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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 14v, page id 00068235:0028
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posito y esse Cem. et y slan. dabilu
s
ulique  et sutuma surdesoidorm ab omnibus radicibus
jam  in secundo termrino est simmina re Ctangulon
a
. Apes
b omnius sadicibus in dicum surdesolinon singuta
ar malle s
nna
e ad aderatiogales abeunt pro denum sutimin
qunum tale rectangulum tantum sumiendum
est lotr
mulliplicandam per numerum rectangulorum
est 15)(+ n + n + p in (5 lam +n+p alleum id est
quia ob rationalitatem unum sundesolidum cimallero com–
cidit, tantum sumendum esse t quadratur praeceden ternim
secundi multipeicalum per nunctiam divsum per 5 et multipli
Catum per numeru, combinationum omnium remm. U
den similiter terminus sequens esset cabus primi divisus
per c, mulliplicatus per conternationum dmnium
rerm. eit ita porro haberentur coefficiemles omnes
equatiogis hubus quaduliquadraticae. Et haec
s
quidam pulitire procedunt, verum video non posse
sista nobis esse nota alioqui habertur X a quale rationuli
nam revera secundus tenminus esset X aequalis rationali
Ergo sufficit nos fingere secundm terminum esse
s
L + m ek. 49  qui si est rationalis videtur tertius
terminus esse hujus cubus modo supindtcto verum dissi cultas
manet quod hoc modo X hiberetur intronaliter quadra
orquadratmce. Contra id quod posirimus componex 4 sinde solidis
Non igitur ex ista Hypothesi sequitur lalis aequato 20 gradiant
sed necesse est dan aequationem
c
Cujus oefficiens secundi ter miniterit aequ. l’+ m + nEt3
evvissime videlmr res suecedae re
mulliplicetur per X3+ h. habebitur X
s
Attoltatur
13
+.  +. et
 +CX
e
20
perto
+hX + en
ad
Aequalio proposita exaltetur etiam ad XE X Xhet
comparando habebuntur h. C. f. etc. quibus habitis
habebitur e5 ope aequavis colicae sit cabus x + PX+G
abfocent  fingatur
equatao dibe cu
9+ C ∞ + qX 2
+ RX + 4 aqu. 0. quaeducta
altetur ad   in a x + h dabis
+ h X + dex +h4
verum jam videonihul hine haberi
et nos assurgere ad aequilime Sh
mudus pro habenda h. vel e