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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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 litet.L. d11d+
Constructia e demonstrario.
Vedcur ex C ordinarim ad diameerum AB, recta
C D, iungacurque BD. dico Factum esle quod pe.
rcu. e, enim segmentum AF, D a aequale seximento
AF C. et cum xquales sinE CB, F, B, criangulum DFB
xequale est criangulo CA B, igicur _ lector ABD equa
is sectori AB C. eduximus isicur, 85. Quod Tix fa-
ciendum. 13.
1. 1.3
PROEOSITIO ZLIX
in 1
AbCanE ADB, C DB sectores equales com
Amunelarus B O, IunOanEurque AB, C. B. .
Dico seomenca lineis AB, C, B ablaca esse InFCL
ChTogmencatuear aequalia, dico ec lectores aquari.
Demonstratio.
VnGAnEUE A, C Oceurrarque AC, linca diamerro BDin
F, cum si A C non sic dinisa bitariam in F: diuidacur bita-
riam in FP aGacUTque per FI diameTeF D R: Ouoniam AC.
linea ordinacim ducta est. 2d diatmeerum DK; erune
ATTR; C TTKD seomenca aequalia: lunc aurem _ ATID.
CTTD criansula xequalia, sectOCS ISITUE ADK, CDK
inter se equales lune, Sed ex hrpochesi quoque sectores
ADB, CDB equalessunE, igicur sectOF C. D K, aequalis
est lectori C D B pars cori. Ouod absurdum. quare AH
linca non dividieur in EI bifariam: nec in alio puncto que
in F: adeogueisitur AC, linca polica cAt ordinacim ad dia-
mecrum BD. vnde AE B scomentum c est aequale le-
Eento CFB. CuncddeM A C B, C L. B criangula aequalia, erxoreliquum segmen.
SInE iam AB, C B SexMenCA = QHalIa eE ex A, B, C punctis diAMCERI PONATUT AD,
BD, C D, dicolectores ADB, C DB, esse incer se xquales. Sin vern: hac CDB se
Rad.huns. CtoriX qualis sect Or dBDF, iunsancurque puncta L B. crir igituF L B segmen
cum aquale segmento C B hoc est AB per hypothelin, adeoque pars aequaliscori.
Ouod heri nonpocest. isitur sector BD L. non est equalissectori CDB: nec alius
quilquam praecer ADB lectorem. Quoderac demonstrandum.
P ROPOSIFIO L.
IF AB C sector quicunque.
Dico lineam ex cenero ductam; que AC
Tubrenlam diuidir bitariam, sectorem quoquebi-
Fariam secare.
Demonstratto.
e
crbir.
cum AB, aqualc elticoteno CB quod erac primum
=45. huius.
AC lincamin L: dico ABD. C BDIccores cAca-
quales: Cum enim AC in F digila SIE BIFaTIAMI, CrUHE
ABF. C B F criangula xequalia, sed, quia A C est ordina-
eim polica ad diamerrum BD, eriam segMMCNEA C AF D.
C FD Cunc aequalia, igicur eorus sector ABD, sectori
C BD aequalc cA. Duod erar demonstrandum.
PR O
Veaeur ex B ceniro diamerer BD. le cans bilariam
 ut ai uttut u suesi su s  e isu es u et otte  t u   us   esti e  t    e e e e  es t  te     u  B   e   s