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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1002, page id 1815201908:1059
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1002
YN. CV L A CYLINDRICA.
11
Demonstratio.
lanEpLanA KGD, X HTO diuidenciare
ctas BC, AB bitariam, ec exhibencia
lineas CD, ITO in superticie cxlindrica,
rectas vero SO, RM in planis, CBF F
ABF. Deinde ex  _M, linea duean-
CUT O P, MN, qua aequidistent rectisR
KFI _e secundum lincam NNI, planum po.
naTUEBaSi A C F. vngulari aequidistans ex-
hibens in superticie cylindrica arcu T N V.
Denique ponatur in planu AB F. per pun-
ctum M recta VM T parallela A B, & haC
sectio per V Y, _ BAIEOS CCHEEUML H pEO-
ducens rngulam, ex qua ablcindetur plane
AB TNV Cesmencu vngulArC AVOTB:
quia R C CA ad RS, VE R FI adRR, XVE
KC ad KS, ita C D est 2d S O, viG; R FI
est ad RR, sCFTO est ad R NI, erit quoque
ve EDad S O, hoc estOF, sIcFIO ad R MI
hoc est FTN. Sed guia arcus AB, BC Cqua-
lessuE; Ve CP ad FIN, ica est superticies cy.
lindrica BP. P F C ad superticie AVNTB,
155. _ ve CD ad FTO, ica elt superficies vnsu-
laris BF D F C ad ongularE, AVO FB.
Tgicur re superticies BL. P FC ad BEDFC.
ita superticies AVN TB ad sIperKCIem AVO TB, de consequenter ve est lu-
perficies BP PF C ad residuam P PFD F, ita superticies A V N FB ad residuam
VNTOV; es aurem cora luperticies AV OTB aequalis superticici AO V B,
_ superticies AVNY aequalis superticiei ANR B. IGICUEVE BF. P F C ad residuam
F PF D F, ica superticies AN B B ad residuam ANEO A. Quod Fuic demonstran-
dum.
PROPOSITIO LXII.
Aca SILVnguta P. F K a cylindro recro decusara alcicudinem AF X-
qualem habens diamerro balis IEF., circumdenc aurem vngulam
plana cangencia F. D I, IDCHI, QC. cerminaca in plano eltipeico F IF K
Producto, erunc plana illa omnia quadritacera, pexrer duo plana contin-
sencia cerminos diameeri F. de KE, qua lunccriangula.
Dico corpus includens ongulam concentum planis ambiencibus, et
polysonis duobus, lemicirculo P. AH de Semiellip(I F. I F K conleripris,
muletarum duabus prramidibus, quarum bales lunc criangula laceralia,
alticudo semidiameter L. K, xe quale esseprramidi que balim habee qua-
drarum diamerri K F, ee alcirudinem L. H semidiamerrum.
25 4. bibios.
Demon-