80 DE FRACTlONIBrS CONTimiS OBSEW. 



r) 





ac-(m-+-i)b I acH-(2m-t-5)6 



^ y-v (2Tn-|-5)( 3m-f-r)__ p z-' (5m-t-n)(6mH -jj_) 



^-U ac-+-(m-Hj)6 II *^ ^ — ac— (377W-6)6 



etc. 1 1 etc, 



75. Si nunc hi valores in fradione continua inuenta 

 fubflituantur reperietur : 



cxy—i ^iac-\-b y;^ 



(2;;/+5)+(^^+(»^+3)^)^^' 



m-H* 



-(3?«+7)+-(^^"-(2'^^+4)'^)^t' 



m-t-» 



Ex hac expreflione patet nequationem propofitam ablb- 

 lute efle integrabilem cafibus quibus i? aequatur termino 

 cuipiam huius progrefiionis - ac ; "^^; "".-^; "^^i 

 etc. " i^^^.i^, deinde etiam cafibus quibus b eft termiuus 



, . ~ , . ac ac ac ac 



huius progreflionis : ^ ; "1(^4^ '1 zim-i-^) '•> etc. r^^ipTr 

 Fradio autem haec continua aequationis propofitae exhi- 

 bet integrale huius conditionis, vt pofito xzno , fiat cxf 

 rz I , fiquidem M-+- 2 > o ; at fl m^ ^ <^ o , tum 

 integrale hanc tenet legem Yt pofito xzzco fiat cxjzz:!. 

 §.77. Ponamus efle b zz o ] atque a:zznCy ac poft 

 integrationem poni ;i^ zz: i ; proueniet ex hac aequatione 

 n c x^dx -+ cfdx -\-dyz:z-0 fequens fradio continua , qua 

 valor ipfius j definieturj cafu quo ponitur xzz^^x 



— (m-H3) 





-(zW-H?) ^ ;2 



li5di:£)-f-etc. fwe 



