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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1015, page id 1815201908:1072
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TNGVLA CYLINDRLCA
2815
Aca sic exlindrirecti ongula F C HL, habens alcicudinem F C parem diamcero
batis e sphera AB CD. Cui sectx plano B N C inscribatur LCOsceliuS COnUS
ABNC. diuisa vero diam cero balis vnsulx P FI, (gux axi AD Sc aqualiS) in R.
vediuilus estaxis AD in M, crigacur RI normalis ad R HI, quam PaCCE IPEMC
essexqualem. hacque sectio KPI. ad cxlindri axem parallela. Luncta demum III
(quam eriam pacecip(is C A eNC aequalem) per TII _c I, planum agacur ITIL.
Archimedes propolicione decimaquarca libri de sphara e cylindro demonstrat cir-
culum deCcripeumradio qui sic medius incer M N _ N A, proporrionalis, Ciue inceF
MC e CA, aequalem esse eori conica superticici ABNC praecer basim. Idem
applicandum est ongula, oltendendum scilicee TFIP. Supertciem criangularem X
qualem esse quadraco facto sub lacere, quod medium sic proporcionale intex rectas
KI, TFT, hOC CA MC, C R. Iunse OF. quoniam G F Cst ex hypocheL par R FF
eric OF dimidia FC. ergo etiam IR dimidia a linex JL. Isicur rectangulum a Ex de
BFTI, IK elt criangulo TIIL aequale. Sed quadracum super media incer III, IK X- monstraci
n +T. BB
quatur rectangulo RI, IFI. illud igicur iplum quadracum est aequale TIII criangu- b Ex de
10. Idem intellige de quauis superticie pyramidali modo explicato.
monstraris
Porro manifestum est prramidem RILFI vngula B FO II inclulam, reprZ. ibid
Tencare conum inscripeum parri sphaerica AB N C ea rarione quam constructio po-
Aulanic. Ouod liquido lector incelliger, si conisuperticiem secundum lonsicudinem
perimerri baleos sue expandi concipiac, quod X I ipH M C, _ TTF ipS C A SIE X-
qualis. Ouod sigitur IT. Forec circulari perimerro expanso B NC aequalis, cum
superticies IHIL non solum repex sencaree conicam luperticiem. se dilli omninox.
qualis existeret.
eROBOSTTIO LXXIX
TVF CCFI IBITaTa PIaHO A E C recto ad axem BD Geuti lecta CAL TC
cylindri recti ongula sectione LM N, quae recta est ad diamerrum
OI. e ari cylindrico parallela: vngularique (egCnTO RL ML. N pyra-
misin (cripca (IE, (phXTICO VETO CONUS ABC F.
Dico triangulum MIK N ad ML N, criangulum candem habere
proporcionem quam AE. C balis coni AB C E, ad superticiem eiuldem
Pexterbalim.
42
Demon-
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