IIVSQVZ rmvs AtlQVOT 43 



CAPVT II. 



De Siinmtatione Serierum coUectiuarum. 



i7-^'l alicuius fenei coliediuae differentia origi- 

 ^^3 ""^Jis niliiio aequalis eft , quilibet terminus 

 in ea ferie erit fumma omnium terminorum qui funt 

 in ierie prioris ordinis : Ex. gr. lit 

 Radices 0123 4 5 



Prior feries ~ ojjiS^a 80 135 

 Pofterior zrz o \ $ i.^ 6$ 145 280 

 Qiiartus terminus in ferie pofterion 145 eft— 80- 

 5 2 -f- I 8 -f- 5 . lioc eft , aequatur liimmae omnium 

 quatuor terminorum prioris feriei •, id quod intel-' 

 ligitur ex conftrudione ipfarum ferierum(§. 3.) 



18. Qiiod fi ergo formula alicuius feriei ge* 

 neralis proponatur , transmutetur illa in formulam 

 fequentis feriei in qua \ltima differentia originalis 

 nihilo aequanda cft, lic haec noua formula erit prio- 

 ris fummatrix. Ex. gr. fit propolita haec feries. 

 5. IX. 19. 29. 41. $$. 71. 89. cuius generalis 

 terminus eft — .v--|-3.r-+-i pertinens ad generalio- 

 rem formulam tertii generis (|.v--f-''-±^.v-}-t-}, erit 



proinde hoc in cafu ^— 2, b—2. et c—i. Qiiarti au- 

 tem generis formula eft ^x'^-^- °-h5 y 2 _|_ ; a-4- 3 &h-6 c ^ 



^o. fubftitutis ergo fubftituendis habebitur fura** 



3 2 



matrix =r^.r^-|-2.Y=-!-^a— *-±lf^-±iif. Verbigra- 



tia, fi fumma feptem priorum terminorumexpeta- 



3 2 



tur , fiat io formula .m.7. vt abeat in •? -4-6.7^-8.7,, 



F a ^" = 



