IN ANALTSI INFINITORFM. 113 



jC O R O L L. 2. 



40. Qiiodfi fuerit m — n^ dummodo \triusque 

 litterae valor non fit = - i , pofteriori tninsformatione 

 non erit opus, fed formulae /a:""'"'^/ P et /x""^'*/ Q^ im- 

 mediate ope problematis quarti reduci poterunt. 



E X E M P L V M. 



41 . Quaeratur relatio algebraica inter x et y^ 



vt hae formulae J^^^ ^' /** {xx-^yjf)* mlores alge- 

 braicos obtineant. 



Cum hic fit V=ri-^ et Zzr^ [xx^yyfy vtraque 

 ergo fundio V et 2 homogenea, illiusque dimenfionum 

 numerus «/ — i, huius vero nzzzo^ fi ponatur y — tx, 



fiet V =: a: t* et 2 — (x +^/) " , ct formuke rediKen- 

 dae erunt 



Jt*xdx et J d X (1 -\- tt)' 

 Tnde fit 



Jt' xdxzzlt' XX - ijx'ttdt 



Jdx [i-\-tt)' — X {i-httf- 3fxtdtV{i-ht/) 

 Ponatiir iam a- n ,- V (i H-«), fietque 

 Jx"ttdt z=:Jzzdt{i-\-tt) = zz{t-\-kt") - 2 J{t-\-\t')zdz 

 JxtdtV{i~\-tt)—Jzdt{i-\-tt) — z{t-\-\t') -J{tv/idz 

 Sit breuitatis gratia ?-|-^?^=:«, et cum fonrulae re' 

 diicendae fint Ju z d z et Ju d s, ponatur 



Ju z d z~\^ a Judz — M 

 fiet u—^ — j^, ideoque z=: ^. 



Tom.V.Nou.Com. P Si 



