245 DISSERTATIO DE TROBLEMATIBFS 



qiiarta, V^Xp^u^^-^du-^Vudu-^KdV , vnde pro- 

 Tenit_ P=D«"-' -H Q , ac B-"^^ \ quinta, 

 n^.Dp^u^^-^du-^^qudu-^KdQ^; atquc fic porro, 

 cum lex progreffionis etiam hic abunde fit manifefta. 

 Subfiftamus nunc in hac aequatione canonica quinta, ex 

 qua , fubftituto IdR pro udu , et multiplicando per 

 yRViu'-p') , tJeducitur n-l^.Dp^u^^duV iu'-p') 

 -{i(^dK-i-KdQ)VK, ex qua integrata progignituc 



^LZll^^ fu^-^duV {u- -p')-Q^, ac euolutis -valoribus 

 Ri 



n.n~i-i ^.n -1- ;.i - =•« — + . 



CtC. 



Erit denique integrale quaeutum ^:zMR^-*"c:[A«"-* 



H-Btt''-'-+-C«''-^H-D«"-'-4-etc. -^Q_](«'^ -;>')'. 



§. 12. Sit nunc dcnuo « numerus quilibet intc- 

 ger , fed impar, -ex. gr. 7 ^ peruenio ad aequationcm 

 canonicam quartam, in qua eft, P-Dtt'~'-HQ.-D + Q> 

 aequatio autem canonica fequens quinta dabit , o nr 3 

 Q,//^«-4-R^Q^, \nde Q_— o , quod etiam ex \a!ore 

 ipfius Q, modo inuento , patct ; et PrzD; ex quo 

 apparet, in hoc etiam cafu quantitatcm propofitam efle 

 abfolute intcgrabilcm , quoties fuerit n numerus impar. 

 Si vero idem n lit numcrus par, cx. gr. 4, inuenio in 

 aequatione canonica .fecunda , N~B«-+-0, et ex fub- 

 fequentetertia, Bp^a^tt-sOwd^w-hR^O^— ,- +R^O, 

 quae multiplicata per V {u^--p^)~VK , abit in hanc, 

 l^p^duV^u^-p^^zi^ilOdK-^KdO^VK; fed haec eft 



integra- 



