PROBI.EMATA DIOPIIAMTAEA. 4p 



3. 1:1.11 pio altcra formi.i!a , cim fit 

 ty~xyj{pp-qq)-\- ^pq/ i uxzzxxj[pp-qq)-7pqv 



fiet 



ttjy-\-hUXX—xxy\pp-qq)*-^^p]Xy\pp-qq)^..],ppqq-/ 



+ ^yj [ pp-qq^-^ipqxj ^pp-C'^)i-^ppqqx* 



quae forma , quia rnanifefto pcr xx^yj cft di- 

 Tifibilis , abit in 



{X x -4- jy) [X xjj [pp -qq;-A-pq xj C^ -v -jj) {pp-qq) 



-i-^ppq 7 (.V* - XXJJ -1-/). 



4. CiiiTi nunc hacc formn. pcr xx-{-yj ir.uU 

 tipli;;Ua nnmerum qiia.iratiini priicbcre dcbe.it, ha- 

 bebimus fequentcm cxprcilionem ad qnadmtum rc- 

 ducendam: 

 j^.ppqqx-^pq(pp-qq^x'y-{-{p"-6p'qJ-\-q')x"j'-^ 



-\- ^pq( pp - q q)X v' -{- Arppqqj* 

 quac quiJcm manifeQo fit qu.idnitum , fi x—j', ve- 

 nim hunc cafum vtpotc facillinuim hinc mcrico cx- 

 dudimus ; fiquidtm tt^ra quatftio liuc rediret , \t 

 2 {t S -i- u U} quadratum efnccrctur. 



5. At poncndo illjm formul.un aequalcm huic 

 quajrato 



{^pqxx-ipp- qq) XJ ^ zp qjj)* 

 deletis termiiiis p.iribus fit 



{p-^Cyppqq^q') xV + m{pp-qq)x/-{p'-r6ppqqM']xy 



--^pq^pp-qq)-^'/ 



hincque ^pqipp — qq^J— i^ppqqx 

 rnJe coUigitur haec (olutio problcmatis : 

 x~2(pp-qq)i j~2pqi hincqus porro 

 t — 6pq'p*+ppqq-\-q') et U^- 2pq(pp^qq)\ 



TQin.XX.Nou.Comm. G 6. 



