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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1134, page id 1815201908:1191
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ADR A FY R A CIRCYLI
Constructio e demonstratio.
Te quadrans circuli ABC divisus
bitariam recta BD, _ sumpEiSD F,
DE arcubus perimetro circuli coM.
melurabilibus qui incer le sinc aequa
les, demissilque perpendicularibuis
E C; F TI ad diamecrum IC, ponan-
TUFP B, F B. Inveniacur deinde arcus
KE a commensurabilis arCUI F F; CX
cuius exrremis punctis demista RN
LM Perpendiculares ad diamecrum
TC incercipiane rectam MN xqua-
lem rectae OFT. vel isiEUFAFCUS R A
aequalis cric arcui L I, vel maior, vel
minor. quod Eaequalis lc, isitur arcus
LK non Tolum eA commenlurabilis
arCuI F F, Sedb aequalis: cum MVI
Ponacuraqualis GTT, _ aFCHS AR X-
qualis P I, AICDEEE AECUS AF, F C. vn
deiceranda est constructio, doncc vel
AR arcusmaior (ICarcu L Ivel C CO-
ETAATCUS L LMAIOTAFCU AR. Sicigi-
EUF. AK arcusminor I I ee ducan-
Per I3. EDx FB, T B. OBonIAM PONIEUE ArCUS A R minor arcu LI, ergo c legmentum
115.
IsE huius. Y. M NK maius est sectOre P. B R. nota aucem est d proporciO (Cgmenti L. MNK ad
=20 huins. segmencum F C HIF, hoc es cad sectorem F. BF: noca cA praecerea racio sectoris
LBR ad sectorem H B. F, CHM ATCUS P K, P. F sine commensurabiles ex constru-
ctione. Igicur noca est eriam rario LM NK ad secorem L BK, que cum noca C
etiam excesus, quo P. M N R superarlecorem V. B K, norus cA; aC proprerca noca
est ctiam ratio lectoris F. B F ad rectilincum exceNum quo SESMENEuM L M N R
excedic (catorem LBR, (excelum aurem cum rectilincum esse posse parec, si iung2.
cur puncta L. R, d criangulo TBR ablcindatur crapezium aequale ex crapezio
L. K NM, adduco enim communi segmenco L. K, eric sector, segmenco _ illicrapezio
aequalis, quare reliquum seomenti eric excestus e quidem rectilincus) ee consequen-
ter nocaes racio corius dirculi ad idem rectilineum, quoniam arcus R F commensu-
rubilis ett perituetro circuli PAC ex constructione: quare peractum est, quod fuic
Beor2I
4143
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