36 



(o/_ 3« + i:,) (2/+ 3n H- ^l) = 4f -h 4c, 

 qnae, fticta evokitione, ad istam perducit aeqnationem: 



haecque siiblatis fiacdonibus abit in banc : 

 A^''B^''(9aa-f-4c)-AV(2/-3n)-BV(G/-+-3n)-jV=:o. 

 Siimto igitur /:iz9aa-}-4c, et facta divisianc, oritur 

 haec aequatio : 



A^''B'' — K'' {if -2a) — B'^ (-/-f- 3 a) = 9 aa + 4c, 

 qiiae pcr factoies repraesentari potest hoc modo : 



(.V^ - 2/- 3fl) (B- - o/_|_ 3 a) ^ 4#-f- 4^- 

 %. CI. Quia hacc acqaalio similis est pracccdenti, 

 iterumqiie pro casu K^'z^Vi^ prodirct 4/, statn.itur iilte- 

 rius A''' ^=- ùff — 2 rt -f- ^,r, et B'' =: 4/-I- 2a + -^r-> nnde 

 postrema aequatio per factorcs foret : 



(2/-5fl4-i:)(2/+5a+^:)=:4/+4c. 

 At facta evolutione sublatisqne fractionibas prodit : 



A"'''B'-'''(25,7a-H4f)-A''V^(2/-5fO-B''V''(2/-H5a)-/^/''=a. 

 Sumendo igitnr s^ ziz l'baa-^ \c et dividcndo per s'^ fict: 



^'-^-^ _ A"^(2/- 5 a) — B'^^(2/-H 5 a) = 25 aa -^- 4^:, 

 sive per prodiictum : 



(A'- ~ o/_ 5 «) (B- - C/-+- 5 n) .-= 4ir-f- 4 r. 

 §. 22. Statuatnr iilteiiu9 i\'^'' nz 4/" — 2fi -j- ',,. et 

 B^'^'' = 4/ ~î- - " ^- pfrr » <^t sn|XMior aequatio per productum, 

 stibstitutis his valoribus , crit : 



