++ DE SERIERFM 



pofito X — o fiatj — I. Q^r.icflio it:i.]uc pcrducU 

 elt ad reloliitioncm ifliiis ;ieq.iati()nis dilfcrenciiilis , qii ic 

 non (bliiiTi intinito teriTiinornni niimcro conlbt , (ed ct- 

 iam omncs di(fcrenti:ilinm gradus in l"e complcditur. 

 Q;iia vcro variabilis j vbiquc plus vna dimcnlione nou 

 habet , et alteriiis variabilis .v non nifi ditTlrcntialc cf x , 

 quod conftuis e(\ airumtum , occurrit , hacc acquatio co 

 modo tradari potclt , qucm in Mijcell. Berol. Tom. 

 VII. expofui. Formetur igitur poncndo z loco £, » 

 z" loco Jfi ct gcncratim z"" loco j^y/acquatio Algcbraica : 



ctc. 



[ .1.; 



quae fumto e pro numcro cuius logarithmus hyperbolicus 

 zr I , tranfit in hanc (()rmim finitam o — t? ~ — i. 

 Hnius iam acqu.itionis omncs radiccs, quarum numcrus e(l 

 infinitus , inueitigari , fen omnes fadorcs formulae c^—x 

 afllgnari oportct. E(t vero ^* — ( i -f- 1 )" , pofito n 

 numero infinito , qui valor , fi (iibflituatur , habcbitur hacc 

 formula refolucnda ( i -|- ^ ) " — i , cuius quidcm vnus 

 faftor fimplcx e(t ~ ^ (hi z : qucm acquatio infir ita 

 ftatim monllrat. Ad reliquos inucniendos in (iiblidium 

 vocari dcbct Theorema , quo demonftratur f^rmulac bino- 

 miac a^ — b^ fi(florcm e^Tc a a — ^ a h coi'. -„ -\- b b 

 denotante k numcrum qucmuis integrum. Praefcnti ergo 

 cafu e(t « — I -4- n ct /; rr i , vnie f irmulac pro[->ofi- 

 tae f* — I omncs fa(ftorcs contincntur iu hac f )rma 

 gcncrali. 



'-HV*-l-^^-2(i_f-^)cof:'r-f-r 



feu 2 ( I -h ^ ) fin. '„ -h*i : vndc himc f;i(ftorcm per 



quan- 



