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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 140, page id 175906937X:0164
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DE L EH I E E B I 5
Prop. 7. X t  lX3 X = B3 H f p+ ∞. 0.
Per transpositionem habebimus x = = l X3 ∞ n3X- p+. Un.
de patet, si n aequalis est ipsi l, tore quoque x aequalem ipsi
Pa
; de per consequens, si fuerint hitermini let aequales, hoc
eit, In xp+, una ex radicibus aequationis propolita a qualis exit
+
lingulis horum terminorum ae qualium lX; & li ina qualestue.
rine, neutra duarum radicum aequationis propositae porerit ese
inter iplos. Deinde per transpolitionem elt x -n X ∞ lx 3 -p+
UInde limili modo patet, six aequatur ipsin, iplam n quoque x
quari ipsi V C.; ideo que siterminihin e V C. equales fue-
rine, una radicum aequationis propoliea xquabitur lingulis ho-
rum terminorum aequaliums; de li tuerint inaequales, nulla radi-
cum aequationis propolitx erit inter utrosque. Porro per tran-
policionem eA quoque xt L pF ∞ lX3 Ln3 X, ideoque l∞3 L n3 X
majuS quami xt, e lXN L n3 majus quam x3. Jam s fuerit pro-
polica aequatio realis, eriex realis, de vel aequalis, vel major rel
minor quam m. Ouod Etuerit aequalis vel major, exit lXX LMNX
inajus quain x3. Sin rero minor sIc, erit x multo minor quam
J. Pn. Ouare utraque duarum radicum propoliex aequationisne.
cellario minor exit quam l. tn. Cuin ee existente x+ L p + ∞ lX3
Ln3X, CTIE quOque L∞3. L B3 x majus quampt. Acqui invenimus
I Ln majorem esse quam x, ac proinde lI- L nn. L 2 ln majus
qua X X, ec 13 f InH. F 2 lln majus quam l ~ X, nCC nON L X f
InnX. F 2 LInX majus quam lX3. FrgOI X -F Inn X F Z ILBX +
n X MajuS CrIE qUaI pA, eE X ajor quam B F Inn L 2UIn +. n3
Ec quandoquidem cubus Cx l- Ln major est quam l3 L lnn. L
2IIn. + n3, mulco masis exie x major quam pt dirilum per cubum
ex l. + n. Invenimus itaque quod qualibet duarum radicum. _-
quationis. propolicae major est quam p. F dirilum per cubum ex
L L H, UE de majox quam B3 = Inn F 2 UIm f n5, at minor quam
l. F n. Praeterea, quoniam l. L n major est quam x, Si fuerie X
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