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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 15
# Folio 1v, page id 00068319:0002
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munifestum est tres numeralores fore
tria latera homologa alterius trianguur
similis in integris; et arcam trianguli
n
rectanguli in fractis per quadratum
illis
communis denominatoris ductam dare
aream trianguli homologi in intigris
per prop. 1. Ergo ut ante, si hec
quae si quadratus esse non potest,
neque id, quo in quadratum ducto ipsa
producitur; nempe area triangule
in fractis, quadratus esse poterit.
Prop. TII. Si in Triangulo rectangulo
uit duo latera quaelibet
habeant communem mensuram, tertium
habebit eandem communem mensuram.
Est enim tertium nihil aliud quam latus
summae vel differentiae qvadratorum
a duobus reliquis. Jam et hypothesi
duo ista reliqua latera habent communem
mensuram, ergo et quadratoum eorum
habent communem mensuram, nempe qua,
dratum communis mensurae laterum. Ergo
quadratorum ab ipsis summam vel differen-
tiam metitur communis horum quadratirum
mensura nempe quadratum communis men-
sume laterum. Quod si ergo hoc quadra
tum summam vel differentiam illanm
metitur, etiam latus hujusmeos quadrati
scilicet communis mensura duorum reliquorum
laterum) latus summae illius vel differentiae
metatur, id est
metietur (latus Trianguli
tertium) metietur.
+(u.g. abc,