->2=>l ) 24- ( li^- 



pcrdu(flae fint ad has fimpliccs: 



d, ct '' 



V(i-*-p pj V 1 1 — 'V "J) * 



quarum vtraqiic facilc ab irrationaiitatc libcrntur, idac ip- 

 fae formulae propofitac opc idoncae fubllitutionis ab irra- 

 tionalitatc libcrari ponunt; vnde niirum non dl, carum 

 intcgralia fiuc per logarithmum fiue pcr arcum circularcm 

 exhibcri potiiific. Satis cnini iain c(l ollcnfum: omnium 

 formularum ditFcrcntialium rationalium integraha lcmpcr 

 "vcl per logarithmos ct arcus circulares, vel adco algcbrai- 

 cc cxhiberi poffc ; quod igitur etiam de illis formulis ir- 

 rationahbus cft tcncndum, quas ccrtae fubnitutionis ope 

 ad rationalitatem pcrduccrc licct. Vnde vicillim plurcs 

 Geometrac conclufcrunt: fi quac formula ditfcrcntialis nullo 

 plane modo ab irrationalitatc libcrari queat, tum eius in- 

 tcgrale ctiam ncque pcr logarithmos ncc arcus circulares, 

 multo minus algebraicc exprimi poffc , fcd ad aliud gcnus 

 quantitatum tranfccndcntium rcfcrri oportcre. Cctcrum 

 combinntio dunrum pracccdcntium excmplorum manudii- 

 cit ab lolutioncm fcqucntium. 



Excmplum 5. 



§. 40. Si propofita fuerit hucc formula differentia' 

 ]is . d y zi IJL^J^ rt-iHj (ius inicgtalc inucnire. 



Hanc formnlam per ncutram fubftitutionem ante 

 Yfurpatam rationalcm rcdderc licct: vtraquc tamcn iund^a 

 ncgotium confici poterit; namquc ciu;. mrcgralc pcr loga- 

 jirhiiMis ct arcus circnlarcs fcc|ucnti artificio cxpcdictur: 

 Forniula cnim propofita in binas fcqucuics paitcs difccrpi 

 poicll, (^uac luuc 



dy 



