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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 33, page id 1815201908:0090
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

1.
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POTENFI A.
eR OPOSTFIO XLVI
Dhrallelosrammi ABC, diameErum AC, Secet FF, aequidistans
ipsi AB in C. Ponatur in supeF BF.
Dico OHI, HA, HIC. cres esse in continuaratione.
Demonstratio.
Cimilia namque lunccriangula, AHTF, BHIC,
quemadmodum e criangula GTIF, AHIC.
quare ve CTI ad HIA; hoc est BH ad HF,
ita HI A ad HIC. Duod crac demonstrandum.
PROPOSITIO ZLVII.
Inc AB C D cuiuscum que parallelo.
grammi, diametri AB, C. D.
Dico diametrorum quadrara limul lumpea, a Guata C Guaatats la
cerum AgurX.
Demonstratio.
DExcrigelimam nonam huius, quadeata AC.
AD aequancur quadracis RC; F A bis
sumpeis: ec per eandem quadraca CB, BD
aqualia lune iildem; scilicet quadraris R C,
EB bis sumpris, sed quadracum C D .Xqua-
TUT F. C quadraca quaceE CumpcO, d AB qu2-
dearum, quadeaco F A quaTEF SuMPTO: PaTCE
erxo vericas proposicionis.
P R O P OS
T1O XEVI
uBC. triangulum ilolceles, duetagueet C, alcetute alet
rumxqualium, vecunquelinca C D, quxe AB laceri, occurrac in D,
hac ip(i C D aequalis D F, iunsancurque L. C.
Dicoangulum BCD, duplum esse anguli AC F.
Demonstratio.
Neutus DA C equalis D eA duobus
angulis D F C, A C F, id est percon.
Aructionem, ansulo DC F vna cum an.
Sulo ACF, id est angulo DC A una
cum angulo AC F. bissumpro. Sed angu-
10 D AC aequatur angulus BC A, cum
ABC sic ilosceles; isirur angulus BC A,
aequacur angulo DC. A, vna cum angu-
10 AC F bissumpro, demproisitur com-
muni angulo DC A, manet angulus BC D, aequalis angulo AC P bis sumpco.
Ouoderac demonstrandum.
b16. ert