Opuscola 4i5 



ALOYSII CASINELLI 



Disquisitiones anaUiicae de numeris triangularibus. 



N .• , • 



X 1 iiraerorutn iriangulanura nolissima scries 

 D, 1, 3, 6, 10, 15, 21 , 28, 36, 45 etc. 

 in tres, quae seqiiuntur, decomponatnr 



, 6 , 21 , 45 , 78 ccc. 



1, 10, 28, 55, 91 etc. 

 3, IS, 3G, G6, 105 etc. 



Harum serierum termini generales sunt, 



9 m'-\- 3 m 



primae ^ 



9 m' -4- 9 m 4- 2 



secundae 



teniae 9^'-+- 15 m 4- 6 



Ponalur 



2 



9 to" 4- 3 m TO'-f-(2/i-|-1 )m4-7j'-+-A 



2 2 



+ 4 m' -I- ( 4 i-f- 2 ) m +*'-M 

 2 



4_ 4 m'4-( 4 g-+-2 ) m -t-g"- 4-g 



■2 

 curaqiie haec aequalio suljsistere debeat pro quocumque va- 

 lore quantitalis m, erit, tbeoremale carlesiano 

 2A4-4/C-I- lg-H5 = 3 

 7.'4- A + A=-hX ■+■§'+ g = . 



Resolvanlur hae aeqnaliones numeris integris *, ac prlmura, 

 ejecta ex ipsis quaniitate h , habebimus 



5 5 



