F R M V L A R V M. 7 



a % ~z(rtft-\~amm)a ^imnb -\-$mm\ b x ~iamnd 



-h ( n n -h <x mm ) b -\- fim n 

 & u z=z{nn*\-*mm)a x 3^2 mnb l -\- ^mnt^ b ll ~i amna 1 



-h (nn-\-amm )b l -\- (3 m n 

 a^zzz^nn-^-amm^a^^zmnb^-^-^mm^ b m zziamna xl 



^h (nn-\-amm)b ll -\- (3 m n 



etc. 



Hac igirur fatione continuo vkerius progtedi licef ^ 



ficque ex Vna folutione, in numeris integns cognita, in« 



fiumerabiies aliae in mrmeris integrte quoque elicientur» 



Coroll. t. 



4. Vt igitur formula axx~\-$x-\-y infinitfc 

 modis in numeris integris quadratum effici poffit , rte* 

 teflfe efi, vt a neque fit numerus quadratus , neque ne- 

 gatiuus, ac praeterea, vt vnus cafus, quo ea flt quadra- 

 tum, vndecunque fit cognitu?. 



CorolL 2. 



£. At fi a fuerit rtumerus pofitiuus non quadra-. 

 tps, tum primum quacrantur duo numeri m et ft. vt fic 

 nzzzV('amm-\-i ), id quod femper fieri poteft. Qiri- 

 feus inuentis , fi ponanrr : 



V ( ax x H- p> -f- y ) ~y 

 atque iam cognitus fuerit cafus> quaeftioni fatisfaciens^ 

 qui fit x— a tt yzzzb r ex eo per primam operatio- 

 nem non forum vnus ,. fed duo noui y inuenientur ob 

 figni ambiguitatem. Erit quipper 



xzz:{nn-\~ amm)a ■+_ zmnb-\-fimm' et 

 jzzzzamna ^(nn-\r ctmm)b-\- $mn* 



ComVL 3* 



