52 DE COMPARATIONE 



fimulquc eft integrale completum huius aequationis 

 ci.Fcrentialis : 



d_x dy 



© — ^^V;v4-2B.-+-Cji*-+-:DxI-+-Ex*)-I-:+;V(,V-4- By-+-C;>-f-2D>»-t-E>*) 



quia conftiintem arbitrariam M inuoUiit , quae ia 

 aequatioiiem diffjrentialtm non ingreditur. 



Inueftigatio cafimm, qiiibus formula 

 ^j^ _t_ Q^^^ fit intcgrabilis. 



16. Dcfignat hic P fundlioncm ipfius x et Q^ 

 fimilem fuiKflioncm ipfius y, ct qu^i hacc formula 

 intgrabilis effe dcbet , fit V cius intcgralc , vt ha- 

 beamus ; 



Cum autcm fit 5^+-^-— o, idcoque ;^— — ,ent 



i,j _. ( P-Q,1dx (P — a)dx 



Cafus er^o inu:ftigiri oportet , quibus haec formula 

 intcgrationcm admittit. 



17 Qiioniam vcro nulla cfl rat'o , cur hic 

 difforcnt alc c/x potius mfit, quam ^r, tcrtiam \aria- 

 b !l~m introd -camus , quac ad \tramquc acqnalitcr 

 rcfcratur , fiquidcm (luantitas V vtramque aequalitcr 

 inuolu.re dcbct. Sntuamus crgo .v-f-rrrj', ct in 

 acquationc diffcrentiali ( <§. 7) pro ((v icribamus 

 ds — dx^ ficque prodibit : . >» 



. or: 



