^;-- 



IMAGINARIIS CONSTRVENDIS, 215 



y-a*-\-^V-a*-la—-{'y~a*. Examen radicis e. g. fecimdae 

 et tertia>; fdcile inftituitur. Debebit enim efle in aequationede- 

 fnncntc{V-ay-{2y-a'-a).-a'-{2ay-a*-hn*).y-a'-a'—Oj 

 h. e. —a V-a -\-2a v—a —a -\~2.a —a v-a —a zzo. 



Denique Cubiis S .Vt definitur per hanc acquationem : 

 x' -\-{iV -a* -\-a)x'-hi2aV -a*-a* )X-a'—o .Vomndo x^v-^ 

 (i2^«!±:i\ fiet a;'*+ '-^'■i;-'-^^^''^'=:o et hinc(§,XXXlV) 



Qiiare cum reperiatur pnrs irrationahs -f-y(....)— o ; fiet 



(per § XXXVll) -y— i«V(2^-2V-i)-f-|«y(2-+-2y ~ 1 ) 

 rr i tf (- I -1- V — I ^-i-la{-i-\-V—i) , h. e. erit 

 i^vz^-^a-i- |V-«', -'^a-i-^V -a^—^-i .{-la+lV -a*) ^ adeoqiie 

 :,)c,={--^±^^)(-la-\-iy.-a*}-i-r-i^^){ .ia-^^-a')=:-^ia-^-a' ; 



3)^i^(--^--^)(-i^+iV-«*)+(^^')(-i«-fjV-«')=+^^-^V-/. 

 Hinc prodit i)xz:i)v-lV-a'-ia—-la-\-lV-a*—iy-a'-{a——a ; 

 2)x~2)v-lV—a^—^a—la—'^V—a-—lV-a^—^a-zz—y—a' j item 

 i3)x—3}v-lV-a'-ia=:-y-a\ 



^. 49. Eodem modo tracflemus aequationes cubicas 

 •completas , per quas definiuntur Cnbi priuatiuae capacita- 

 tis in §. XXXXIII. defcripti. Nimiium cubum y.Vt 

 definit haec aequatio x^-\-2ax'-\-2a*x-\-a^=o , quae , 

 ponendo xz=:v-a ^ trnnsfoimatur in hanc , 1;'***— o , 

 adeoque ob 1; — o , erit i)^-' — — i.o — o; 2) v z=. 

 {^-)-o=o; s^-y-^^i^^^^.o^o^^.XXXVI). 

 Vnde , ob x — v — a , habetur i)x — o — a — — a:, item 

 ^)x——a-, et 3)x=z—a. Habet igitur Cubus y.Vtj 

 primitiuo a.PT oppofitus , tres radices priuatiuas , etiam 

 qmad formam exprejjionis , inter lc aequales. 



Pro 



