FORMVLARVM. 



«7 



Exemplum 1 



2 2 . Tropofita formula V(2xx-f-(3x-f-y)ry, 

 inuenire infinitos valores integros ipfius x , quibus haec 

 formula rationalis euadit , fiquidem ma jolutio conjlet. 



Sit folutio cognita xzzia etjmb, et ob «~2, 

 habebimus p~V( zqq-t- 1 ), ideoque #~2 etpz=3. 

 Hinc (ecundi valores erunt : 



Cum igitur in §. 19, fit R~6Q-P-j-(3 et V = tf T-S, 



habebimus fequentes feries valorum fatisfacientium et 

 quidem integrorum , fi (3 fuerit numerus par : 



Valores ipfius y 



± b 

 4*±3^-+-(3 



140^-4-99^-1-35 (3 

 8itftf± 577^+204p 



475^^±33<>3^4-ii89j3 

 etc. 



Tum vero cum y eosdem retineat valores , fi pro x 

 fcribatur — x — ?, etiam hae folutiones locum habebunt: 



Valores ipfius x 

 a 



99«±7c^-t-r(3; 



5 7 7 # ± 4° 8 b -f- 1 4 4 (3 , 



33^3^^-378^-r-^rPi 

 etc. 



Valores ipfius x 

 -a-\$ 

 — 3^-j-2^-(3 

 -i7*4-i2£~i(3 

 — 9Qtf-f-7°6^— 25(3 

 -, 77^408^-^(3 

 -33^3«-i-a37S^84.ip 

 etc. 

 Tom. IX. Nou. Comm, 



Valores ipfius y 



± b 

 4^±3^-f-(3 

 340+ i7£-f-tf(3 

 i40<7±99^-r-35(3 

 8 1 5 a ± 5 7 7 b -f- 2 o 4 (3 



475<5*±3363£-r-ii89(3 

 etc. 



C Etiamfi 



