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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 15
# Folio 5r, page id 00068319:0009
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inaequates non quadrati;
prop. LV. Duo numeri integri quorum
in se invicem ductu producitur quadratus
habent aliquam commurem mensuram
ut ab b vel ab bc
v
Jan
unde fit ab vel ab
C
Nam alte ter eam vel est multiplus
crjademduali vel non. si non;
necesse est at dum ducitur in atterum
duratu e e seum ut poducat
Nam quivis quadratus producitur ex
factoribus laterum in feuu totem
panle dictis ex quadratis factorum
lateri. Itaque i dividi potest in duos
factores non ns tribus modis, vel enim
omnia quadrato divelluntur, uno latere
hinc, altero illinc manente, et uuo illi
factores sunt aequales nempe radix; vel
nulla quadrata divelluntur, et tunc
aliqua quadrata hinc aliqua illinc
consistunt, et uterque factor est qua
dratus (v.g. a, b
quadrata divellunturs, aliqua non
divelluntur; et tunc latus ejus quod
divellitur, hinc pariter atque illinc
consistit, a d b, bc2) ac pronide
duo factores divellendo facti habent
mensuram nompunem nempe hoc
ipsum latus. Ergo  duo factores
quadrati aqalis sint inaequales
se
et non quadrati habebunt commu
nem mensuram, numerum salicet
aliquem:
rop VI Area Trianguli Rectanguli pri
mitivi in numeris integris quadratus
se
erale dixi.
in triangulo rectangulo primitive duo
0
latera circa rectum nullam habent
communem mensuram (quia per
prop. 3, tunc etiam tertium haberet
communem mensuram eandem, ac
+(u.g. abc, 
esse non potu