71 



L ort.tar + aarjrr i; II. hhxx-\-^^yyz=il ; 

 qiiamm diffeientia : {a a — hh) XX -\- {aa — PjS)// rr: O, 

 nos perduceret ad relationem inter x et / : at veio po- 

 tius inde investigemus seorsim tam xx quam yy. Primo 

 igitur ab aequatione posteriore, dacta in aa. , prior, ducta 

 in (3(3, subtrahatur, et obtinebimus hanc aequationem : 



{aahh — (3(3aa)xxrr(3(3 — olcl. 

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

 plicata, dat (aa66 — (3 (3 a a) }^/ n: 6 6 — aa. 



J. 8. Incipiamus ab hac postrema aequatione, quac 

 per factores ita repraesentetur : 



(a6-f-(3a)(a6 — (3 a) /j rr: (b -f- a) (6 — fl), 

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



a6-f-(3rt = Qcd{aa-{~hh) — 2ah{cc-\-dd), 

 sive ab4-<3a =r:*î2 (ctc — bd) (ad — 6c). 



Porro vero erit ab -{- ^ a :=z 2 (ab — cd) (aa — 66), 

 eonseqaenter y y z= ,(,,_,,)(6cl.«d)(at-c4r 



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

 modo vidimus factorem membri ejus sinistri esse 



aahh — (3(3 fia =: 4 (66 — aa)(6c — ad)(ac — bd){ah — cd). 

 At vero pro membro dextro (3(3 — aa habebimus primo 



(3-}-arr:(6-f-a)(66 — 2a6-f-rta — cc~\-2cd — dd) 

 == (6+ a) [;6-a)^ - (c-d}*J == (6 H- c) (6 - o -^ c-d) (6-a- c-i- d). 



