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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 409, page id 175905688X:0431
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DE REDHCTLOHE AE OLATIONUM. 409
Exemplum, ubi ultimus Terminus non evanescit.
SiC in aquatione X3 =3 a X x = 2 bb x = a3 ∞0, S(upPO-
+3 ab - b3
  Aa -  a a b
+ bb a
naTUIF a ∞ 0, retultabie, inde x3 -=B X x L 2 bb x - b3 ∞0. Ouia
autem haec aequatio reducibilisnon est, certum estneque PFODO-
Titam reducibilem fore.
Exemplum, ubi ultimus Terminus evane scit.
Siimxquatione xs - abx t + 0C3 X3 F  a3bXX - == aaC3 X f 1265d ∞0
3aA + C6B
bba
abccd =  abbc3
L54 ab3
suxponantur d d a ∞00, reluleat inde x 3 +503∞0. Ouia vero
hac aequatio erium dimensionum reduci nequit, arxumentum est
heque Propolicam ad pauciores dimensiones quam ad tres, redu-
cibilemFore.
Sic etiam supponendo d ec b ∞ 0, vel tantumc ∞ 0, orientur
bae dux aquatiOneS
X5 = 3 A A X 3 = 63X X = = 2 Aa63 ∞ O.
_5 =  ab X 3 = bb aXX F a3 b x + a ab3 ∞0.
3Aa
DHx SI rEdUCINON POTCRUnE, denOtabUNE Propoltam aquatio-
nem, ad pauciores dimensiones quam ad 5, reducinon poste.
Dico, illam non ad pauciores dimensiones reducibilem fore, quippe
aliquando continsere potest, ut Propolita ae quatio ad cundem di-
mensionum numerum sic reducibilis. quemadmodum continsit
In hac X + = = a X3 L + AA X X L = b3X =- + a b 3∞0, Supponendo
A ∞ O: exlurgic enim x3. F 2 b3 ∞00, quae non pocestreduci, et
tamen ae quatio Propolita eA reducibilis per X - 2 a ∞0.
I. R F G V E A.
Si in aequatione licerali pro una, vel pluribus, vel
Omnibasse laluratibus cogniris, supponan-
 fF
EUE