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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 463, page id 1815201908:0520
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=520
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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 0.81
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

ebitu
: I.
ehor
Deigi
nPa.
otum
anci-
olum
quae
naius
para.
ilicer
naio.
aqul.
sinC
cclin.
5, d4
rian.
xhy.
nqui
cum
ect
iese
P AR AB C
L 1
463
mentis, cora crianguloru tes, id cAt 2 parabola AB C, est ad criangulu ABC.
primum leciettermunum, reglaluo adctta. Uoatui demonttranaM.
Corollarium primum.
Inc manifectum el ceransulum maximum AB C, eripsum else resattorum le-
omencorum AC. B, B F C. cum enim coca parabola, ad criangulum maximum
inlccCum, (IC VE quaTUIOE AdETIA; PATCEIPLII ETIAHSULUMI, EKCS GUATEASCOMEinerCPA-
rabolae; adeoque er residuorum elle rriplum.
Corollarium secundum.
EquITIE SCCundOLESENEL AFB, BF C cNcincer se equalia: criangula enim
ABD, BD C linsitca lingulorum tripla lunes e incer sc xqualia.
PROPOSITIO CCXRKIS
IE ad AB C parabeta diarmerrum BD, ordinatim applicata AC,
Aisqueper A_ C contingentibus, qua cum diametro DD conue
nianein E, ponacur per B COnTInSCNS, quX AF, C E Aneis OcCuItal in
DicO FEC triangulum, maius esse dimidio ssiLa COMCAUE AFC B A1
Demonsrati.
matus quoque ell. Ouod erac demonstrandum.
Corollarium primum.
Fi X ance demonstratis Faclle deducicur criangulum F P. C, maximum ese illorum,
ux inera erians lm A F. C ab alia quanis concinsence auterri poAumE.
Corollarium secundum.
(Equicur quoque, ABC. criangulum, duplum esse criangoli F. P. C; est enim P. D d vbid
S
TVnsantuE ABC. quoniam AF. parabolam
concingit, e AC ordinacim ponieur ad BD,
cF D, AB, C F, in B, F, C punctis bissecx SUnE:
quare F B F, AB F criangula, icCM V B F, F BC;
ac proinde EOTa F F C, ABP a qualia lunE. Scc
AF. Bcriangulum maius est dimidio figure mixri
lincx ABC F A, cum A B lacuS CadaFinETa P a-
tabblam convexam, cllal clum isicur LP. C illo
el.le 1
delor, CsBSEIAN
a 231. ha-
ins.
B87. De
srverestoni
odupla B. B. _ A C dupla F C
EHOEIOSELLBML CGXXXIVop si n0n 2it123
Arabolum ABC cuius diameter AD Com  Co
licerit. Ata ENIER B1OS SeGWIII
nexoccurrarin, ma ex l alaetet sB, a pel  Ponatul con-
tingens, ua AF, F C lineis occurrarin H _ l.
Dico criansulum A F F, quadcuplum ese crianguli HIF 1.
111 B5. 1O(75.1I P (5
veniens cum diamerro in L, actaque per A contingente, qua C. F. li-
Demon.