^S EVCLVTIO FORMVLAB 



int^grali ab * zz o ad jrn: x extenfo ; eiusdem pfo- 

 dudi cafu quo gzzo \alorem per formulam inte- 

 gralem aflignare. 



S o 1 u t i o. 



Pofito gzn o m formula integrali mfmbrum 

 (^t — x^J" euanefcit , fimul vero ctiam denommator 



(j — x^y- 



^"j vnde quaeftio huc redit vt fradionis — — — 



l^alor definiatur cafu ^ — o, quo tairi numerator 

 ■quam denominator euanefcit. Hiinc in finem (pe- 

 &.tvsit g vt quantitas infinite parua , et cum fit 

 ics.^gsix fjg( x^^i-^-glx ideoque (i ^x^]"-g\-lx)'- 

 "zrg^^liy i ex quo pro lioc cafu farmula nollra in- 

 tcgmlis abit iu //.t^- '^:t (/;.)" ita vt iani habcatur 



n 



f——=ffxf-'dx& 



feu I. 2. 3 n=p-*-'fx^-'dx(l'i)\ 



CoroIL I. 



8. Quotics n cfl numerus integer pofitiuus , 

 intcgratio ^^rmulue fx^~'dx 1'^f fuccedit , eaquc 

 ab ^ — o ad a* — i extenfa rcucra prodit id pror 

 du<ftum , cui iftim formulnm acqiKiIcm inucninnis. 

 Sin autcm pro'« capiiintur numeri frndi eadcm for- 

 mula integralis infcruict huic progrellioni hypcrgco- 

 metricae interpoland.ie : 



\Mvi. 2,- I. 2. 3; r. 2. 3- 4; i- 2. 3 4 5; etc. 

 fcu i; 2; <J; 24; 120; 720; 5040; ctc, 

 -j,u. Coioll. 



