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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 992, page id 1815201908:1049
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YNEVLA CYLINDRICA
eutae lupeeee. Muacacu gicur AC non elt minus exlindrica vun
sulxe superticie; quare cum neque maius elle posse, supra oltenderimus, necesle est
velic aequale. Duod erac demonstrandum.
392
surdum est; nam omnia illa pa simul cum criangulis laceralibus exlindeicam vn:
L Ldt
ALV.
Aca Cicvngula, qualis ir pra CCachei, ad cuius diametrum AD duet 2
notl 2 Gununsuba funcoefiu inupeet est
dricarnsula recta Ill.
Dico cylindricae superticiei vngulam CinSCnLIS PaTCCM HTC RD X.
qualem esserectangulo AD6.
Demonstratio.
CInCSaS, crit rectansul ADC, velmaius vel minus supersicie H Z CR D. sC
primo aius, _ excCHuS sic planum F. Arcui FIB D inscribe Aiguram aequilate-
tam coc, adeoqueram paruis constancem lareribus, rerecta AR subrendensareum
RB A, qui cum arcu D R complec lemicirculum, deficiac a diamCEro AD; quan-
cicare minoridaca, adeoque rerectangulum sub A R e D C, luperetur arectansu-
10 lub AD _ DC. Plano minori quam F, quae omnia ex elemenris factu Facillimas
Duoniam erso rectansulum AD C superat rectangulum AR, D G plano minori
quam P, quo superare ponitur superticiem FITCR D, erir quoque rectangulum
ARDC maius superticie HITCRD. Aequi rectangulo ARDC aequancue
2plana quae secundum lacera tisurxe aequilacerx inscribuneur suxerticici TITCRD.
eroo _ plana illa inscripea maiora lunc superticie HIT CRD, cui inseripea (unE.
quod estabsurdum. Non isitur rectangulu AD C, est maius superticie HX CMD.
Ponatur deinde rectangulum AD C minus esse superticic HITCRD, delellus
autem sic planum F. circum leribe arcui EIBD figuram xquilaceram eoc lacerum,
ve ductis per illa planis ad cylindri axem parallelis ongulam rangentibus, postre-
maplanum versus D, quod esttriangulare, minus hcplano P. Quodnecessario fu-
curum aliquando, est manifeltum. igicur rectangulum AD C rna cum plano illo
criangularis adhuc minus eric superticie HTC R D. Scd plura superkciem HIT CRD
A2. huins. ambiencia, demprorriangulo,  aequantur rectangulo AD C. ergoeriam plana am-
bientia vna cum criangulo minora sunt superticic IIT CR D, quam cingunc. quod
eAt ablurdum. Non igirur rectangulum aDC minus cA Cuperticic IITCRD,
Sednequemaius ese octensum est supra. necele igitur est ve eidem sic a qualis. Ouod
crac demonstrandum.
Dico leomentum superkicier ndrice rnoula ambientis IB N L C L 1
aequale ellerectansulo quodrectis AD, MO COnTIneTT.
PROPOSITIO XLVII
Aca sieongula, qualis suprâ, ductis deinde lineis MII, O N ad dia.
metrum AD rectis, per has ponantur plana ad axem cylindri pa.
rallela, quae in rngula superticie cHCianE ReCtaS TK, N L.
a Foroll. 4
bnino.
Demon.