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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 210, page id 1815201908:0267
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=267
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

mu mmppnem
DLR, OV, L
5.
AF FC Vna CUM reCtanGAL AFD bis Tumpto:
11.
AE B rectingulo bis Cumipeo, aelari quadratis AF, F C minus AFD
Ouod si aurem alceta ineta aleam circuli callar, alceta CKITaS dico
quadeara AF, LC e l B lectansulo bis Cumpro, x quari quadratis
5B Sii
o. Dem onstratio.
2 21s c
Lenim CAdAE CB, CF, inea aream temi-
circuli, constitucne angulos obculos, AFC.
AFC, Cum ABC, ADC recti unc, unde
per clementa quadrate AP, P C, cum rectan-
Bulo A B B, bis CumpCO, QuadrREO AC aqua
lia crune; sed cidem AC quadrato aequalia
(IINE AF, F C, quadrata una eum rectangulo
A E D bis Cumpro; igituE qUIadEATA AF,, FC
cum AE B rectangulo bis sumpro xqualia
sune quadraris AR, FC una cum rectangulo
AFO bis sumpeo. Ouoderacprimum.
Si vero CF, C, F exrra cadane; Pater angU.
lOS AF C, AF C eNC ACUTOS : quALE tam
quadraia AF, FC minus rectansuIO AL B
bis sumpro, aequabuntur quadearo AC; quam
quadraca AF, F C minuis AFD rectanigulo
bis sumpro: unde vericas secunde parris quo
que manifesta est.
Parris cerrix demonstracio ex anre dictis
clare pacer; isitUI, XC, Duod erat demon.
Aranaum.
eROEOStTIO LXXXI
BC triangulum iuatibatuE ABC, 2 cujus verrice 2d
Dico ADC rectangulum. _ lcclangulum ABC; denique quadra-
Demonstratio.
EA A F, F C, rnacum rectangulo A E B bis CumPtO, aquari quadratis
bis lumpeoi
Si vero extra circulum occurrane, dico quadrata AE, F. C, minus
AF, FC minus rectansulo AFD bis lumpco.
cum AC in concinua esse proportione.
cum demictatur verpendicularis BD.
Vadracum A C cIF 44 FCCLAIISCIII A BC, hbC ett
AC BD rectangulasu ve b AC, ad DB: led a
est rectangulum ADC, re AC 2d BD, igicur con-
cinvane candemlarionem A C quadracum, rectangu.
lum ABC, rna cum rectangulo ADC. Duod tuir
aeonaha
rectangulum ACBD es ad quadracum BD chOC
RC.
  p     e  ete  en et  ee    e   t      e   e   e   e   i sa  a   at que