11 



§. 3. Incipiamus ab haram aeqnalionum prima, at- 

 que ut fractioncs evitemus, statudmiis xx-—j-y^?j(J:)b — aa) 

 zzz 12 f g [pp — (]q)', Linde cuni sit 66 — aa m ^fg Q}p — qq), 

 faciamus b -{- a =: q/ {p -^ q) et 6 — a z=: 2 g [p — q), onde 

 erit b =: (/ + ê) /J H- (/— g)q et « — (/— g) /j-f- {f-i-g)q. 

 PoiTO vero pro aequatione xx — )■/:== i2fg(pp — qq) 

 statuamus x + j rz: 6 g (p + f/) et x — f:=.2f{p — (j); uude 

 fiet a— (3ê+/)/J+{3§-/)q et jz:=(3g-/)p 4-(3§+/)q. 



5. 4. Jam aggiediamur aequationcm secundam 

 a^ X + j • j zr 4 c c H- a a-\~bh 

 îitqiie ex valoiibiis iiiodo inventis ropeiîetai" 



xx-hj/+2 (9g§+//)(P/^ + 77) +4(9§§— //)P7- 

 Deinde vero erit 



b 6 + rt a =: 2 (// 4- g g) (/?/? + 77) + 4 (// — SS) P 7- 

 Cum igitur sit 4 c c =1 1" x -f-// — (6 b -f- a a)^ erit 

 4cc=z l6gg{pp-{-qq) +(4o§g—8//) /îq 

 quocirca habebimas ce zz: 4 gg (/jp H- 77) H- ( l o gg — î2_^) /}g , 

 qiiam ergo foimulam quadratum reddi o^îortet, 



§. 5. Hinc jam ad tcitiam aequationcm piogredia- 

 mur , quae est zzz=z 2 {aa -\-bb) — ce; unde cum sit 

 (aa 4- 66) 1= 4 (//+ gg) {pp + qq) H- 8 (ff— gg) pq et 

 ce = 4 êS (pp + 77) + (1 o S§ — 2//) pq , erit ' 

 . ^-'^ = 47/ (pp + 77) + ( 1 oy/— 1 8 gg) pg , 



