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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 66v, page id 00068073:0132
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h. hac dezostatum
qua numerum ratio natem vel saltem numeri  cubum ejus
Esse numerum rationatem Quod t si etiam d et e facias aequ. 0.
surdesolidum
saltem necesse est, ejus quaratum esse numerum rationalem. et
ita porro. Quod si itaque saltem per simplicem radici;
alicujus extractionem poterit inveniri. Quod si imposibile
esse ostendatur, probala erit impossibilitas quadraturae.
seratursed subest ndnae nova sufficio et sublilitas exentiendo
in alio exemplo qaequ Y, sit autem 8 ago at 1b
Sumanus
fiet qaequ. Ya B + YVb_ et q rsa aoqu  Y sb.. Ergo fier
g- 2gr sa + ra aequ. r b.
itaque jam videt non procedere hypothesin nostram nec aequationem
3. sumi posse progenem generali, adeoque nddo conferr potest
Itaque generulis aequatio erit talis:
 ag + b r + re Y9, C92+ dpE +  etc e
2
r92
ibi lemini Y9  smplices tum remum relinquendi, cum Z est
a
numerus par
Et generaliter
video nullo modo esse necesse ut
diidendo pr  a) + bY per 9- X evamspat
sucieml divisio quia potest suberesse Yq.  N +. r quod
tanen o et destiui contrad sequeas: Y9, , 9 + +Y2
relicto altem iterum novo aliquo vel cum so compositam rursus
exhibere quantitatem divisibilem aliquid relinquentem, ita
A contnnando. Tandem in ultim residum destriatur
ad saq aquatio 3. minime est generalis,
sed ese nec ververa duarum incognitarum sed
uni nam ejus ope inveniri potest Y incognita
patet enim posito
() ut in aequ. 7.
OnquQ solam superfore in ea
idendum an aliter procedere liceat, quod antequam
Sacium prius Nimirum generaliter
a aequ.
p
372
+
r4
etc.
aequatio infinita
quantur an in certo Casu dentur duae aequationes finitae
u expri harum trium a. e Y. f. relationem inter
se exprimentes, ponantur eae esse datae nempe udcunque
ga +tq + Era etc. omnibus adhibilis potest
1
seminus ahomogeneis ex a. t. Y. compositis rationalibus
idemus daequ.n
quae est adhuc alia qualis ista
orte plus minus ve assurgens revera si explicetur
s
N. huc
e
0 aequ