AEQVATIONIS DIFFERENTIALIS. 221 



rydx^-^^^i A^Q_+ B^R+ CS+ DH^) 

 qadjdx'-.&e A^Q+/ B^K+g C^S+iD^T) 

 ^raV^^x^-^-^C^^A^^Q^+fB^R+^^C^S+i^iyT) 

 |;^VyA:=z^(^^A^Q4-/"'B^R+g'C^S+i'D''T) 

 a* /j' :ii^(^^A^Q+/^B^R+g^C^S+i*D/T)+X^x'Xr A^ 



+/^B/+g'C^ + i^D'') 



QimiTiuis enim difFerentlando ay inueniatiit: a: dy 

 :=: dx [e A''Q_4-/Ba<-f-g C^S-i-iD/T)H-^X^a-(A/-f-B'' 

 4-C''-+-D'') facile tamen colligi poteft, quod ^^dx 

 non ingrediatur dy ^ fic enim valorem ipfms a ddy 

 ingrediretur dyidXy quod quum non contingat fla- 

 tuendum eft , quod fit A''-+-B'-hC''-f-D'' — o. 

 Similem ob rationem 'X.dx^ neque ingredietur 

 valorem ipfius d^y , nec ipfius d^y , in differentiali 

 vero d^-y neceflum eft Yt X^x reperiatur , alioquin 

 enim non fieret a^dy -{- ba^ d'ydx ~\- ca^^ddydx* 

 ^qadydx'~\-rydx*i:zXdx\ Seorfim itaque con- 

 fiderando terminos, quos fub determinatione difFeren- 

 tialium dy,dy,d'y inuenimus — o et terminum , 

 qui determinando d*y prouenit :=: i , fequentes 

 liabebimus aequationes , inueniendis A^>B^,C^jD'' in- 

 keruientes nimirum : 



A^-l- B^4- C^^- D^no 



e'A'^fB'-\-g'C'-{-i'D'z:zi. 



E e 3 Dam 



