DE PROCRESSIONIBrS HJRMONICI^. 155 



/3 = I -f- 1 - 1 -f- 1 -I- 1 - §H-i-f-|-i-|- i, -^Z, - ,^ etc, 

 /^^i-Hi-f-y-l-M-H^-f-i-H-^-l-^-l-rT-^ etc 

 / 5 == I H- = + 54-i - 1 -i- ^ H-7-+-^+5-/5-}-TT-i- ,'. etc, 



/^ =: I -i- ^ -i- IH- l-i-^-l-\-j-h^-hl-{-^o-^u - i^ etc. 



etc. etc 

 Vnde pro cuiiisuis numeri logarithmo fiicile feries con- 

 uergens inuenitur. 



§. 9. Ex his feriebus aliae eiusdcm formae , quae 

 fummam habeant rationaiem , polTunt deriuari , Nam, 

 quiii feriti — /n duphim aequale ell /4, fi feries i -|- 

 i-l-i-i etc. fubtrahatur ab liac 2 — i-|-| -|etc. refiduum^ 

 nempe haec feries i -i-f-lH-H- , -5 etc erit ~o, 

 feu i — i-fi-i-i-H-iH-l -f-i- /g etc. Similiter fi 

 feries / 6 exhibens fubtrahatur a fumma lcrierum /2. et 

 /3 exhibentium , refiduum , nempe i -l- !-{-{- l--\-l 

 H-7-;-|-t"o etc. erit =0 Ibu i — i-f-|-|-i- i- |- 

 i -h I -t- i -h yg etc. Pari modo huiusmodi fenes in- 

 numerabiles poterunt inueniri. 



§. 10. Serics illae log.irithm.os exprimentes con- 

 uergunt quidem , fed admodum tarde , quare, quo ea- 

 rum ope logarithmi commodc erui queant, requiritur 

 aUquod fubfidium. Ad quod inueniendum notari opor- 

 tet eas feries non aequabiliter progredi, fed certas ha- 

 bere reuoUitiones , quae tot termuiis ab(o{uuntur, quot 

 n habet vnitates , tot igitur terminos fimui fumtos vnum 

 feriei membnim vocabo. Ita in feriei pro /2 duo termini 

 conftituent vnum membrum , in ferie pro /3 , tres, in 

 ferie pro /4 quatuor et ita porro. Membra igitur irta 

 V 2 aequa- 



