I. aaxx -^cL(iyy:=: i; U. hhxx -^ ^^yy:=z i , 

 quarum dilTeientia : (a a — 66) xx -f- (aa — (3p)// =z o, 

 nos peidticeiet ad lelationcm inter x et / : at vero po- 

 tins inde invesligemus seorsim tam xx quam y y. Primo 

 igitur ab aequatione posteriore, diicta in aa, prior, ducta 

 in (3|3, SLibtrahatur, et obtinebimus banc aequationem : 



(acihb — |3j3ao)xxrr:(3(3 — a a. 

 Contra autem, prior per 66, posterior vero per a a multi- 

 plicata, dat (aa66 — ^(^aa) yy -ziihb — aa. 



§. 8. Incipiamus ab bac postrema aequatione, quae 

 per factores ita repraesentetur : « 



(a6 4- |3 fl) (a6 — (3 a) /7 = (6 -f- a) (b — a), 

 et jam, substitutis pro a et (3 valoribus supra datis, erit 



a6 4- pa zz: 2cd(aa-\~bb) — clab(cc-\-dd), 

 sive a6 H-|3az= 2 (rtc — bd) (ad — 6c). 



Porro vero erit a6 + (3a z=: 2 (a6 — cd) (aa — 66), 

 consequenter y y =z ^^^,_,j^^,,L,d)^ab-cdy 



§. g. Pro altéra aequatione , qua xx determinatur, 

 modo vidimus factorem membri ejus sinistri esse 



aabb — |3paa=:4(66 — aa){bc — ad)(ac — 6d)(a6 — cd). 

 At vero pro membro dextro (3(3 — a a. habebimus primo 



(3 4- a =(6 -h fl) (66 — 2a6-f-aa — cc-\-2cd — dd) 

 = (bH-a)[(6-a)^-(c-d)»J=:(64-a}(b-o-»-c-d)(6-a-c4-fi). 



