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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 353, page id 1815201908:0410
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F. L L I
sectores AZB, BH C, ecc. xequales: sunc aucem illi smul sumpei aequales toci et-
lipH, ioiene sectores duo AZ B, BZ C hoc est quarca pars sectorum, crune
quadrans ellipsis ABC. Jam guta XT, XV ex centro ductae BisecanE BC, a 50. BN-
AHLa crunclectores C X T, X A V dimidii sectorum aequalium BZ C, A Z FI, ac in-
proinde incer se aequales. addicoisteur communisectore AZ T, corus sectorVX I.
lectortori AX C aequacue quare eum A X C. sic quadrans cllipleos, eric de VXI.
ErgodVZ, TX diameeri sune coniuracx, 2d quas A FTC B sunc ordinacim po- b46. huins
Tice auterences sexmenca aequaliasigieuc quadratum PO bis sumpeum, est xequa-.
le qualtaris AII, CB simul sumptis: eodem modo ostendicur idem quadratum
PC bis Cumprum equari quadratis AB. C FT Simul Tumpeis: adeoque P9 qua-
dracunt suario sumpcum aequari quadtacis CBs B A, AHI, EIC, id est. quadracis
GF, P_. E D, D C. quare de quaulacum P O suniptum octies quoc lacerum est por
ygonum, aequale elt quadracis lacerum corius polysoni ellipE inscripei lrerum cum
1
106. bv-
dEc vresliplis ABC ad circulum LMN, ita sexmencum AB id est P  2d (c. 8187. h.
simencum LN erune TK, NO diamorri c in R ee S, proporrionalicer divila,  C 188. hi
quadratum. POC aequale quadeaco L M. ergo quadtacum P,  octies lumpeum ins.
aquacur quadraris laterum polygoni circularis. Sed quadrarum. P O octies sumpeum, E177. b-
equacur eciam, ve lupra ostendis quadrarislacerum polygoni xllipricis ergo quadrara
lacerum polysoni ellipeici simul lumpra aequantur quadracissacerum polygoni cir-
cularis mut lumpris. uod erur demonstrandum. I
Corollarium.
Incpater: E eidem ellixs duo intcribaear porsroua patium numero lacerums
Quadracalacerum vrius polygonisinul sumpra, aqualia eAC quadracis laceru
alcecius vols Bohl biul tchipcis.