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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 998, page id 1815201908:1055
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5+. hrtus.
TNCVLA CYLINDRTCA
Demonstratio-
Vmacur BC xoualis diametro A F, X pla.
noperpuncta L, A; C ducto ab codem c
lindro decussecur rnsula F. BC A. Cum osten-
Cum 2 sic superticiem ABC P, 3d supersiciem
ABD F, cam racionem concinere que eA incet
lineas B C _ BD; etiam incer quadeacum AP
quod per +5. buius par est superticici ABC L
e superficiem ABD F, intercedet tario BC
ad BB, hoc est extirpochesi AF, ad BD. sed
ve AF ad BD, sic eA quadracum AP ad re-
ctangulum rectis AF e BD, comprehentum;
ergo quadratum AL, ad suiperticiem FBD A
ee rectangulum AF BD eandem habee racio.
nem. isicur rectangulum AF BD, xquale est
superficici orxulari P BD A. Quod erat de.
monctrandura.
122S it e
aii
Mllarium
Dari argumenco probabimius, si rngula quae.
visplanis secerur secundun rectas BR, C F.
diamerro normales, superficiem rngularem
COA xqualem esse rectangulo quod diame-
De isin cribaseos parce P A. X vnsulx alcicudine BD
rectansulo Facto ex AL a BV.
concinetur; icem supertciem BDOC aequari
Posira enim C vgua AC E, cuius alcicudos B C par BE diatietro AF. ExiE
b+5. huius. Lupersicies CD A aequalisrectang F AF. ergo rectangulum L A F, est ad su-
perticiem OOA ve supees CP A ad superficiem COA, hoc cA vE CB
ad D B, PEF SG
hoc est, ex conul. DE F A 2d BD, hoc est, ve ipsum rursus rectan.
Bulum F. A A F ad reclangulum F A, BD. cum isicur rectangulum L. A. AP. ad su-
perticiem CO A. eandem habeaerationem quam ad rectangulum si A, BB, erir
hoc luperticici CO A aequale, Fadem est secundi demonArario. ui .usb Los ccura
R OP O 5 + Y 1,O, L. V 1.
AcuS Sic cylindrus AB CKD, cuius alcieu-
do DK par diarierro baleos A D, ab hoc
aBTCMIa SE rngula AB CD ciuidem alcicudinis
ducta deinde recta PP. qua Cieperpendicularis
ad AD, Secundum F F. hac sectio axi parallela
qua communem incersectionem cum superticie
Cylindri exhibeac lineam P G FI.
Dico superhiciem vngulae F G D ad Cuperti-
ciem F HIED, cam habere proportionem qua
CsF InEEFreCtAM FD _E E D curuaM.
Demonstratio.
ctangulum AL FP, LIuC FD K: eM aurem rectan-
pulum
cendimus cluperticlei tisnali ab aequarire