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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 171, page id 1815201908:0228
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# Lines: 49 recognised, mean confidence 0.87
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oc
CTR CVLVS
ConteneuS, puncta C e D obtinear; cum
igitur anguli C AD, CBD, arcui CD
insistences sincxquales, crunt quoque an-
ouli HIAO, FBF reliqui aquales; a0
proinde arCUS FOF, FOFT, adeoque
iunatx F, C, FTF equales.
Tereio punctum C inera A CFB circuli
spacium concincatur; D vero punctum
exera collocacum sIE. Ducatur CI aequi-
distans CB, iungancurque HII: quoniam
CT. CB aequidistane; anguli ACB,
ACI, aequales lunc; unde ee angulus
A FTI aequalis eA ansulo ADB: quia
ATTL, acum AOT, hoc cA ACB
duobusrectis equalis est, sicuC est anBu-
lus ACB cum ADB. Vnde aequi-
distanEeS TunE FTI _ DE, adeoque
_ areus FTB, FPe consequonter LIF,
BI xequales. quare _ iuncta HTF id cA
BI iph F C aequatur. Ouoderac de-
monstrandum.
PROPOSITIO VII.
Seo AB C criangulo rectangulo, cemicireulus interiprus AF D con
Scinsens AB, BC. lacera in A X F: _ per P ponatur recta D F. Occur.
renS AB, in F. 1c1
Dico AB, BF lincas, Equales esse.
Demonstratio.
Vngantur A F: etirigicur angulus AFD in Cc. X
micirculo rectus, vei ex reliquus A F F: qui pro-
inde aequalis est duobus angulis E F A3 P AF:
esaucem angulo F A F aequalis BP A, cum AB,
B F Iinc concingenees ex eodem puncto eductxs
adeoque aequalesi reliquusigicur angulus AlF.
reliquo BF F aequalis cAt: quare BF rectE BF,
hoc est AB, aequalis cAt. Quod erac demonstram-
dum.
PROPOSITIO VII
iEse
Virculum ABC, contingar intus circi
slus DE B, in B. transienS peF D cen-
erum circuli ABC; ductis in(UPEF PEF D rectis AD F quX CITCHIODE B
Occurrantin E: Ranc D F. rectis aequales DH, e perpendiculares po-
nancur FII ad diamerrum BC.
Dico FB, H + lineas, aquales este. i
lacer
121C
demon.