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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 99r, page id 00068197:0197
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impossibile est exprimere polynomii
potentiam irrationalem per seriem
finitam. Ideo impossibile etiam Exprimere
potus nomn potentiam generarem per seriem
sit a+ l
finitam
aequy Aio Z a existente
numero irrationali, exempli gratia S2
non posse inveniri finitam formulam
2
exprimentem potentiam hanc
a + b
quemadmodum alio qui ea haberi potest, quando
7
vel 3. ve 4s
est 2. vel alius numeius rationalis integer
2
e
tunc enim fit: at a a +2al. + b
2
vel a +3 ab + 3a + B3 vel a+4b+ab
4 4ab+ b. Impossibilitatem sic ostendo.
ponatur tam aquam b esse aequ 1. Expri
contt
jam 1+
 esse aqu. ex primendo secundum
hanc serrem formulam finitam, ea constabit
ex meris potentiis ipsius 1. numere Z ut–
e
unitatis
cunque affectis; jam omnes potentiae ipsiuse
sunt unitates. Ergo nutt Z non esset amulus
e
in exponente, sed solum in coefficientius
haberetur ergo quantitas agebraica,
tali
aequalis transcendenti
12
2
quod
est impossibile Hinc in irrationatibus
exponentibus necesse est nos esse contertas
serie
intinita