( 208 ) 



hfncqiie fit C = / 3 — B z= / 1, 

 A-hBh-C-+-Dii= n- 1 -t- 1 H- 5 

 -A = -I 



A-HBH-C-+-Dl=I-(-l-t-|H-5-l-|-H|-+-|-f-;-»-|-»-/5-^/l-Hll-H . . . . ' 



4Tt 

 I l 



3 • • * • n. 



B^-C-+-Dm-^1-+-| — ?-K^-t-|-^-^-t-+-i-+-/,-Hi'i-ii-+-ctc.=:/4. 



confequenter Dnz/^. — (Bh-C) = /3, 



Q. E. D. 



Corollarium. 



§. 8. Cum igitur fit 

 A-hB-hC-hD-+- etc. — /§-f-/i^-/|-»-/|-t- ctc. 

 fiue ctiam 



A-+-B-+-C-+-D-+- etc. = / T-^.3.4.;. ■ ■ ■ m-^T) 



o. 1. ^. i- 4^ . . • n ' 



fcquitur fore 



A-4-B-HC-f-D-H etc. == / ^ -H / (« -H i). 



Eft vero A=/i=z/;7, ergo B -+- C h- D -h etc. r /(«-+- i) et 

 A— (B-f-C-+-D-+- etc.) =/^-^=10, 



ideoque 



Ar=:B-+-C-4-D-HE-+- ctc. 



Summa igitur omnium tcrminornm ferici harmonicnc naturalis 

 ab I vsque ad J aequalis elt fummae omnium tcrminorum 

 fcquentium vsque ad — : diffcrentia enim intcr ambo hacc in- 

 finira /« et /«-+-1 videtur nulla. Interim tam.en non praetcrc- 

 unda c(l obfcruatio, in integratione formulae ^^ ncgledam 

 fuiffe conftantcm, qua adieda erit A — /«-i-C, hincquc 

 A — (B -<- C ^ D -+- eic.) zz:C, 



cnius littcrae C valor cft C = o, 5 772i5<^<^49- ^^^ <^'^^" 



rentia inter fummam feriei harmonicac naturahs ab i vsque ad 



I 



