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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 15
# Folio 5v, page id 00068319:0010
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primil
proinde triangulum ipsum non foret primi
tivum)
Ergo etiam latus unum et
alterius dimidium nt maple nullam com
s
st
munem mensuram habebunt (N si dimi
dium latus A. dividi potest per ea divisorem
seu mensuram lateris B. multo madis ipsum
A integrum per eam dividi poterit) jam ex
latere unorcirca rectum in alterius dimidi
un ducto sit area Trianguli. Ergo area
trianguli fit ex duobus numeris (imequalibus
nullam habentibos mensuram habentibuo
communem. Dite autem numeri isti, non
posunt esse ambo quadrati per prop. 5
Ergo arta trianguli se quo agitur fit
ex dubous numeritore in aequalibus non
pet prop
quadratis adeoque inde esse non c
qua non potest esse quadratus. 2. E0.
Prop. V. Omnia latera trianguli rectanguli
primitivi
in inteoris sunt numeri impares praeter
unum latus qu circa rectum, quod semper est
par (S. quidem area est integer)
primum patet omnia latera non posse esse
paris, alioqui triangutum non esset primitioum
quia communis mensura foret binarius. Nec
duo quaelibet possunt esse pares, alioqui et
tertium foret per prop. 3. Ergo si quod est par
erit unicum tantum ex tribus. Est autem semper
aliquod tag e si quidem area est
integer, quia alioqui latere uno in alteria
cirta rectum dimidum ducto non potest prodire
integer.  quid fiat cum area non est integr
non est huus loci, quaerimus emjus aream in
integris quae sit quadratus.