52(5 Petri Callegahi 



j(i)^_..._Hi ('')J=LKo-t-... -1-1^-1) J-4-Li(<)-H....-+-i (''-')J-f-...-+- 1 . 



Posito n = 2 habehiiiuis 



tm — 1 ~i rm — 1 n pm — 2") 



1 (i)-Hl (2)J=ilO). J-HLlcnJ-f.....-t-1 ; 



idcirco series niuuororiim naluraliiim exsiirgct , si successive 



poiiaUir 77J = I ;, =2 , =3 J videlicet numeri figurali sc- 



cundi ordinis habenlur , qiii generaliter denolati eruut e for- 

 mula 



[l (1)^1 (2)]. 



Igltur manifeste patet nuineros figuratos secunr/i ordinis (([ui 

 triangulares eliam appellanlur) ex successiva additione nume- 

 rorum priini ordinis gigni. 

 Si fiat 7z = 3 , erit 



[l(i;_H^T2;_f-i(3)]=[i(iT-+.i(2)]-K[i(iT_i-i(2)]_H. . .-<-l . 



Hinc numeri teniae seriei deducunlur , posito successive ?n=1, 

 = 2 , = 3 , cnjus terminus generalis denotatur ex 



[l(1)_Hlr2)_Hl(3)]. 



Interea liquet, ex additione successiva numerorum naturalium, 

 seu secundi ordinis numeros figuratos tertii ordinis nasci . 

 Ex eodeni processu deduciiur generatim, formulam 



(r,j [iw-H...-Klw]= ^2/3 ;^„_,)^ 



denotare tei'niinum fn"""""" figuratorum numerorum ordinis 

 7. Ex aequatione (C), subsiituto n-t-i loco 7^, eruiuir 



p m — 1 -1 r m — 1 -i r m — 2 -t 



(D) Li (' )h- . . . -j-1 ("+1 )J=Ll (1 )-f- . . .-t-1 (")J-+-L1 (^ >•+-• • -Hi '■")>+- ■ • -+-1 



;«(»j_j_l) (w-+-« — 1) 



~ 1 .2.3 « ' 



videlicet 



« Summam numerorum m figuratorum cujusdam dati ordinis 

 « 7i"""' aequari numero in"''"° numerorum figuratorum sub- 

 « sequentis ordinis (n-t-1 )'"""• 



