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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 410, page id 175905688X:0432
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420. IOH AN NLS TIUDDEHEL EPTSF: L
cur numeri, vel alia quancitates ad libitum, atque eo
altimus Terminus non evaneseat, neque aequatio, (IVCnu.
meralis, sre liceralis, quae hinc resultat, reducibilis (II,
certum est, neque Propolitam aequationem reducibi.
lem Forc; l vero ultimus Terminus evanescat, acque ctiam
inde Relultans aequatio non existat reducibilis, aequa
tio Propolica 2d pauciores dimentiones, quam ilta Re.
sulcans, reducinon poterit.
Excempla, ubi ulrimus Terminus non evanescit.
c. Si in hac aequatione x 3 =  a X X L 3 b b X = 3 a 3 ∞ 0 sup.
+3 a b - 3b3
L+ aa = a ab
L abb
DONaEuE a ∞ F, d b ∞ Z, relultabie inde aequatio numeralis
∞3 --3X X   x -3 ∞ 0. Oux, quoniam non est reducibilis, in.
dicabit, neque Propolicam aequationem reducibilem esse.
2. Sic etiam, (i habeamus hAHC X SXXX F + aabb ∞ - 10 a + b∞0,
atque supponamuS + a ab b ∞
a3 bC
3a3bB
 6 == b3 a
a=6, seu b ∞ = a, exlurget inde
X5 X X X X = 277 45∞ 0. Ouia vero haec aequatio reducinon
potest, certum est, neque Propolitam reducibilem fore.
3. Non secus, (i im XquationC X5XX =- 3 43 XX L = Ca3 X-2 a Cd ∞0
= =aaC + aCCd
TUDPONAEUE -- 34 3 = 2 a 46 ∞ 0, PeUC ∞ = + 4; 2C +Ca3 F aC6d ∞0,
+ a a
Seud ∞ -
het inde xSX X X X + 8 a 5 ∞0. Ouoniam rero
haec xequatio non reducibilis exictic, certum est, e5c.
4. Fodem modo se res hrabet in aequationibus, ubi quantitares
Trrationales reperiuntur: nam, exempli graria, (i decurhaecae.
quatio x5X X F ∞ x V = a a F bb, X. 1 a3b V C. 543 + , abb ∞0,
Lupponendo : a a -+ b b ∞ 0, seu bb ∞ -  a a, relultabiE
a 5 X X X X + a 3 b V C, 25 a ∞ 0. qua, quoniam reduci non
Porest, certum est, 85c.
LNeM.