PROBLEMATfM DlOPHANTAEOWM. 179 



Valores ipfius x 

 I. n 



bUf-i) 



ni. 2q^n-i-2pqm-i g. 



— 3 qn —p m \ 



~-Sq^?i—^pqm 

 n 

 etc. etc. 



Vfllores V(ax--[-lfX-i-c) 

 m 

 apn-{-qm-i-^ 

 2apqn-\- ^.q^^m-^-bp^ 

 — m 



^apq-n-{-^q^m-\-2l/pq' 



— apn — ^qm-^^ 

 Sapq^n-^^q^^m-^-^hpq^ 



— ^apqn-^q^m—^bpq 

 ■m 

 etc. 



Huius progreflionis haec Huius progreffionis haec 



eft iex. 

 term. quicunqueA 

 liuac fequens B 



T> A . 6 ( q — 1 ) 



eJft lex. 

 a^F-E 



H:ie igitur progrefliones , quousque libuerit exiguo k- 

 bore continuantur. 



§. 8. Perfpicitur ex his formis alternos admini- 

 ,mum terminos efficere ax'^ -^bx^c numerum qua- 

 dratum integrum \ atque omnia omnino quadrata fieri 

 jQumeros integros fi fuerit bp numerus par. Omnes 

 autem ipfms x valores erimt numeri integri, ii b{q 

 — I ) diaidi poteric per ia\ fin vero lioc non fuerit, 

 ialtem alterni ipfius .v valores erunt numeri integri, 

 nam qq—^ i- e. ap'^ femper diuidi poterif per ^, 

 fi quidem , vt ponimus p tx. q fint numeri intcgri. Prae- 



Z 2. terea 



