i5s 



f^l f — q _ 2 ^^^ _i_ ^j ^^^ __ i,^ ((^ _ ^;,^ ^ 4)^ 



3 2 * ■ 



Quod si igitur )Donatui' 



t^JL — 2 (a 4- 6) (a — i), 



f-'' =r (.1 — 6)= — 4, 



a 



hine pro /^ et q naiiciscimur yaloies 



p =: (a — b) a a ~\- 'b) — Â, 

 xj z=i {a — b) (3 6 -1- a) -f- 4. 



ri'obleanati igitur proposito satisfiet ponendo 



y HZ (a — b)^ —— 4. 

 His enim valoribus substitutis formulae propositae fient 



scx 4- 2aa'y -\- yy =z [(« • — b) (3a + 6) — 4]* ; 

 aa? 4- 2 6xî/ -f- yz/ =r [(a — &) (3ô -}-«)_ 4]^ 



C o r o I 1 a r i u m 1 . 



§. 2. Valoies hic pro x, et y, p et q traditi , si habeant 

 factorem communeni , ad miDores numéros reducuntur problemati 

 aeque satisfacientes. Hoc evenit , verbi gratia , casu quo ab -^ i 

 est multiplum quodcunque ipsius a -f- b, veluti si fuerit 



a b -^ l :—. n (a -{- b). 

 Tum enim, ob y z:r (a — bf — 4, erit y -+- Aab r= (« + bf — A, 

 hincque y ZZL (a -h b^ — 4 (aô + 1) , sive 



y zzz (a ^ bf — 4 /i (.a + b) 

 X zzz A {a ~{- b). 

 Tum vero habebimus 



p — Aab z^^ in — b) (3a -f,^.) -^ 4 (ai -}- 1) 

 sive etiam 



p — Aabzzz{a — ■ i) (3a -f- 5) — Ân(a-^b) 

 unde intelligitur fore 



/) zr (a + 6) (3a — b — 4m). 

 Simili prorsus uiodo obtiaebitur 



I 



