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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 20
# Folio 8r, page id 00068269:0015
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jam his quatuor in se invicem ducti
producitur fractio cujus denominator est
Y, numerator vero fit ex his quatuor.
V, a -y. X. X+y in se invicem
non
ductis. Ergo si haec fractiocest
quadratus, cum e nominator sit
quadratus erit et numerator
quadratus. Eego quia.
non erit
productum non- quadratus per
quadratum in (fractio,) ver
quadratum (denominutorem y2) multiplicatus
producit (nume ratorem) non quadratum
Ergo factum ex his qualuor.
y
X- y. 2. A + y
non potest esse quadratus. jam horum
tres posteriores sunt progressionis arithm
ficae, primus vero est differentia progressio
nis. Ergo factum ex talibus quatuor
numeris non potest esse quadratus, quod
demonstrandum proponebatur
prop. IV. Area Trianguli rectanguli
in numeris non potest esse quadratus
huig
Latera triangulian numeris sunt
generaliter expressa sunt:
X = V.
ut a
2XV
X + V.
ed dumnotum est. Ex his duo
priora sunt crca rectum, itaque ductu primi
tertium est hypotenusa. Itaque ductu