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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 21, page id 1815201908:0078
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=78
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.86
# 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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Ca
A R S
PO TENTLA.
dF. C
De Frianculis, eorumque propriecatibus.
PROPOSIFIO X
 Sto AB C ciangulum Ilolccles, habens
sds AB, AC, lacera aqualia; duCanEUTG.
ao ex A et B normales AF, BD, adt op-
in F.
Polita latera, occurrentes (ibi muruo
Dico esse AF ad BC, vE AD ad DB
Demonstratio.
Voniam anguli ARB, BDC; per constructionem LCCISunE, de anouluS P BF,
Lcommunis eriangulis E BE, DBC, erune R B F, DB C crlanoula incerse simi-
lia. F. odem modo ostenditur criansulum AF D, simile criangulo DBC: vnde ve
AD ad DB, sc AL ad BC. Quod erac demonstrandum.
P KO P OSITIO XX.
X quovis puncto baleos eriangu-
Lli ABC IIolcelis eductA DF, D F.
extribeane angulos aquales E. DC,
FD A, IUAGANEUTGUe AE, CF.
DiCOAED, CFD criangula else
incer se aequalia.
1
Demonstratio
iVmenimcamangulus FD A, angulo F DC pet constructionem, quam an-
LguluS F AD, angulO F CD aqualIS SE, CFUNE A FD, C F. D crianoula inFCF
se similia. OMarC VE AD ad DC, AC ED ad ED. Rursum cum angutuS FD A,
aequecur angulo ED C, addico comuni angulo F D F, eric angulus F D A, xqua-
lisangulo C D F. Vnde cum ex latera, ae quales ansulos contmentia, reciproce sInE
proporcionalia, aerum AP. D, C FDccians ulaincer se aequalia. Ouod ex ac demioH- a ls Seut.
Arandum.
PR OPOSITI O LAL.
Tne duo criangula LCOperimeErA
ad ABC, ADC, super eadem bal
AC consticura; divisilq; AB, C D la-
ceribus proporrionalirer in F _ (2;
AHCaHEUE F F, GFI parallelae Ba(IAC:
Dico lloperimeera quoque
EBF, DGHI criangula.
Demon-