-441 )■ " C %'^<» 

 Problema 5. 



■§. 18. Si fuerit X fundio rationalis hinarum va» 



riabilium x et s ^ exijlente s — V °"^^^ , formulam di^eren* 

 tialem X dx ad rationalitatem perducere. . 



Solutio. 



Pofito s — -V''/^^''—z, erit ?:±i*- r= 2" , hincque 



X —-^- , conicawenitT d X — -^ ~ — ; J 



hisqiie valoribus fubftitiuis tota formula propofita Xdx 

 ad rationalitatem erit perduifla. 



' Problema y^ 



§. 19. Si fuerit X fun&io binarum quantitatum 

 X et J, exijlente s — V [a -\- b x x)^ formulam differentia- 

 lem "^-^ ab irrationalitaie Hberare. 



Solutio. 



Ponamus s::^y (^a-\-b xx) — z, erit a^bxxzizz, 

 hinc XX — ^-^" , et quia In fundione X tantum qua- 

 dratiim x x, eiusque ergo poreftates pares occurrunt : hac 

 fubftitutione iam fuudio X euadet rationalis. Sumtis vero 

 logariihmis 2 I x — l {zz — a) ~ l b, difFerentiando fit 



, d * •_ .^z ideoque ^ — ^ ^* ^ 



z z 



Hoc ergo modo formula propofita X.^^ prorfus reddetur 

 rationalis. 



B a Exem- 



