•70 DE FRJCTIONIBFS CONTINVIS OBSERV. 



mmus Vzzx'^-'^! -.xV(p + ^^^T / et R=r.^^ Ciim 

 autem effe debeat {a'{-yoL)IVK^i^x—x(i?-\-yt)fPK"*'' 

 dx-i-{c-\-yy )J?K'-*-^^x , hincque ob P et R datas fiat ex §. 

 52. S i=:^JC^-''(i-^^/(p-i-^A-^)*'(V.r*^H-eji:'--a) 

 , dS (m — r)dx nrx^^'dx Karx^—'dx 

 ^ X —i-\-x'^ ^ p-^qx'^ ^ 



s. yrx^^^^dx-Y- '^rx^^dx [a—0L)rdx 



yx^^-^%xr^—cf. (XX 

 (ab - ^^)nr^~"'^.r ^-(cc^- ya^rx^^^^^dx 

 —^-^^:^-^) • Sit nunc (p+^x') 



(x^^-i^zziyx^^^^^^x^^-a^entyziiq^zzip—qttazzip. 

 Sit praeterea^^=z«2--r, erit ^zr^. Vnde debebit 

 porro effe nqr-i-Kqr^ iqrzz-^-^"^^^ fm czzj^-^-n 

 ^H-(K-h2)^,et tandem l;~Vli2zS)^(^n-\-i)p-(K~\-i)q. 

 Dummodo ergo m et n-i-i fuerint numeri affirmatiui, quo 

 R^^^^S euanefcat pofito tamx— o,quam xzzi^ prodibit 

 (equens expreflfio 



/a:'"-*-^-' dx{ i-x''Y{p-\-qx'')'' JVKdx 

 J^-^dx{i--xf{p+qxr "^JVdT ^"^eP^-^Pt^^^ a^q"^- 

 lis erit huic fradioni continuae 



rnp 



•»(J>-9>-KnH-0i»'-(H-Hi )grH-pg(7n-t-r)(m H-nr-hfK- t-2)r) 



^(p-g)-H(^-h2}i>r-(H-f-2}gr-f- p<7'm-|-:r)(m-h(nH-0rH-(H-H2)r) 



§. 64.. Qiio ffadio continua fimpliciorem induat for- 

 mam , ponatur m-^nr^rzza '^ m-\-Kr-\-rzzb\Gt 

 m-i-nr^Kr-^rzzc , fict k — ^'^ • nzz^ et mzz 

 ii-\rb—c—r\ ideoque erit 



4i^-^bq-^ pq{:.-\-.b—c ) ( c-f-r) 



ic-i-r) j>— (6>HrJ3-h j>g^q-f-^-^-f-r)(cH— r) 



(a-i-zr) f»— id>-t-«»') g-i- ^.7(a-t-&-c-4-;r)(c-f- r) 

 («-t-3 r)^-(^-<-i »')3-H«'^C' 



