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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 103v, page id 00068195:0206
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estat ut similiter oculari demonstratione exdibeanus
aequalitatem. quadrati ACFd, et rectanguli CKTL quod est prion
aequalitate paulo demonstratu difficilius sine extrinseci assunta
segmradem  tamen qua ante via, incedendum erit per onvest
gationem segmentorum. Primumigitur ut KFd transferatur in HdA, epod
tet ab ACFd resecari CFdM, restabitque cAM. Rursus HTK, cum transferrit
deleat in ALC resecari debet ab HDA. Cum etiam Denique etiam Kdm ause
in debet ut rest qua translatione babebitur ex AC M DI, fiet
A K T LCM D unde aufer refecari debet KdM ut fial Ck TL. sectiones
dem la port figurae transferendae faectas in faciendas in cino loc
amus et in alio um ergo k FC secta sit pe  deo per MD, ideo
imiliter HdA secetur per vio ductam congruenter. Et cum Hd A secta sit
TK ideo similiter KFC fecetur per FX et per KM ideo similiter
XFC secetur per =Y congruenter positam ipsi TK, et Y congruenter posita
 ipsi KM. et ut KM seravit Var secat alicubi tm, nempe in X; ita
ix secabit alicub. Md ut nempe in T. quia Et quiq YF  in KFC respon
et insi Kdm in HdA id unumque ex alio fit transpositione ipsius kFC in
Na dei sectiones ipsius XdM repraesentando in YF ip, repraesentabitur
W per Bd. Et = Y repraesentabitur per 42, et Y per ZC0. Postremo quia
vel HTK transfertur in ALC idso sectuis sctio ipsius X Z Y per X W
repadtentetur in ALCper No. ita d tandem assecnti sumus desideratum
n
mnes partes quadrati ACFd transpositae constituant rectangulus
Nam CAn manet utrique omnune, 2 L Z+ co transferetur
in A0HG Zd in NLCB, +BNC H in XAM XVAM, et denique 2G qued intrur
XTL
Unde talis pro CKTL, Unde talis prodit transformatio: quadratum  ACF
secetur in duo tria Trapezia BMC ,  DDGZ, ZPCo, et duo tri
angula CAM, ZFC n et manente CAM, transferatur _ ZFCd in AON,
et 398 in ON LC, et D M C( in XVAM, et denique  ZGY Co in KTVX, atque
ex iisdem tribus trapeziis durnus triangulis AX AM, et AN AON tribus
traperiis ONLC, XVAM, K TV. X fiet rectangulum CKTL. Schema
tale erit
ACAM = CAM
FC = AON
ACFd = DBGZ = ONLC = CKTL
DNCI = XVAM
(2YCO = KTIX
postquam ergo quae situm assecuti sumus remoto jam pegmate
omnibusque machiramentis ratiolinationis, rem ipsam velut de integro
aliis sic exhibere licet, hactenus dictis omnibus refecti dissimulatis:
Theorema: Quadrata crurum trianguli rectam
guli simul sumta, aequantur quadrabo Hypotenusae
demonstratio ocularis
sit Triangulum rectangulum BAC uius angulus rectus A, dico quadrata
super AB, et quadratum super AC simul sumta aequari quadrato super BC
constituantur quadrata ABGE super AB, etCACFd super AC; et easdem partes BCKI super
t
Nam ang 1BG = ung CBA, et BI = BC, et BG= BA, erqu. B
unt 1391 et BAC, et ang. 1GB = ang. CAB ergo angulus 1GB rec
BC adet i in GE
ad angulus BGE rees ex constructione ergo recta 1C, et EG cadunt in
gicum act eotur
1GB, a
G ipsi, erunt  id et E in directum, et Gt h eu Ac minor q
g. 1BG = aug.
minor GE(= AC
cadent G+, E
1B = BC et A = BA congruero
et ob ang. BGE reZ
ectam
alem
GerC
ex constructione, et 1GB etiam rectum (quia
aleo
irectum, et 1 in B ectum, majoremque kF (id est AB) ipsa D F, id est A C) cadere, 
in ret FK et eK secabit Ad,  sitque punctum intersectionis M
ectum et c
ob angalum rilectum, e
F, D, X, i
ostendemus  pusto Anm
in
d ttu
oqi di
15 et per sputatur par allela ipsi AC socans AB, BC, in 5 et A
dan
in A + se Sectonergo foi est quadratum ABGC in
per
le
iangula
in ABtK, 1G2P, et 
otidem traperia et triangula prio
scilicet duo ABIR ASAL (congruum ipsi 1GQp) et duo triangula
imiliter rectangulam BITL,
AFR (congrnum ipsi Beg) et BS A (congruum ipsi 1EK) ATR, BSA, quia Cergo
ute et
=ASAL, et BPZ= ATR, et 1EA= BSA, aequalia erunt
13p9 BGt E
Fnspectire prroribus congrua, trape
BIR, et +G2
(Trapez 1G2 = Traper. ASAL -p1IL rectang
ABGEquadrat Triang. BPZ =
triang. IER = Triang. BSAS
Ergo AB GE = B1 7 L.
Unde schema tale segmentorum congruentium n AGEstaBI
(Trapez. ABIR = Trape Z. ABIR
Triang. ATR
et AE lecabu
A
ABR
ABG2 et BITL