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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1011, page id 1815201908:1068
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Y N GVLA CYLINDRTCA
TO1L
exPCIIEur ab vrsia, aaaSula PaFalClA QUX PEMIALIS SUnEBaCES, FCFerunE duOS
Parallelos circulos, qui bales lunc cxlindri. planum vero L. Cet allastrla.
sulares prilmacis bases medium, repraseneac curuam. exlindri superticiem mediam
incer duascrlindri balescirculares. Quemadmodum enim ex demonstracis ab HI-
chimede deduermus duas cxtindri sphaeram ambientis bases esse dimidias superticiei
spherica, ica e nos octendimus duo criangula prismaris nempe nsutam concineneis
Bales, dimidias esse superhcicirngularis: _ sicur ex eodem habemus Archimca
superticiem curuam cxlindri aqualem esse luperticiei sphaere, ita plane ostensum à
nobis est planum F P. HG supertcici rusulari eAle xquale.
e R OP OSI TIO L X XIV.
ala sic cflindri recti rngula E.DC, cuius alcicudo BD pax (IE cir-
cumterencix circuli EBC.
Dico supetficiem ongula quadruplam esse circuli F. B C.
Demonstratio.
X cenEro A ducacur AD: Rectangulum
sub diameteo basis F C, de alercudine vn-
sulae BD aquarur a superticici ongulari cy-
lindricx. Sed rectangulum F. C BD, duplum
est rectanguli AB, B D, ac proinde quadruplum
crianguli ADB. ergo luperticies ongularis
E. D C quadrupla cstrrianguli AD B. sed erian-
sulum ADB equacur b circulo R B C, quod
eius balis lic radius AB, alcicudo aurem BB
par circumterentix. Ergo superticies rnoularis
EDC quadcupla eA circuli F. B C. Quod erac
demonstrandum.
Analoeia cum Sphaera.
DVis rurtum hic non agnolcar sphaeram in
Longulas Eiuldem enim circuli EBC, e
Superticies rngularis F DC, e Cuperficies (phx-
rx crius diumerer P. C, qua druplX lunF.
PROPOSITIO LXXV.
TNgula EDC cuius alticudo BD
quaecunque, (in spice houram pro-
policionis7 4.) secerur perrectas AB, NI M ad diamerrum normales pla-
nIS AB D, NNO, qua axi cylindrico equidistene.
Dico luperticies vngulares FDB, BDOM, MOC: candem d MetLC
_ adcoram insula Cuperticiem habere rarionem, quam parres diamerri,
velincer se relad cocam diametrumi.
demonstratio.
VperhcieS E DB Cxquatur reCtangulo E ABD: X SUPEThCIESB D OM, rECtAn- C C roll. 55.
sulo ANBD; SuperhciCS VeTO MO C rectangulo NIC B D aqualis cst. TuPCr-
e COa L.DC LCcCaHBIIO L. CBD Ctt a _ GHaIIS. ICa L. 6. Il d LCCL AH B Cdu 855. brin3.-
tunc
n   e    .   u 11 1 .    11    1      .  . e   t .    1 e  l p     e  e u pue 1  . a  1   ete a t    r ul