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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 988, page id 1815201908:1045
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N OVLAACYCLNDRICA
210. Vndec.
b15. naec.
C16. Vndcc.
dL. Sexti
Demonstratio.
Ctciragueongula AB C, à eylindro recto ab-
scisa habens alcicydinem O B diametro
bascos A C parem: eius basi inlcripea sIC AguT2
regularis ADF FOC, de ducta lic AC ad
terminum vicimi laceris CC. Denique plana
Ponantur per latera polysoni quae requidistene
axi cylindei exhibeneia communes incertectio.
nes cum ellipsi ABC rectas AM, M N, NO
Dicoplana haec omnia Bmul Cumpea, nimi-
TUM ADM, DENM, E. FON, LOPO8
CCP, aequarirectanguloC AO.
Duod sic ostendo: PX CCMETO AUCATUE SO
normalis diametro, de à puncto O ducacur in
superticie crlindrica recta O B, que crie rnou-
la alcicudo, et ex hypochesi xqualis diamecro
AC, iungatur deinde SB, ductis insuper D II,
E I, FK, CE normalibus ad A C, iunsCTINI.
INRO, T. F. Ouoniam OS, DFT LinE p2.
rallele, icemque BY, ND, anguli BOS.
ND FT aequales acrune. Rursum quia OS, Q B
aequidistanE DII, DMI, plana SOB, IIDM
suncbparallela. ergo carum sectiones commu-
nes cum plano elliprico CB A, rectenimirum
BS,MTT, Sunccparallela. Cum isieur OS,
BS xequidiltent DH, MFI, crunc ansuli
OSB, D LTM xquales. crianoulaivieur BSO.MHD Sumilia tunE, erBOVE BO ad
O.5, ita HD ad D HI. Sed BO ex hrpocheli por Cst diametro AC, adeoque du-
plasemidiamerri S. Ergo ex MD dupla eA D FI. Pari modo octendam rectas
NF. OF, P C duplaS esse rectarum F L, F R, C F. Precerea quoniam exlindeus ex
Ayporhiea rectus est, a quo decusaTUE VnGULA, CTUNE M D, NE, OFs P Crectae pla-
nobaleos AO C, adeoque per definitionem 3. vndecimi angulosrectos Faciune cum
lineis AD, D F, EF, F G, GC. TrIanGUIA ErSO ADM, COP rectangula LIIME, d
PIANADMNE, P NO F, FOPO, crapezia rectansula. Ouoniam isitur MID, crian-
suli ADM es alcicudo, eaque dupla est octensa iplius D HI, criceriangulum ADM
rectangulo sub AD _ D II aequale. Jam vero rectis P D, NM bilectis in Y ec V.
iunctaque TV, rectam TV dimidiam eAe (IIIIX rECtATUM MD, N F; de rectan-
Gulum ED TV, aequari crapezio rectanguIO MNR D in sequenEI, FGUTX OpPOTEI
nicarersi, demonstrabimus. Ouare cum rectansulum lub F D _ MI D. N P canquam
vni guae duplae suncrecte T. V, rectanouli E D TV duplum asic, cric quoque rectan-
gutum sub E D, XNTD, N F. canquam vn2; duplum plani MNE D. Ouin aurem
rectae MD. NVF, octenlae lunc duple rectarum DIT, FI, rectangulum (ub PD; 8
MD, NP Simul Cumpris duplum etiam est rectanguli sub F. D, _ D HI P I simul
Cumpeis. planum igIEUE MNY F D aequacur rect angulo (ub D R, SINC AD _ED IT. BF
simul sumpris. Pari argumeneo octendam planum P. NOF, aequarirectangulo sub
EF id eA AD, _ B I, FR; planum veroF O. P C rectangulo sub F C, hoc est
AD _ FK, C E,criansulum denique CP, C ostendam rectangulo lub eC, id est
AD, d C:T aequari, veoltendi supra criansulum AD M aequari rectansulO AD II.
omnia igicur plana vngula inseripea Cmul sumpea xequancur omnibus rectangulis il
lis simul sumpris, hoc est per Corollarium praecedentis rectangulo quod rectis C A.
AC ContinCTT. Quod erac demontlrandum.
Corol-