FORMVIARVM. 



t 9 



Praererea vero fcribendo — x— § pro x prodibunt 

 valores ipfius x 



-2tf-j-0-I(3 



— 362 a + 209 £ — '-f- (3 



-1351* + 780*-^ p 

 etc. 



valores ipfius,/ 



±* 



3^-4-2^^-1(3 



1 2 <7 -f- 7 £ -f- 2 (3 

 45 #-4- 26 £-4- ^-(3 

 168^+97^^-28(3 

 627^-4-362^-+-^ (3 

 23404-4- i35i^-H39o(3 

 etc. 



Prout ergo numerus (3 diuifibilis fuerit per 2, vel 3 , 

 vel vtrumque , hinc eo plures folutiooes in integris eli- 

 ciuntur. 



Exemplum 3. 



24. Propojita formula VCsxx-hpx + y)—^ 

 tnuenire infinitos valores integros ipftus x , quibus haec 

 formula rationalis euadat , Jiquidem vnus cafus fuerit 

 cognitus. 



Pro ca(u cognito fit xzza et ^rr^, et ob «r 5 , quaeran- 

 tur numeri p et q , vt fit p~ V ( 5 ## + 1 ). Fiet ergo 

 4 ~ 4 et /) zz 9 ; et hinc fecunda iolutio prodibit : 

 a l z=z ga + 4^ + 1(3; ^iz: 204 -4- 9^-4- 2 (3. 

 Cum ergo fit a u ~ iSa 1 -*z + §(3 et ^"—iS^- b % 

 fequentes folutiones habebuntur : 



Valores ipfius x 

 a 

 r 9<z-4-4£-4-f (3 

 l6i g-f- 73 -^ 1.6" 

 28890 + 1292^+^p 

 etc. 



C 2 



Valores ipfius j 



±* 

 200 + 9^+2 (3 



3604 + 161^-4-36(3 



6460 # + 2830^+646(3 



etc. 



vbi 



