Aliae nonkuli-ae applicationes etc. 551 



j«H h/ -\ r-h H/H 1-1=0. 



r /""' J' 



IIujus aequadonis primum niembrum generaliter per S„ deno- 



1 

 teturj posito y-i =z, ex successiva subslitulioue habetar 



S,== -t-1 , 



S5=^5_^.2*_4^'_.3z--^-3^-^-1 , 

 Sc=z«-f.2*— 5s'— 4z3_hGz^-j-3z_1 , 



Bene attendentes coefficientibus comperlinus illos priinarum 

 duarum linearum verticallum esse nuraeros figuratos primi or- 

 dinis; illos duarum linearum subsequentium esse numeros fi- 

 guralos secundi ordinis; et ita deinceps. Hinc scribi poierit 



(A) S„=Jj^n]z JiUnjz _Ll (1)^1(2)].- _[i(iMC2)]3 h4.1(')h-...h.1C3)L 



_ n— 5 -, n— 5 p n— 6 n— 6 ^ n— 7 -, n— 7 



*[l(1)-H...-*-1(3)Jz _|_1C1)-H...*iri)jz _[iri)H....-4-1(4)]z 



Z 



n— 8 - n— 8 



[l0)+...^1(5)]2 H. _0j 



eum sit 



(B) [l(i )+ . . . H-1 0)] = [l (i!U- . . . *1 ('•)] + [l(i)+ . r. *1 ('-o] 

 aniecedeas aequalitas transforraari potest ^ uti sequiiur 



T. TIK 7t. 



