QVORVND. PROBL. DIOPHANTAEORFM. i£& 



Iam fingatur yzzzt~r-u, vnde quidem maxima limita- 

 tio nafcitur, et aequatione per %tu diuifa, reperietur 



(pp-\-pp q -q)t-\- (p-pq q -\- qq)uzzzt -\- u , feit 

 i = zjg±±j*gf : capi ergo poterit : 

 tzzzn(-pqq-\-qq-\-p-i) a uzzn(-ppq-pp-\q-\-i) 

 vnde elicitur : 



xzzzn(-ppqq-\-pqq-ppq-p-\-q-\-\) 



jzzzn(p~\-q-pp-rqq-ppq-pqq) 



zzzzn(-\-ppqq-pqq-\-ppq-\-p—q — i) 

 ay-zn(-pqq-ppq-pp-\-qq-\-p-\-q). 



Hinc autem fit zzzz-x et vzzzy , qui eft cafus per 

 fe obuius, 



13. Sequenti autem modo folutio ktius patens 

 eruitur : Ponatur 

 xzzzmt~\-pu \ yzzznt-\-qu et zzzz—nt -\-ru } eritque 



x z -ry z -\-z z zzzmH 3 -\-^mmp r ] -\-zmpp r ) ~\-p zf ] 



-\-3nn q\ttu-\- 3 nqq \tuu~\- q z \u* y 

 -r^nnr^ —^nrr] -\-r z S 



quae fumma cum debeat efle cubus =r © 5 ponatur : 



uzzzmt-\ mm u\ eritque diuidendo per uu 



Zt(mpp~\-n(qq-rr))-\-u(p z -\-q z -\-r z ) ~zz 

 ~ 3 (mmp-\-nn(q-\-r)) s -\- ~- 6 (mnp-\-nn{q-\-r))\ 



Gcque neglecto communi fa&ore , qui ab arbitrio noftro 

 pendct , erit 



tzzz m e (p z -\-q z ~\- r 3 ) — (m m p -\- nn{q -\- r)) z 

 uzz$m z (mmp-\-nn(q-\-r)y-$in(mpp-\n(qq-rr) 



X 2 quae 



