£ i, e. z — 
c m * ) 
— , — I + v — i 
m+Vn +' ~ 
x ra — V n — — m — / — 3 n,J quae tres erunt Radices 
iEqaafionis Cufaicse z ? = § qz + 2-r. Debite autenteon- 
nedtuntur Radices iftse ad modutn prscedentem, quippe 
qua: fic conncxas, Sc more vulgari in le invicem continue 
dudfae, iEquatiooern z3 == 3 qz + 2 r reftftuunt. Deni* 
quc fac z - x — • p. Sc iEquatio fiet x 3 — 3 p x 1 -P 3 p j x 
— p 5 = 3 q x — gpq + 2 r, quae univerfalis eft, 8c 
cujus Radices evadunt ut fnpra fnerunt exhibit®. 
Hie obiter notatu dign utn eft, quod ^quationis Cubic® 
eujufeunque Radices omnes fiat pofiibile3 8c reales,quoties 
Binomii membrum irrationale V r z — q 3 impofiibilitatem 
in fe compieftitur 3 hoc eft, quoties q eft quantitas affir* 
mativa, & fimul cubus ejus maj or eft quadra to ex latere r. 
At fi membrum iftud V r 1 — q ! fit poffibile, hoc eft fi q 
fit quantitas negativa, aut ttiam fi affirmative cubus fic 
minor quadrate ex latere r, tunc unicam tantum agnofeit 
iEquatio Radlcem poffibilem Sc realem, reliquseque duae 
erunt impoffibiles. 
In hoc Theoremate fi fiat p = o, hoc eft, fi defit iEqua. 
tionis terminusL jeeundus, tunc deventum erit ad cafum 
Regularum qua: djeuntur tardani, cujus folutio continetur 
in prscedentibus. 
§. 2. iEquationis Biquadratics Univerfalis 
x* ~ 4 p x* + 2 q x 2 -+■ 8 r x -f 45, 
— 4 P’ — 4 PQ — q 2 
2 r 
Radices quatuorfunt x = p. — a "t ^P 2 + q — a* — . — >, 
2r 
8cx = p-Pa+Vp 2 -f q . — a 2 + — , Ubi a 1 eft Radix 
\ 3 - 
iEquationis Cubical a‘ = p 2 a« — 2 p r a 2 + r 2 . 
+q — * 
Jam data iEquatione quavis Biquadratica, inter ejus 
hujufque iEquationis Univerfalis terminos fingulos inftitu- 
enda 
