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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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Senci.
pus
69. h1
106
E
EIR CY LVS.
Demonstratio.
Vn enim F C, BD aequidistene, erune anouli
DBC, BCF, id est anguli DBC, B AC 0b
P C tangencem requales; hmilia igieur sune crian-
suta DBC, ABC. vnde vE AC ad AB, 112
BC eAt adB D: PacCFigITUT ABBC, d AC BD.
rectangula cAC X qualIa.
eDPOSITIO LXXI
cinuicem circuli duo quotum vnus per cencrum alcerius cranscat
AC. quae punccalectionum coniunsir, lc diamerer cir
culi cran lcuncis per cenerum alletius; ad quam erigarur per B, in perime-
Ero ABC alsumpeunat, dormalis DB C; occurrens AD C. perimcero in
Dicorectangulo DBC a Gua AC BF rectangulum.
Demonstratio.
Veta CBFT, cum circulus AB C per alEe-
eius cencrum cranscae, cric b HIB aqualis
AB. inde ABC rectangulum xquale est re-
etanoulo TIBC, scd TTBC aquale cA rectan-
sulo DBC; isitur e D B O aqUaEuE ABC
id est c AC BF rectangulo. Ouod crac demon-
Arandum.
PROPOSITIO LXXII.
lamerrum circuli ABC, secet AB,
normalicer in E, ponancurq. quaeuis
EHI, Occurrences AB in C.
Dico E G HI rectangulum vnacum F C quadraco, aquari F. G HTrC
l G, _ AC in F.
angulo vna cum quadrato FC.
Demonstratio.
oacadinila in F, ex quianon bitarium
dinita elt in C etlc A C+ B, rectangulum vua cum
quadraro LG, daequale quadraco AF. Ccd AC B
rectangulo aquale est FCrHIc rectangulum; addico
isicur FC quadraco, cric PC II rectangulum vna
cum quadraco FCr, quadraco AL aequalc. igicue
Toniam AB ans Cu au Mamcrrt CD.
e LCitl cectangulum, rna cum quadcaco Ln
aquale cA F. C HI rectangulo vna cum quadrato
FC. Duod crac demonstrandum.
PRO.