432 OpuSCULA 



I6m'4-2R"J4-12 -im^-hGin^l Am'-^-Cvn-^-^ im^+Gm+l Am'+IOm-^-G 

 2 ~ 5 ' 2 + 2 *" 2" • 



Igitiir unaqiiaeque formularum 



1Gm"4-4w 1G«r.4-12m-H2^ 16m'+20»» + 6 16/rt'-f-28 ;«+ 12 



dccomponi potest in quatiior nntneros triangulares. El qiio- 

 - , 1t;,-ji'-f.4m, 16w'+12m + 2, 16nr-l-20/»_f.6 



mam torniulae ' ^ ' -— » 



2 2 2 

 16w»'-H28m4-12 . , 

 ^ — omnes numcros triaugulares comprchendunt- 



ergo 



THEOREM A VIII. 



Omnis numerus triangularis decomponibilis est in qualuor 

 imnieros triangulares. 



Forniulis supcrioribns conslderatis, facile apparebit nume- 

 rum quemcimiqne trinognlarem constare tribiis numpris Irion- 

 gularilms aeqiialions, et quarto numero triangidari i!lis con- 

 liguo vel aniecedente, vel subsequeutc, scd aggregatum duo- 

 rum numerorum iriaogularium, qui contigui siut, est numerus 

 quadra lus, ergo 



THEOREM A IX. 



Oninlj nnmcrus triangularis compouiiur nuraero quadralo, 

 alque duobiis numrris triangnlaribus. 



Reapse £irnplicis?iaia rcduclione obllnemus. 



IGin^ + im , , Am''-\-'2in 4 nr-!- 2 ;» 



= \r.i Ar 1- 



2 2 2 



16m--J-12m+.2 . - . „ 4;ji'4-2.7/. lm'-H2w 



2 2 2 



16 7n'-}- 20 TO + 'J , , , , , , , 4«'-f.«,«4.5» , 4to'-1-6w4-2 



2 T-T-T- 2 2 



16m'-{-23f7i+12 , ,. Q , , , 4 ,»'+ 6 n; -t- 2 . 4m'4-6m + 2 

 2 -T- -T" -r ^ -r 2 



Series Dumeroiuna iriaugularlum in quiuquc quae scquun- 

 tur decoiuponalur. 



