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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 443, page id 1815201908:0500
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=500
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.80
# 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.

2
10
o
ile
V.
A.
F-
NE
12-
1i.
P A R A BOL A.
Demonsirati.
Voniam tam AD, aB G, KC, qLAM DE, BGFT, GF proportionles TuNE, N ~g2. H
EEIAIM RG, GC. est auremratio F G 2d GB, COmpOSITA ex FacIOnC F G ad ∞K, bui
K O, propoconales Sinc) _ exracione K C ad G B id est iccrum B C ad A D, igicuE
FC 2d G B, criplicacam habet eius quam act  ed aet CH A . ubd
fuie demonctrandum.
PROPOSITIO CLXZEVII
Ntertecent icerum se se parabolx duae ABC, C B D in punctis B, 
Lhabentes communes diamerros FC, HILEL, D A quasin MI _ N, lc
cerrecta C B.
Dico TM ad M E eandem habere racionem quam habet D N ad N A.
Demonstratio.
T DHC rectangulum eAt 2d
rectansgulum DL C, ACALC
2d AOC, rectanoulum. (ed ve
DHC ad DFC, siC FTY 0 ad
EB, _E VE AL C ad AG C, sic
L K linea est ad C B lineam; ivieur
ve IIL ad F B, SIC K L ad B C: &
permurando converrendo ve FB
ad B C, AC TTIadRL. est aucem
ve FB ad BC, lic HM ad ML:
igitur ve H L ad RL, SICHM ad
ML: VnAELC LM C CAAd MIK, VE H M ad NI L. I eA DN ad N A. Duo d Euit e13 quimi
demonstrandum.
qPROPOSITIO CLLLAVIII
Sto ABC parabola diameter A B qua in D secet ordinatim linea
dDC: dein per D parabola describacur D B, habens ADCClcingen-
cera de diametrum DC e commune cum alcera sectione latus rectum L.
occurrar aurem DB Parabola, Parabole AB C in B, _ ordinatim ducaTuF
linea BF.
quam habec FB ad FB.
AD prima, aequalis primX DE, racio K C ad C F, c duplicata estracionis B  B07 hums
ad CHI, id ell BC ad K C, cum enim D, D C d lincae xequales (INE, XGUANEUF C 26. L
ression
C47 haius.
id est ex duplicacararione R C adt GB, hoc e BC dd AV, (cuim AD, BC, a g. huius.
Dico AF lineam ad lineam FB, rationem habere duplicaram eius
Denonso.
lllaccigue leccloi Comue Cllid EB. BC Oec
nauim policx, eruncram B, si B, AF linex, quam B, BC
id est FD, e D G proporricinales. unde cum P. prima lic
communis, racio s A F ad DC, id est ad FB, duplicara est
rationis FB ad B C id est ad PD. Quod tuir demonstran-
aum.
DOnacur BC equidistans AD. Ouoniam igitur P latus
KKL 2
111 1 St 1C
ioni
C
nolla