4i6 Opdscula 



ciii aeqnationi evidenter satisfacinnt ^==0.^ = 0, atque inve- 

 uicmus h-^ — 1 . 

 Erit ergo 



9 m'+ im m' — m 4 to' -4- 2 m 4 m''-\~ 2 



in 



, . m" — m 4 m''-\- 1m 4 m'-|- 1 m 



sed numen — y- , ^| , ^ 



sunt triangulares j ergo omnes numeri triangulares in formula 

 9 TO"-4- 3 TO . . , 



2 conic nti, uecouipom possunt m tres numeros triangu- 

 lares . 



9m'4-9m+2 to''4- ( 2 A +. 1 ) m + A'-t- A 

 Ponatur = ^ 'y ' 



4- 4 m'^ ( 4 t ■+. 2 ) TO -<- A'+ A- 

 2 



+ 4 »t'-4- ( 4 g -I- 2 ) m + g'-f- g 



2 

 Erit igitur 



2/i4-4^-H4g4-5=9 

 h'+h -4- ^'-4- A- 4- g'+ g = 2 



quibus aequalionibus salisfaciunt h-=o, k=i , g:=o. 

 Ergo erit 



9 ra"-4- 9 TO -f- 2 m'-\~ TO 4 TO'-t- 6 ffi -f* 2 4 to'-|-*2 m 



2 "^ ^2 ^ 2^ 



_ , . fn'-f- "» 4 m'-4- 6 TO -H 2 4 to'-U. 2 to 



Sed numeri — ^ — ' ;: » 



2 2 2 



sunt triangulares*, ergo omnes numeri triangulares in formu- 



9to'4-9to-4-2 . 



la ^ contenti, decomponibiles sunt m tres nume- 

 ros triangulares, 



_, 9to'-H15to4.6 TO^-f- ( 2 a -+. 1 ) to 4- A'-f. a 



Ponatur — — = S ^ V- — - — -I^- 



2 2 



+ 4TO'-K4^ + 2 )iw4-A''+;t 

 2 



4 '4TO°+(4g4-2)TO + g'4-g 



2 

 ct erit 



