OPUSCDIiA 417 



qulbiis aeqnallonibus salisfaciunt g= 1 , k= i, h=\ , iincle 



9m'-4-15m-|-f; m'+3mH-2 4m''-4-(Jm-t-2 4w'_}-6m-4-2 



.-^~ L_ 



Sed 



2 2 2 2 



m'4- 3 m -t- 3 4 "»'4- 6 ;» -f- 2 4 m' -f- fi m 4- 2 



2 ' 2 ' 2 



sunt numeri triangnlares^ ergo omnes numeri triangulares, in 



9 rn ■-)- 1 5 nj -f- (J . , 



^•ormula r contenii, decomponi possunt in tres 



numeros triangulares. 



Lum formulae , ■ « , ^ 



omnes numeros triangulares comprehcndant, et carum una- 

 quaeque decomponi possit in Ires numeros triangulares, con- 

 cludcre possumus hoc. 



THEOREM A I. 



Omnis numerus triangularis potest decomponi in tres nume- 

 ros triangulares. 



Tribus aequationibus 



9 in'-\- 3 m m' — m 4 m'-f- 2 m , 4 m'-4- 2 m 



■ ;= I ' •+- . 



2 2 2 2 



9mM-9w_+2__m'-f-TO 4m'-t-6m-f-2 4 m'+ 2 w 

 2 2~""^ 2 ' 2 



9 «i'-f-1 5 TO -t-G_ ;n"4- 3 '" -H^ 4 m'-f- 6 m -4- 2 4 m"-f. 6 m 4- 2 



2 2" 2 "^ 2 



addalur quarta 



9 m'-t- 2 1 ,» -4- 1 2 _ m'+ TO 4 m°-4- 1 rw -4- 6 4to'4-10;;i -+-(5 

 2^ _~ 2 _ 2 ' 2 



quae emergit e prima, posito m-f-i loco m. 

 Addilionc primae ct sccundac habemus 



9 TO -4- o TO + 1 =: TO -4- 4 TO 4- 4 m 4- 1 -4- -f. . 



scilicet 



T. II. 53 



