53 P R O B L E Al A T A. 



6. En Qv^o roliitionciT) piiina infinite patea* 

 tem , quoiiia:ii niiineroi p ct q aJ nrb.truirn caperc 

 licet ; reJiidis fcilicet niiirjeris t et u aj minimos 

 ttrmiwos , et qiiia parinde elt fiuc fiac polltiui fiuc 

 neg.it iui lubcbimus 



xzzzipp-qq)', t — -i (pp" -\-ppqq \- ?') — | .v.v A^yy 

 y- 2 p ^/ ; u -• {pp - q qf iz-,xx 



hincquc repcritur 



X X -irY y — ^p* -\- ppq q i- ^ q' 

 ttxx-^-uiivyzzxxyy^ivxi-vvXpp^-qqf^izxxlxvi-yyyjsXx-^-vy) 

 uuxx^ttyy-^ppq j[x'\'^ryjtP^-\-lppTI H*")' -{xx-\-yy ,C,xx-\-yy)\ 



7. Vt ali.is folutioncs inucniamus , ponainus 

 fuperioris formac radicem quadratam : 



z p p X X — (p p ~ q q) X y — 2 p q y y -\- A jj 

 cuiLis quidraco illi acquali pofito prodibit aequatio: 



( A \ -^^pq) yy- 2. X(^pp-qq)xy \-[^kpq-^ppqq)xxzzo 

 hic fi Arr+p^ prodit folutio praecedcns j at pofi- 

 to A zz p q fi' 



-^- -ipqy -\- ^Kpp-q qy.^' = o , 



quae cum illi pariccr con^ruit. 



8 Poiiamus \zz — 2pp proJibit-]uc haec ae- 

 quatio 



(p/>4-i/"?)i'»'4-'/'p-'7'7)v/-(2/J7'4-y?).v.v = 



quiie psr x -f- v diui fa dat 



(pp-^zp q) y-{2p q 4- q q) X =z 



vndc 



