PROPORTIONALIVM. ipj 



Quocirca prior feries a+a^x+a^^x^-^-a^^^x^-^- etc, 

 nafcitur ex euolutione huius fracftionis ""i^—^J-hbx 



pollerior vero b -]- ^ x ~\- b^^ x" + b^^^ x^ -h etc. 

 ex euolutione huius ^l:-z£l±ir5 ita vt vtraque fit 



1-2 X -(r- i)xx * 



feries recurrens fecundi ordinis , fcala relationis exi- 

 ftente 2, (f— i) , hincque pro ferie priori a^a\of\ 

 i/'\a'^^^ etc, fit primo a^zna-^-b, tum vero 

 a''-2a'^r- 1 )a; a^^^-^a^^-V^r- ly^ a''^'=:2a^'^+{r- i)a'' 

 ctc. ex hac vero ngfcitur altera ponendo a~bttb-ra. 

 Hinc adeo huius feriei terminum generalem definire 

 licet ad quod valores quantitatum P et Q in fradio- 

 ces fimphces refolui oportet. Cum igitur denomi- 

 natoris communis £idor fit i-x-xV r~ i -x(i -\-Vr\ 

 pro qu3ntitflte P ilatuatur fradio fimplex inde nata 

 ^ nrf7Zv7) > ^^ demonftraui fore 5( = — '-^—r- 

 pofito 1—x—xVr, Ynde fit 2(zz| , pro altero 

 autem fadore tantum Vr negatiue accipi opus eft, 

 ita vt fit 



p — J ! L ' 



1— jc(i_f.yr) " a — x{i — VrJ 



Simili modo pro Q^ fi fradlio partialis ex denomina- 



toris finftore i— x(rH-Vr) nata ponatur ^ 



rcperitur ^~ ,_^^^y^ pofito i~x:=:.xVr indeque 

 ^ri 7^^' Q"^^^ ^P^^ ^ ^ binps valores tribuendo fit 



ficque fumftia prioris feriei a^-a^^x-k-a^^x^-^-a^^^x^+Qic. 

 erit 



— / ? V^ •+ ■}> T , a^Jr~i I 



2 V r' • 1— *;i -i-Vr)"' 2 Vr * 1— x(i-Vr; 



JB b a cum 



