(202) 



fumm.im terminis fibi inuicem verdcaliter fubfcriptis, ob « 

 numcrum infinitum, omnes eius potelhtes praeter fupremam^ 

 in numeratoribus cuiusque membri delet, 



§. 5. Quo Ledores, qui librum citatum non prae ma- 

 nibus habent, completam fibi iuftamque metliodi ab acutifllmo 

 Fontana adhibitac ideam formare queant, fimulque pcrfpiciant, 

 quomodo valorem indagare liceat illius feriei , ad quam tan- 

 dem hac operationes ducunt, tertiam heic fummationum mo- 

 do expofitarum, ad mentem laudati Audloris, demonftrabimus, 

 poftmodum vero aliam methodum illas fummationes demon- 

 ftrandi, ex fingulari principio deriuatam, cxhibebimus. 



§. 3. Sit igitur fummanda haec feries harmonica ex 



infinitis terminis infinite -paruis compofita : 



I 

 • • — 9 



2n-Hi i7i-t-2 2n-(-3 »n-|-4 j n. 



et fingulos terminos feorfim euoluendo prodit 

 ' — - — -. H- .-. — -i-7 -H ctc. 

 = r^-r4. + .-^. — 4^+ etc. 



»n-f-2 171 4n* ' 8nS 16 n* 



_-L_ — -1- — J_4--3i— Jl_-4- etc. 



in-f-3 in *n' ' in^ 16 n* ' 



' — j_ — j i- _il jtL- -u ctc. 



3n-f-4 2n 4»' I n* 16 n* 



etc. etc. 



vndc porro, tcrminis fibi inuiccm fubfcriptis in Vnam fum- 

 inam collcdis, nafcuntur fcquentes feries: 



~\- ±. (1 -{-i _4- I _j_ I _j- I _}- etc), 



— 4-lv> ^^ + ^ + 3 4- + -+- 5 -H ctc), 

 ►H ,-^ (r-{-2^ + 3'+4' + 5M- etc), 



— ,-;-4 (1 + ^' + 3' + 4-' -h 5' -i- ctc), 



At 



