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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 37v, page id 00068200:0076
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lateri autem primitivi in Amensuram ducto fit latus homo.
logum, derinativi. Ergo pacta area primitivi in quadratum
mensurae fit area derientivi.
rectanguli
prop. EII. Si area Trianguli primitivi in numeri
integris quadratur esse non potest, nec derivativi
ullius area quadratus esse poterit.
Nam esto derivativi area quairatus, dividatur ea
per communem mensura quadratum, proveniens
erit quadratus. Provenit autem ared primitivi
per prop. 2. ea ergo erit quadratus contra id
quod posuimus. NNam posuimus id fieri non posse.
posito ergo aream primitivi non posse esse
quadratum, nec area derivativi poterit esse
quadratus.
prop III
a
d
2
29 aequ X 47V
Ergo; (84y) aequ (Y 2Xy
for: 
xa yr (3237+3
C sit = quod f.. 2Y+2Z
inerris fieri debet, fier
 aquu
DEdo fF aegr. 2. seu B
si duo numeri non habent contra ad quoo postulatur
Si summa et differentia eorumem duorum numerorum
aliamquam binariu
habent communem menfuram, ipsi numer duo
eandem
numeri habebunt, communem mensuram.
X +1
_
X
co
X+y., = x +y aequ.
co
aqu.s.
-s.
nam Xty, 1X-y rt
Ca
14 9 16 25 36
8 X -y aequ. Z
2
X+ y aequ XCS
X aequ cor - y aequ. qr 4,y. Ergo y aequ Co-
et X aequ co - c0 +Z)
5+4 aequ. 9.
aeqo cd+
5- 4 aequ. 1
haequ 9+
a
v
(2-est, et r non possunt simul ex quadrati, nan
et
4 aequ 9-
si XY sit quadratus ves Xit y fiunt conmensarabiles, vel
et xer y. sunt quadiati, sod hau X- y qoa est quadratus.
nam itergu vel X+y et X-y sunt conmensumbiles, vel sunt quara
si ergo debent, X. Y. X - Y. X+ V. simul esse quadrati sed
hoc est impossibile quia non dant tres quadialu procgressionis
arithmeticae
grum diferentia he quallatus