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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 15
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Mathem
THEOREMA PYTHAGORICUM
Empirice demonstratum
circa rectum
Trianguli rectanguli duorum Laterum quadrata aequantur
Quadrato Hypotenusae
ut horumlatera cd, BG se secent in L
Ecthesis: Esto Triangulum rectangulum ABC, dujus angulus rectus B. dico quadrata
acela lateris AB, et lateris CB simul aequari quad rato hypotenusae AC.
ppapiratio: Super AC erigctur quadratum ACdE, et super CB quadratum BCFGP. Ex E opposito
prua mon-
strata
ipsi C agatur in AB perpendicularis EF. Cum et super ea erigatur quadratum EFCH
Denique ipsiDL sireatur in AL aequalis AM et ex M
ad partes 9  latuseai d geat in ABs agatur porpendicularis MN
Et aequatur ipsi AB. Nam ang. EAF + ang. FAC = rect. et ang. EAF + ang. AEF = rect
ergo ang. FAC = ang. AEF. Ergo triangula EFA et ABC habent eosdem angulos, et agum
loppotenu jam hypotenusas habent aequales AC et AE, ergo triangula sunt congrua inter
sE, seu et EF = ipsi AB. Cemmn etd esi conguua elet ect
itaque ostendendum, quadratum ACDE aequari quadratis BCFG et EFGH simul,
cum quadratum ipsi ab EFGH aequatur quadrato ab AB
sad pri oetendemus sed prius ostendemus HG transire per D. Nam cum angulus DEH sit
aequalis angulo AEF, et DE, EH, ipsic respective) AE, EF, congruent DEH et AEF, ergo HD ipsi FA, et
angulus HFE, angulus ad F ipsi angulo HD ergo et Hic est rectas, ergo, sed angulus DE GHE itidem est rectus ex constructione
Orgo Hd et HG cadunt in directum, cumque D et G sint ad easdem partes et Hd minor quam HG, itaque HG transit
per d.
destali Ceta
Demonstralio  onstratio Eminirica
EFGH
catur aqu’aece
DEFL + EHD + DBB
edL t DEFL
aequ
ACDE
aequ
aqu
+ EFA + ANM
aqu
edtm
FGL  CBL