-> 



) 5( 



— P -jr ^^ ^(3 (? -4- 4 g v 



1 y ' 



His notatis differentietur ifta formula, vt fiat 

 d s-nux''-' dx — {n+ \) ^ x^ d x — {n -{• 2)yjr"+' d Xj 



vnde per partes integrando et integrationem tantum indi- 

 cando fiet 



noL/x"-' </Arr:(;7+i)(3/jfV.v+(«+2) yfx''-^' dx-\-f. 

 Hinc, fi pofl: quamque integrationem, ita peradam, vt in- 

 tegralc euanefcat pofito x — o, fiatuatur 



quippe quo cafu fit j = o, erit 



nct''x''-' dx- («+ i) PA" dx+ [n-^ 2) y/jc"-^' dXy 

 quae eft eiusmodi relatio inter ternas formulas integralcs 

 fibi fuccedentci, , qualem defideramus pro formatione fra- 

 «flionis continuae; quandoquidem hae formulae integrales, 

 fi loco « luccefiiue fcribantur numeri i, 2, 3, 4, 5, 6 

 etc. nobis luppeditant qnantitates A, B, C, D etc. 



^. 4, Scribamus igitur loco n ordine numeros 

 naturales i, 2, 3, 4, etc. vt prodeant irtae relationes: 

 oifdx— 2 P/a- </ Jf -+- 3 yfxx d x 

 a afx d X— ^ (3/jf x d x -{- ^ y J ^^ ^ ^ 

 2 aj X X d X — ^^/ x^ d X ^ 2 yfx* dx 

 4 afx^ d X zz s ^fx* d x-\- 6 yfx^ d x 

 etc. etc. 



Hinc igitur habebimus 



A zi^fdx zzx^:- g^iJ^ P-^-» v\ 



B-fxdx=:lxx = l{=-^^z^^^^^^^-^y, 

 C=fxxdx — lx% D—fxUxzz^x* 



"^- ^''' . Tunc 



A 3 



