'214 OptJSCULA . 
tdy — d)>iy \n qua ^NT dabitur per , dy ^ clt ^ & conflan- 
t€S, fed ita, ut differentialia linearem obtineant dimenfio- 
nem . Si in formula hac inventa methodus exiftit ieparandi 
indeterminatas 5 ut ah'quando accidet , res erit perfeda j fin 
minus, noftra methodus quoque deficiet . Verumtamen per 
illam aequatio, in qua differentialia affeda funt exponenti- 
bus quibufcumque integris , vel fradis , reducitur ad aequa- 
tionem , in qua differentiaiia linearem tantum obtinent di- 
menfionem . 
XLVIII. Exemplum unicum propono . Sit xquatio 
ydx ^ ay dx^ hy^ dx^ ^ cy'^ dx^ 
Fiat X — ^tdy , & dx ^ tdy y fadaque fubftitutione erit 
^tdy ■=!. yt ay^t^ H- hy^ t^ -t- cy"" t'' ec. , & different'ando 
tdy tdy -Ar ydt-\- lat^ ydy lay^ tdt -f- ^ht^y^ dy -f- ^hy^ t^dt ec. 
five 
— ydt = lat^ydy -f- lay^tdt -f- ^ht^ y^ dy -j- ^hy^ t^ dt ec 
in qua , quoriiam licet feparare indeterminatas , utilis effc 
methodus . Fiat igitur yt — z , & — ^ — - , & erit 
~ lazdz -f- 3 hz,^ dz H- /^cz^ dz> ec. , five 
— dt 
= 2adz, H- ^hzdz H- /^cz'^ dz ec. & integrando /A — - 
It =: laz ^ -^hz^ ~ cz^ ec. , in qua , quando habentur 
incognitx feparatx , conilrudio eil in poteftate . Uxc dida 
o , ut appareat , non omni methodum utilitate carere . 
VI N- 
