= (34) === 



I. Pro aequatione tertii gradiis: 



■vbi erat radix 



x~Yaal?-{-}/ablf. 

 Hic fi aequatio refoliicns ftatuatur 



j'j' — A j -i- B = o , 

 eius radices eruiit aab et abb^ ideoque A ziz a b (a -{- b) 

 et B := a"' b\ 



II. Pro aequatione quarti gradus: 



x^ rz: 6 a b X X -h ^a b (^a -i- b) X -\- a b {a a -h a b -h b b) 

 Hic eft radix 



4+4 



X — }/a^b-\-y'aabb-\-y'ab'^y 

 vnde fi aequatio refoluens ftatuatur 



f — Ajj -hBj — C r=z o , 

 cius radices erunt a^ b ; a a b b ; a P , quocirca habebimus 



A=zab(aa-hab-hbb)^ 



B — a^ b^ (a a -h a b -h b b) et 



Cz=:a'b'.^ 



III. Pro aequatione quinti gradus: 



x'zizioabx^-i~ioab(a-i-b)xx-hSob(aa-i-ab-hbb)x 

 -h a b (a^ -h a a b -\- a b b -\- b^) ^ 

 Hic igitur erit 



.V = ]/a' b -h -/a^ bb-\-yaab^-^yab^^ 

 vnde fi aequatio refohicns ftatuatur : 



.r — Ay^ -\- Byy — C j + D = o , 



cius radices erunt , a'^ b ; a^ b b \ aab^; a b* ; vnde coUigitur 



fore 



