1^6 DE INFINITIS CVRVIS 



JBdXy crit dz — Vdx-\-^f{nVdx-Axdx) in qua 

 intcgmtione a conftans habctur. Erit igitur/«P^x — 

 nz^ et fAxdx — ?x-jVdx oh jAdx — ?. Habe- 

 bitur itiique dz — Vdx-}-~(n-i-i)z — ?x)^ id quod 

 prorfus congruit cum praecedentibus. 



§. 25. Retinente P fuum valorem n dimenfionum. 

 Sit z —/A P X dx , \bi A fit fundio ipfuis <7 et X ipfius x 

 tantum. Erit igitur ^—J?Xdx. Pofito d? — Adx 

 -\-Bda, (in quo litteni A cum altera quae eft fundio 

 ipfius a tantum non eft confundenda ) erit «P— A.v-^ 

 Ba. Ipfius PX diflfcrentiale igitur pofito .v conftante 

 crit BXda. Confequenter habcbitur d. j; — ?Xdx-\-- 

 daJBXdx=z?Xdx~\-^ Jin?Xdx-AXxdx). Eft 

 vero Jn P X dx i= f ct / A X .v dx =?Xx-J?X dx - 

 J? xdX. Qiiarc fiet d. ^ z=: P X dx - '-f^" -+- ^-^J^ -" 

 -^^J?xdX. Nifi igitur /P.vr/X rcduci potcrit nd 

 J?Xdx vd prorliis intcgrari , aequatio modularis dif- 

 ferentialis primi gradus dari nequit. 



§. 27. At fi fucrit dzzR/P^/.v, cxiflcntc R fun- 

 d:ione quacunquc algebraica cx a , .v ct ctiam cx z con- 

 rtante, at P fundione ipfarum a ct .v dimerifionum n. 

 Qiiia ell j=J?dx erit d. ^zzP^.v-^^^C-^^-P.v) 

 = ^-^ feu Kadz-zadK-{n-\-x)Kzda — ?K.' 

 adx-?K^ xda. In vniuerfum autem tcncatur, quo- 

 ties z—J?dx ad aequationem modularem rcduci pof- 

 ■fit, totics etiain z:=Kj?dx ad acquationcm modula- 

 fem rcduci pofTe. Nulium aliud enim difciimcn adc- 



rit, 



