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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 20
# Folio 8v, page id 00068269:0016
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primi in secundum dimidiatum
id est ductu
quantitatis X ist in a quantitatem
Xy, fit area. Jam X-y, fit ex his duabe
quantitatibus X- y et X+y in se invicem
ductis, et XY fit ex his duabus X. y.
Ergo area trianguli rectanguli fit ex
his quatuor quantitatibus in se invicem
ductis:
X - y.
X
X+
sed ex his quatuor quantitatibus non potest
produci quadratus per prop. praeced. Ergo
nec area trianguli rectanguli in numeris
potest esse quadratus. Quod
Scholivn
operae pretium est adjicere analysin. Ex qu
Area Trianguli ectanguli in numeris, analytice
exp. essa est: Xy - XY; aquanda quadinto.
ponemy loco X, fiet
m V my aequanda quadrato. Ergo et m-m
aequanda quadrato. Quod impossibile esse analytico
as
huc
statim primo obtutu patet. Artificium analyseos in
lo consistit, ut literas plures revocams ad urtum
atuem revocemus quantum licet ad pauciores. Nam
re ad unum literatu reducta sempe aut solvere pro
blema possumus aut ostendere impossibilitatem
Eodem modo demonstratur M+ + 1 non posse
aequari quadrato Ergo nec X2 41 Ergo nec X+
aliaque innumera, uno generaliter summa