«»>. 



) 9^ ( 



§. 4- Cognita autem forma integralis quaefiti, facile 

 crit pro quaciinque aequatione difFerentio - differentiali huius 

 generis ope integralis fi(fli integrale reale afllgnare. Sit 

 cnim propofita aequatio fimpliciffima haec : 

 '^ '^ * ^ a a tzzz b ^ cuius fingatur integrale 



t — A coi. a z -\-B fm. a z -\- C , eritque hinc 

 11 — — A afin.az-\-Ba cof a z et 



d ■z, 



iAL — — A a a cof. a z — B a a fin. a z ; tum vero 



a a t — -^T A a a cof a z -\-B a a fin. a z -{- C a a 

 ita vt colligendo fiat 



^-U- -\-aat — b — Caa'. idcoque C =: — 

 quo fubftituto integrale reale erit 



f =: A cof a z -{- B fxn. a z -{- — 



vbi litterae A et B defignant certas conflantes ex natura 

 aequationis determinandas. 



§. 5- Sin autem porro accedat terminus in partc dextra 

 c cof m z , ita vt propofita habeatur talis acquatio : 

 ^^ -\- a at—h -^- c cof m z , flatuatur integrale 

 / — A cof a z-\-B fin. ^ s + C + D cof m z, eritque hinc 



^ — — A a fm. a z + B a cof a z — D j?i fin. »/ z et 



d d t 



— — A a' cof a s — B «' fin. c s — D w' cof m z ; 



tum vero 



a a t — + A a^ cof a z + B a^ fin. a z-{-D a- coC. m z-^-C a a 

 ita vt fit 



L^ -\-aat — b-\-c cof m z — C a a-\-X) [a a — m m) cof w « 



vnde partes confUntes et variabiles feorfim aequatae prae- 

 bent C — — , vt ante , et D ~ E , quibus valoribus 



fubftitutis integrale reale aequationis propofitae erit 

 t — A cof a z-\-Bf\n. az-\--LA E — cof m z. 



a a ' aa — mm 



M 2 Quodfi 



