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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 105r, page id 00068197:0209
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Desectu Geometriae Empiricae
migianae, rem per ne investigane.
volu. Patat he ratio exdemoninanoce
Investigano
monstrationis Empiricae heor
Comnuni faciendi Empiricaem, namm uscu hicjum
emonstatione clagiiquae est prina earummatis. Pothagonie, seu
msnotia atc
vec
trianguli ABC angulo A existente recto
∞d
dica
indendum est quadratum super AB
una cum quadrato super AC, aequam
quadrato super BC
quadratum super AB sit ABGE et
quadratum super AC sit ACFd; et quadratum
suner BCsit BCKD. ostendendum est eBGE + ACFL
equati ipsi BerC1.
Productae DC, et FD con-
currunt in et et recta per H et A socet IK in T, et
BC in L. guadualum primo quoduatum 
aequae
rumo gAHi quia BGi, et AEH sunt aequalta.
Ideo secundo ABGE (id est ABIE+ BGI) et ABIH (id est
ABIE+ AEH) sunt aequalea Tertio quia ABLa et
4)
6
imi
pay.
absoluta pes trac
pugina, sed sequa
si remotis jam
praepriationibus
exposita
B1 T aequalia
Tsunt aequalta ideo Quarto ABIH (id est ABIT LHIY
(id est ADIT + ABL) sunt aquale. Crperartic 2 et 4. sunt ABGEet
et
Qvinto
inda quia CFK et ADH sunt aequilia ided deposeptimo
nitre
DCia A EFK- KDM + MAC) et AC H (id est ABH - XDM+ MAC) sunt aequalia
sunt aequalia, hinc NOnO ACKH (d est ACKTLHK
L
quia eavo ACL et HR
CK TL(id est ACKT + ACL) sunt aequalia. Ergo  (per
et CK TL sunt aequalia
erriculos 7 etq) sunt decimo ACFd
autem Undecima BCKI aequal:
BITL + CK TL.
ergosper
atirculos. 5 et 10) od Belit aqual. AB. C
uedecimo BCK ( aequal. ABGE + ACF D. Quod erat demonstrandum
aec demconstratio praeparatoria ad Empiricam Aaterintem sclicet
ruiet ad vem in Materia oculis exhibendamNempe ex laminis firmipl
ca detelligantur quabrata AB  in partes modo dicende sectis facta intelligantur
vadrata ABG et ACF D. Dico ex Laminis estis dissolutis et debite reconjunctis forma
posse quadratum BCK). Nam, ex laminis quodrati ABGE dissolutis r et recon-
in
sa punctis formari potest  para helogrammum rectangulum BITL quod sicostende
atur in EG producta sumatur  1GN aeqvalis ors HI, et ex N in B) agatir perpendicu
rif AB sicans ipsam BG in g. Quemadmodum ir sicat AE in R. Et resolutum etita
=EIR, et BQD et
magratum ABGC in quatuor Laminas binas triangulares ER
jus trapediat
aequalis ips
ARI, et (1D9, Hinc fiet B, Y1. modo tali. In AB sumatuu B5
et seducta ad angulos rectos sRoccurrat ipsi BC in. 
b  Lomnntum ex ABGE formabumus
et
elinquatur suo loco lamina capehi BARI, quigne utrique communis
ina
meta
une ergo trancpositi
nsnaturm B et altera vero Gidetranideratur et int
riangula vero transteraneur
in 
et facta est trans format
Ljade ratione secuneo ex lamnis quadrali
hin SB et BPC
Eit
= qua rati ABGE in parallelogri 
a
 ACFD dissulutis reconjungendo siet parallemram rum
rectan B
et parall larefrective ipsis  rM
ingaata CkTL: santa RB) aequali HK esduiantur XV VW aqua
currentes ipsis exk, CWF. Et
et BITL
simili Methoe
a
e
ETL. Y