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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 39r, page id 00068200:0079
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26 Xb7. 1678
screda 1.
XypX-y
13)
32y
Trea Trianguli rectanguli
in numeris non potest esse
quadratus.
x-1. Ergo y= Z pZy. posito 7+y aequ. X
et positus Xypcy
Latera Trianguli rectanguli in numeris
sunt.
Xyp Xy. Ergu ZY p1 . Z
32 2ty, 3+2y
area ergo est
2
egi X - y. 2XV
X+ y2
latera circa rectum
Hypotenusa
abc, Imn.  abclmn, abcaremd = X V. seu: X, y, X~y, X +y.
ajo hanc aream non posse aequari numero
quadrato. Nam dividi potest per X. et
prot ita residuum per .
verte
Nam duo exquatuos ejus factoribus enempe
de. V. Omnes enus divisorci (nempe sin
qualuo uadisi X,=LCy) hebent
esse Congmensurabit
alsum
ergo et commensuranles esse debent inter
e. sit eorum commen maxima communis
c
mensura 3. et prox scribamus e
pro  vero 2n
ex
fiet area productur
4Z, VZ, X.y, Xty (nam in
caeteris explicare X et y nihil est necesse
ad nostram demonstrationem) Seu
productum ex eeXe
- 2
t
s
Ve
aequalu quadrato ergo etiam divisendo
per 52
quadratum, quotnens, nmpe
F1X, X-y, X+y, quadrato aequabitur,
itaque duo factores 4v. debent exx
Commensurabiles inter se quia radici
squadrafi. Sed absurdum test eos e
comnensurabiles esse, quia prodieree
X, y dibisis per maximam commun
es
mensuramt. itaque impossibiles est Hypolss
la