±1 METH. INTEG. FORM DIFFERENT. RATION. 



tot conftans mcmbris longarithmicis, quot x in dcnomina- 

 torc fbrmulac propofitae hibct dinicnlionci, 



§.19. Ficri autcm ncquit , vt honim mcmbrorum 

 Tllum cuancfcat , icu vc vnquam fiat F ~ o , nifi ia 

 ipla formula ditfcrcntiali propofita communis diuilor nu- 

 mcnuoris ac dcnominatoris cxifiat. Qiiod vt clarius ap-. 

 parcat ponamus numcratorcm fiac"tionis valorcm ipfius P 

 exhibcntis — v hoc c(t A - ^ B -f J, C - ^i D -+- ctc. 

 zz o. Hacc autcm cxprcllio rclLikat cx nunicratorc for- 

 mulac ditfcrcntialis 



A -h B.v -\- C.v' -4- D.v* -h ctc. 

 poncndo - 'p loco .v ; quarc cum hacc poftrema cxprcfi*io 

 fiat — o pofito - p loco .v , fcquitur .v -\- j, f-u i -r px 

 cius diuilorcm cfll- ; hcKquc cafu quo P r^ o ncccfic c(t , 

 Tt numcrator et dcnominator fi)rniulac ditfcrtntialib pro- 

 pofitac communcm habcant diuilbrcm. Contra autcm fa- 

 cilc cucnirc potc(\ , vt valor ipfius P in infinitum cxcrcs- 

 cat eu.incfccntc dcnominatorc 



i^-l) i^-f) (x-,-)(i-;-)ctc. 



quod cucnict fi iutcr rcliqui-, httcras </, r, J, f, ctc. \nt 

 plurcsuc rcpcriantur ipfi p acqualcs. Ponamus cflep^^, 

 lcu dcnominatorcm 1 -i- ct.v -j- (3.v* H- ctc. 

 duos habcrc fidorcs acqualcs , tum in vtraquc fraiftione 

 ,-^ ct ^^::^ numcrator in iufinitum cxcrcfcct. Intcrim 

 tamcn inttgralc ip(iim non crit infinitum , ob bina ifia 

 infinita (c dcfirucntia , fcd fiuitum , atquc adtt) ad quan- 

 tit.ucm algcbraicam rcducctur (|uantiras alias pcrpctuo a 

 logarithmi>) pcndcns. Tridamus igitur modum illam in 

 ic^ralis partcm , quac a duobus fadoribus acqu;ilibus oritur 



dcii- 



