19^2 OBSmVATlONES DE CASIBVS 



'Demonjiratio. 



Ponatur j'r:^^.r^-f-7/, fiet 



m^-'dx ^ -- - ax^-'dx 



bjxUx— ^^x^-^dx-\r-hux^dx 



cy^dxz=. tJ-x dx-^-^^ux dx-^cu dx 



- ify— du-^ax^^^dx^ 



qu3e eftipfa ceqiiatio E, fi pro u ponatur^, atque fimilU 

 ter , d iiliqua lEquatio integrabilis revocari polTit ad B 

 demonftratum eft xquationem A efle integrabilem. 



Exempl I. 

 Cum xquatio ax^-ydx-^-hyx^dx-^-l-y^-dxzzidy, ■ 



fit integrabilis (fit enim J— =^y ' ) erit etiam 



(^^y'%x-\-i2b^yx^dx-^-±y ' dx-dy inte- 

 grab. qujE sequatiorevocaripoteft adhanc formam 



^^fb^-^^c^^bVb ^^ac ^x-\-hrx^^-^'''^-^^^^_^l_.dx 

 -^cy^^dxdy. 



undeeruitur^f-'±li.zi!!l^ a^ ''^ * 



Exempl. 2. 



_2&— flc -_&_a<; 



Quoniam acquatio ax ^~ ~ dx-hhyx'"^ dx 

 •^cy^ dxzzdy 



eft intcgrabilis , (fit enimjm^x *• -^x ) 



crit 



