folutionem hic rubiungamus , quae quantitates irratlonales 

 quascunque in fe comprehendat. 



Methodus generalior 

 traie6lorias reciprocas algcbraicas inueniendi. 



§. 32. Denotet X fradionem quamcunque, quac 

 quidem fit rationalis, fiquidem poteflates , quarum expo- 

 iientes funt irrationales, non inter quantitates algebraicas 

 referri, fed interfcendentes appellari folcnt, ac propofita fit 



haec formula p — -i^ — ^ ^ ^^. , quam ftatim in hanc 



transformcmus ^^— r^, (latucndo fcil. |-±-2 — r, eritque 

 propterea j rr/r^ ^jc — r^ .V — /r^"~' .v^/r, quam crgo po- 

 llrcmam formulam intcgrabilem reddi oportet , ita tamcn, 

 vt X fiat impar ipfius q. 



§.33. Hunc in finem ftatuamus /r^"' A'^r = T r\ 

 ficquc fiet j — r'^ (jf — X T); ac vtro fa(fta difFerentiatioue 

 r^^' X d r z=z r^ d T r^~~' d r , vnde coliigitur 



^ = Vr"^^T' idcoquc j'— 



d r 



Hoc modo iam ambac coordiiiatac x ct y rcdditac funt 

 algcbraicac, ac problcma forct fohitum , fi modo confta- 

 rct, qualcm fundioncm pro T accipi conncniat: eam au- 

 tem ita comparatam eflc oportct, vt indc prodeat xzz 

 fun(ftioni pari ipfius q, 



§. 34-. 



