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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 22, page id 1815201908:0079
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E. LN E A R V MI
Demonstratio.
Voniam in criangulis ABC, AD C pro-
Lportionalicer lectae sunE lineae super b2(
CrECtR CFUNEVE AB C limot CuMPEX, adt F BF
Cmul Cumpeas, ica AD C simul lumpex ad
TID Olimul lumpeas, S permurado ve AB C
lacera ad lacera ADC, SC F F B 2d IIDC
Timus Lumpea; Sed ex liippositione aequales
rectis ADC: ErgOeciam F B F, rectis FIDC. Sed _E reCtA FF
xequalis est linca C PI. Peicur Iloperimetra quoque sunc criangula E BF ec HIDC.
ROPOSIF1O XXII.
Riangulorum I(operimetrorum super eadem
baliconsticurorum, maximam habet alcitu-
dinem ICoscelium.
Demonstratio.
InE ABC; ADC criangula iloperimCEFA, et ABC
quidem ilolcelium; dico AB C maioris esse alcicudi-
nis quam EE A D C. Flabeac enim si tieri postic eriangulum
ADC, candem cum A B C criangulo alcicudinem: produ-
Cacus CB III F, VE PF linea sic aequalis linex C Biiun-
Bancurqne BD, F. D. Ouoniam AC, BD linex ex suppolciore lunc parallele.
eric anoulus ABD, aequalis angulo C AB, id est anguio A CB, id CA angulOT B D;
sune aucem lacera duo BF, BD duobus AB, BD laceribus rqualia; igirur erianguli
ABD aequale rriangulo F BD, e AD lacdsslaceri F D ae qualc. ScdF D, DC lacera (-
_ AD, DC lacera limul Cumpea; inaiora lune lateribus AB, B C. Duod est corrahy-
Pochelin. inde criatscant AD C, cande non habet alcicudine cum criangulo ABC.
Hlabeaciam ADC criangulum, maiorem alcieudi-
nem quam ABC; ducacur ex B linca BF, ParaHe-
la basi AC; OcCurrenS AD laceri in F; iungancurq;
CF. Ouoniam AF C criangulum, candem habec al-
cicudinem cutriangulo AB C, _ ABC Sc TIOCcelium;
CEUHE AF, CF lacera smul lumpra, maiora laceribus
AB, BC Smul sumpris per primam parcem huius peo.
polcionis; sed AD, DC lacera maiora lune laceribus
AF, B C; cum B cadar intra D, igitur _ lacCTA AV,
DC, mulco maiora sune laceribus AB, BC. Ouod
est concrahypochelim. igirur eriangulum ADC, n2-
iorem non habet alciendinem criangulo AB C; Led neque xequalem haber; isieur
eriangulorum iloperimerrorum super cadem basi constiturorum, _c. Ouod erac des
PR OPOSITIO XXIII
Sco ABC criangulum rectangu-
lum, de exB, ad AC balim, de
missa normalis BD
DCo AB C triangulum; ad eria lare-
rum quadrara, cam hrabere rationem,
quam BD linca ad quadruplum linex
suine
X
A B
abd Fuic demonstrandum.
mul sumpca, maiora lunt lacere R C, hoc estlaceribus AB, B C limul lumpeis; igieur
Demon-
Monltrandum.
eroposicio haec aliter demonstracht bro nostro de Fllipso.
 u i it ut ius e  er  t   u u  i pe te  u e a  p  ip i  pa u  pi u e t i  t     e  p  t  u . e    t p    pur