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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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IN GVLA CYLEN DRICA
sunc. Tgicrmanifectum elC pLa a t omnia delpeis eriansulis, unam ingulam an-
biencla ascaltaene placs  pe sa attela al sb ta
sulis. Ouod erat demonstrandum.
PROPOSILLO XLV
Vperticies cylinde a Cuus rusa d cplindro recto decustatx, cu-
ius alcicudo par elt cameto circui quibalis est rngule, aequalis est
quadraro diamerri.
Demonstratio
Dico cylindricam lperticiem vngule
quadrato diamett AD aequalem eNc. Si
nesas; Ac primo, Acri pocest, quadeacum
AD mdius crlindtica Caperhcie quernou-
lam ambir: excellus durem sicplanum F. Fiac
eroo rectangulum DA F aequale plano F=
e CrISATUE LL normalicer ad diamerrum
AD. Deinde polroonum aliquod regulare
inscribacur circulo ABD, cuius vicimum
demitracur FI C normalis ad A D diameerU.
Ouia quadratum AD, 2. Secundi, SapCraL
rectangulum A D F rectangulo D AF, id est
ex constr. F. plano, quo eodem extesu qua-
deaeum AD ponitur superare superficiem
cplindricam ongulx, cric rectangutu AD F,
Cylindricae superhciei rnoule aquale. ergo
rectangulum AD C maius est cylindrica
Superticie que vngulam CEEIHAE. CFHO re.
Atangulum A D E eadem muleo est malus.
sed rectangulo AD FI aequalia sunt aplana
omnia limul sumpea qua per lacera polrgo
niihscripei ducencur axi parallela cerminara
in elliprica basi rngularis corporis. Igitur eriam illa plana maiora sune cylindrica su-
perticie quae ingulam ambic, quod Acrinequic, cum lingula plana sinc minoris d laci-
rudinis et longicudinis quam sinoule parres superticiei cxlindricx quas decusTarunE
ab ipsa ongulari superticie. Non isicur maius est quadracum AD cylindri supertcie
quae vueclam ambic.
Sit deinde, Gheri pocest, quadrarum A D minus eadem superticie exlindrica
ambienee ongulam; ee defectus sic planum F. Erit erodguadraeum A D cum quan-
FitaCC N quacungue, qux minor sic quam B, adhue minus ingulari superficie quae
vngulam ambic. Circumleribatur isicur aliquod potrsorium circa circulum ABD
coclaterum ve ductis per lacera planis ingulam cansgencibus, criangula remancane
AOK, D L MI, qua Smul sumpra x qualia sine auc minora quanticare NF; (quod ali-
quando fucurum est, cum mulciplicaris in infinicum polrooni conscripei laceribus
ErianGUIOTUM AOK, DE NF, cum BaseS AO, DE, cum alcicudines OK, IM AanE
tandem daco minoca) e plana ponancur lecundum lacera tiuins polrgoni quae axi cy-
lindeico aequidistene. Pgicur quadeacum AD Emul cum eriangutiS AOR, DL NF
minus est cylindrica superticie que rngulam ambie. Aequi plana unsutam ambiencia
dempriscriangulis, aguancur quadeato AD per peaecedencem. ergo criam illa vnd
cum criangulisminora lunc quam superticies exlindri, quae rugulam cingic, quod ab-
RK 2
surdum
Tevngula A B C D, cuius alcicudo B C, CIV
aequalis AD diamerco baleos cslindri
recti a quo decultaca cAt.
IacuS A FF minUS SE CubEenHZ aECUS AI, ∞
aE