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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 54v, page id 00068200:0110
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Januar. 1679.
Artificium solvendi problemata
aut demonstrandi imposibilit
tates in integris.
et Quaritur
integer qui sit:
mI Ponamus m aequ. L. et
M- 1
m +1
ter loco frectioro fiet
m 1
n
n
est
V
cui fractioni quaeritur aequalis integer
sit per n+ p aequ. 9. et ee equY.
et n-p aequ. r. fiet B aequ 4+r. et
paequ. q et loco n +p
n =p2
valores quantitatum x n, et p.
fiet. qFrgr+r, +4- 29r +Y
9+1
2qV
debet
4 gr.
seu
quae quantitas integro aequari
Quod est impossibileqe in si
aequares quod alit tum perpriora
G et Y sint unitas quo facto fiet
q+Y aequ. 1.
es hutene ca
2 qY Sed hoc absurdum patet ex valoribus
et . ouora pressitis
tac ratur quaesiti exematum non nis
e
Unicem: alias rem impossibilem sic
et
ostendo quia Y dividi potest per Y, ergo
et 9. adeoque et 9 dividi pot est per Y.
Ergo g. quia non sequalis erit major quam
Y. Sed pari jure demonstatur Ymajor
quam g. e idem simul ergo erit majus et
iminus altero, quod est absurdum. Itaque
impossibile est quod proponebatur.