Oposcdla 4ig 



qui iiuraeros est triangularis j ergo 



THEOREM A III. 



SI nggregalo duoruni nurncrornni triangtilarinm ncldnlur pro- 

 duciiiin coium radicum ininorum, crii summa numerus trian- 

 gulariij. 



Lreneraliler aggregalo — o— + 3 — "^ 2 -17- elc.addaiur 



mn^mp^,iif/^c\.c.-\-iipJif.n(/^ etc. 4-/7(74-610. scilicelsum- 

 ma omnitiiii proclucioiujii ex radicibus ininoribus binis sum- 

 ptio, Iiabel)iiiiiis 



tn'-\-m >r-\~ii zj'H-w 7°-I-'7 



— — H — - — 4-' 4- i-cic. 4-'"n^-''V"^-'"7-l-c•.c.4-"/'-f-''9^-ctc• 



4-^,J,4>ct^•. ^ 



^in ~\- Ti ~{^ 11 ~\- q ~3-. PAc") ( ir -f- ;; -\-p 4- ,7 4- etc. -|- 1 ) 



qui uumerus est triangularis', ergo 



THEOREM A IV. 



SI aggregate plurlnmmimerorum triangularium addantur om- 

 nia prodiicla ex radic'bus minoribus binis suinptis,erit sunx- 

 ma numerus triangularis. 



. , . , . m'4-m , 7j'4-i« 

 Aggregalo duorum nunierorum triangulariura — ^ i -— 



addatur (/?J4_i) (^4- 1 ), productum scilicet ex radicibus 



Jnnjoribus, habcbimus — ^5 H — — + ( »» 4- 1 ) ( » 4- 1 ) = 



(m4-«4-l) (m4-r,4-2) . . • 1 • 

 „ quv numerus esi iriangularjs, ergo 



THEOREM A V. 



Si duorum numerorum triangularium aggregate addainr 

 productum duarum radicum majorum, summa quae cmergit, 

 est uumerua triangularis. 



