1) 



M N 



(//•«, 4/i)=(//(/i4.1)N-M ) V __i i^ ' M N 



4 . . . ( 4 At 4- 3 ) 



etc. 



etc. 



etc. 



(") 



/ 



Inductione iaveniemus quoque formam aequationis esse 



X 



h(b-i-1>iH-1 



— A X 



bhn 



— B X 



hlin-h 



— C X 



hhn-2h 



etc. 



h(l,_1)n_1 h(h-1>-h-1 h(h-<)n-2h-1 



— A X — B X — G a: etc. 



h(l.-2>-2 l<h-2)n-b_2 U(h-2)n-21— 2 



—A x — B X — C X etc. 



m.-3)n-3 Kh-3Jn-b-3 hCh-3>-2b-3 



— A x — 13 X — (j X etc. = 0. 



etc. 



etc. 



etc. 



(h-1) hn-h^i (h-1) bn-2h+1 (h-1) hn-3h+l 



— A X — a X — L X etc. 



Aequailonibus auxiliaribus notae fiunt quaniitales 

 ikn.l) , {Zhn,2) , (3^n,3) , (,4k n, 4) etc. 



(hr,,h + ^) , {^hn,h^2), (Zhn,h^Z), {4h n,h ^4) eic. 

 {hn,%li^\), C2 /« n, 2 ^4- 2) , (3A«,2/i-t_3), (4 A n, 2 A -M) etc. 

 {hn,-}>h^\), (2/in,3A4-2), (3/i n, 3 A -+- 3) , (4 A n, 3 /* -|- 4) etc. 



etc. etc. etc. etc. 



{[k'-lh)n,h-Z), ((h'-2h)7,,h-2), {(h'~h)n,h-\), (/,'«,/,). 

 ( (A--3/0«,27^-3) , ({h'-U,n,U-2), {{h-- h)n,2k-1) , (f>'n,2/t). 

 {{h'-Vi)n,U-Z), {{h'-2h)n,yi-2}, {{h'~h)n,Zh-'[) , {h'n,Zh). 

 {{k'—Vi)n,4fi—i), {{k'-2k)n,4h-2), ( (//'— A)«,4A_1), {h'n,4k). 



etc. etc. etc. etc. 



qmbas regula praescripta dcfiniunlur coefficientes aequationis 

 T. V. 60. 



