156 



Sumto nunc c rr 2, habebiinus 



72 n nr v'- — 6 l' z' -j- 9 , 



unde extracta radice prodit 



n ' zzz V V — 

 Cura igitur slt x zn vv — 1 , y 

 XX -i- 2nxij -{-yij z=z{ 

 XX — 2nxy -\~yy z=l(^ 



zz — et n zzz vv — 3, erit 



%■■> -^ 2T,;2 — ÔD 2\2 



-'r 



Solutio altéra probl. 2. 



^. 7. Quoniam xx-\-yy zzipp ~\- qq i\. 5.), huic aequationi 

 satisfit , si titrumque membium statuatur :=z (aa 4- 66) (Jf-^ gg), 

 tum enim erit 



X :zz rt/-f- % 

 y r=.ag — bf 



— Pi 



p ziz ag -4-, bf 

 q =z af — bg 

 erit 



Unde cum sit nzzi'^ (§. 5.), 



__ ( ag-l- hf) ( af — bg ) 

 "■ (aZ-t- bë) Cag — bj)' - 



Statuatur nunc 



/JL (af — b g) r= V (a/ + b g} 



ita ùt habeamus 



v_ ag -h hf 



ft ■ ag — bf 



Aequatiû autem _u (q/" — bg) zzz v (af -\- bg) ita Fepraesentari potest : 

 (a — v) a f zzz {]^ -Ar v) b g 



onde sequitur fore 



/_ fr + y) 6 . 



^ (p. — v) o 



Sumto igitui- /" mz (juf, -1- k) 6 et g zzz {^ — y) a nanciscimur pro u 

 hanc expressionem : 



_y (ft — v) a g - I- (;i H- v) 6 6 



;j. ■ ((J. — ») a a — f/j. -|- v) 6 6 



UbI semper pro 6 et a ejusmodi valores accipere licet, ut denomi- 

 nator obtineat valorem minimum ; tum vero numerator plerumque 

 divisionem per fjt. admittet. Denique erit 



n 



