QVOKFND. PROBL. DIOPHANTJEORVM. i$ 3 



Gafu fecundo fit: x-\-yzz^pp-6pqzz^\o quadrato; 

 ergo pp — zpqzz quadrato, cui fatisfit ponendo p~zm m< 

 ek qzzmm — nn\ vnde oritur 



x~~' ^m*-{-6mmnn—n^ 



yzzr-^m * -t-6mmnn-\-n*'' 

 Cafu; denique terdo fit x-\-yzzz6pq — %qqzz% n' et" 



ipq—qqzzu 

 xndv fit: pzzmm-\-nn et qzzi±mm\ ideoque- 



x zz - s m* -+• $ m m n n -f- n ** 



Eh ergo ternas fblutiones problematis- propofiti i- 



Fxzz A.mn($mm--%mn-\-nn) 

 \y-~ (m — n)(^m-n)(^mm-\-nn) 



TT ^x-z n(m*-— 2?n s 'n — imn*-\-n*) 



\yzr, m*-+-4.tn z n-6mmnn-\~4.mn*-\-n*'' 



mC x =r 3 m* -f- 6mm nn— n 4 -'* 

 lyzz-zm* -\-6mmnn-\-n^ 



\bi : quidem fecunda forma in tertia,, quae- cum quarta' 

 conuenit, contenta deprehenditur , ita vt fecunda, vti ma- 

 gi& complicata, omitti: poffit=- 



Coroli r.. 



3T3 - . Si hae formulae, pro x et y inuentae, per' 

 numerum qujdratum quemcunque mukiplicctitur , eae 

 quaefito aeque fatisfocient v ita fcilicet fumma cuborum 

 &?-\-y 3 fiat numerus quadratus , vnde numeri quotcun- 

 <jie non primi iuter fe obtinebuntur. Simili autem 



modo 



