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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 105v, page id 00068197:0210
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Jag.
Al ta pasition
figara
duplices literae ascribia
loci praesentis, alterae pri
pareathesi inclosae loci a
terig. An et desi
quid pprius quid posti
Lner A ducta TRL 
BLC, ITK
ad angulos redi
Et ct
mant
sed reliqua trans-
fernatur in loca
congruentia, nemper
quia 
GIP
V sAL A
Vxm
CWVnX
2
YeL2
AMKI
rectum
ul
potandam)
unae Specimen Geometrica empiricae quod
excogitavi ad demonstrandam per laminatrans
positsas, aequalitatem quadrati hypotenusae, cum quadralis
un
 C+
aterum Trianguli Rectanguli
Qvia id huc arbitrariam, quod secu est in motu
sit Triangulum rectangulum ABC, dico quadrata laterum  nempe
AB ab A qa ABGE, et ACFD aequari quadrato hypotenusae BCK
Et primum quidem ABGE aquabitur rectangulo BITL, et RCFD rectangu
CKIL, quae duoreitangula faciunt BCKI. Utramque aequalitatem trans
formatione ostendamus. Ponatur quadrata ita esse erecta, ut
i occurrat majoris lateris AB quadrati A BGE lateri EiG in I, at CK
occurrat alterius lateri AD in M, latus deque et KI, secet AE in R.
jam in Btsuaatur DP aequalis, AY, et ex P ad angulos rectos educta
Locurtu ipsi b i
a
dnaetur et po in ABua pars 6)
ex gu
eee
psis AR, AF, jungatur pQ aequalis ipsi 2R. Et in
Arespective aequales ipsis EI, IR) jungatur Sa aequalis ipsi Et
e
sectumq erit quadratum ABGE in partes quatuor, nempe duo Trapesia
atut pasis
G1P8 et duo triangula EIR, et BQP. Ex his relinquatur
Bis B
Suo loco BAHI, cum sit commune ipsis ABGE, et BITL, G P8 tran
t
At,
feratur in ALAconu te (quia s (id ust AB. B5)
a
anid est LT-
aequo ipsi ibidist _ 1B B esum sint 1B L r B1 L14 IB, et TAC
facientes
sit C, Cx aequalas
agi jam in BG, et BF sumantur BY BP respective aequalis
ra
BSColi   C+s est CCEI
ta sea passe
respective sps m
unde AM, AT, et ex
1d et hormacita
ductae ipsi FDoccur.
rant eiuu inv
erunta AV, V, ipsis
TL.K Maequales.
epson
1
2
la
 lid est LB-Ba) aequa eosidestk
id est FI 1B et AC saequ AE)va 6 sid est  GB- Da
seu EA. AA et cuctrusHt Et  rectae respondentibus sunt
paralleta adeaque et angnta
cocicar etgo lna
denique in AC, AL, suman
tuis AY an aequales
 homoloqi sunt aedcales.
eique Mnhtr tranfeatur trian
 etEIR transferatur in SBD _ngruen
P in AR comens. ita (x ABGE transforman
factum est BI. TL. similiter sectum erit quadratum ACFD in
b
partes quatuor, duo scilicet triangula CAM, VFlo, et duo trapezia
duxM, et CWVX. Ex his relinquatur suo loco CAM cum sit commune
ipsis ACFd et CKYL. Sed reliqua trans ferantur in loca congruentia
e
VFV m A
respectioe ipsis VE, VW, e
1Z et DVXM in YCLZ; Set CWVX in At AMKIC
itam ex ACFD transformando factum erit (KT]. A.
aa
en duo Et quia proxime ante ex ABGE factum est
urmando tactum est compositum ex  ipsis B1TL er ex
d
17
id est quadratum BCKI. eeed ergo illaduo quadrata simul
et
huic quadrato sunt aequalia. quod de prat demonstranda
e s
n
bitur
ant
s