DlFFERENTIO-DIFFERENTIALIS. i35 



ifa Tt hic pro i fcribamus f-4- a — p. Q110 fado 

 vt ambo valores ipfiu9 g congruant fieri neceffe eft 



SLli-^-aYab^izi^ZoL— i^ae-bc^—^iiab-^-^zir^-i^iae^-bc) 

 et 2(i~{rCL)ab — ae-\- bc—ziab-^-ae — bc 



cx. qua fequitur aab—ae~bc. In priori autem 

 fcribendo aub Iboa ae — bcy prodit per ab diuidendo* 



z (f -f- a)' — 2 a / — 2 a 0^+ a — z /i + 2 a i + a 



quae cutn fic identica pro omnibus valoribus ipfius /, 

 habebimus a — -^-^^ j. ^^^e expreflio debet efle 

 nuraerus- integer. 



X. Quoniam igitur infinitos vafores pro litte- 

 ra ^ eruimu&, quibus aequatio propofita integratio- 

 nem admittit , atque adeo^ formula algebraica pro sr 

 fatisfaciens aflTignari poteft ;, operae pr-etium eft , vt 

 hos cafus acsuratius perpendamus. Denotante ergo 

 i numerum quemcunque integrum fiue pofitiuum 

 fiue negatiuum , euolutio prior §. 7. fadia has duas 

 conditiones poftuiat :- 



n{n.— i)b -\-ne-\-g-=^G er 

 [n •-'i)(n — i- i) fl H- (« - iyc-^rf^ o 

 cx- quibus deducitur r 



„ . & — cH- vc(& — p)*-*^g) ' er ' 



ib 



n — i -- g — c -I- V ((^^ -_gl!jn:i££) vnde iit 



. 6c — ae-j-o V((& -f)^ — + & g^ ^6 ■/((a -• c)^ - 4 a/) 



t ' ~^^ ' 



Quoties ergo haee fbrmulh 



qc — ae^a V ((&-g()' — ♦ 6 g) - & Vi {{a — cf - 4-^0/), 

 ' iub 



R 3; "^i» 



