DE SyMMIS DIFISORyM. fti 



fjt « = 7, "it /7 =:/<J -+-/5 -/2 -/o — 12 -I- <f 

 - 3 - 7 r:z 8, et fi fit w — 12, erit /i2~/i i -h/io 

 —/7 -/5 -^fo— 12-+- 18 — 8-<5-f- 12 — 28. 



DEMONSTRATIO. 



Formetiir feries z — xji -4- ^-'/2 -f- :i' Vs + •*" Y4 

 -4- .v'/5 H- etc. vbi quaelibet poteftas ipfius a: multi- 

 plicata fit per rummam diuiforum exponentis eius po- 

 teflatis. Qiiodfi iam fingulae diuifouim funr.mae relol- 

 vantur , m_anifeftum eft, hanc feriem transforman in hanc 

 formam 



-f. »(jcS-j-x'o-+-x'5+x'Oh_x'5-|-<^c. _(_«(x«-|_x'2-+-x"-+-.i(.*'»-KPc"'-+ete.) 



etc. 

 qiiibus feriebus geometricis fummatis fiet : 



2=:— -4-— -f-^-f-^-4-^H--^'. ^- ctc. 

 Multiplicetur haec forma per — -^ , ac produdi inte- 

 grale erit 



-/^rr;/i-.v)+/(i -AU-H/(i-.v*)+/(i-A-*)-i-/(i-;i''j 4-ctc. 

 feu -/ ^ :rr /( I -.v) ( i -XX) ( 1 -A,'* j ( i -.v*j (i -a'} ( i -x*) etc. 

 quae exprelfio poft fignum logarithmicum , cum fit ea- 

 dem , quae in propofitione praecedente vocata efi: rr j, 

 crit — /-— zz: l s, ideoque alterum \alorem pro s fu- 

 mcndo, ent quoque : 



-/5J= =zKi-x-x^x'^{-x'-x'~x'-\-x'-^x** - etc.) 

 Tom.V.Nou.Com. L cuius 



