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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 501, page id 1815201908:0558
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.82
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B.
1d
ini.
D
ir.
ex
d
FA
AD
Cin
icue
dll.
atet
O.
P A R ABO L A.
PROPOSITIO OOOK.
Scocirculo ABC inscriprum rectangutum ABCD, ee vnilacerum
AB, duax parallela E GHIF: RanE aurem CHI, HIF, FI prOPOF.
clonales.
Dicopuncta B, 1,D esse ad parabolam.
Demonstratio.
Voniam eAt ve GTI ad FTF, Sic
LHIE ad FI; eric componendo
invercendo ve CTF, id est F FI, 2d
GH, sic HIL ad HIF; rectanoulo
igituE B C F, id eA PHF, aequale
est rectangulum CrFII. e C HIro
cangulum ad rectangulum CTII.
DE R HIF rectangulum ad rectanou
lum R FI F, id est BFTD ad BFTD,
rectangulum; sed GFII rectandu-
lum est ad rectangulum GTTI VE
HT linca ad lineam HI; isieur ve
BHD sectangulum ad rectangu-
lum BFTD, SC HI linca ad li-
neam HII. puncta igicur BID ad parabolam suns
PROPOSTFIOMCCCZI.
Nscriprum siccirculo A BC rectangulum AB CD, ductisque vnila-
lcerum D A parallelis E GFIF. Fanc L. C F rectangulis xqualia rectan.
gula HIGIE.
Dico puncta AR B esse ad parabolam. c 4
Demonstratio.
()T EOF rectangulum est ad rectangulum P. O F, CC
AC, B reccangulum est ad recrangulum ACB: igi-
cur e HIGK rectangulum eAt ad reccangulum HICK ve
AGB ad AGB, reccangulum. Sed HICK recrangulum
estad rectangulum FLC K ve CK linea ad lincam GR;
igicur ee AGB recangulum est ad recrangulum, A C B,
oc CK linea ad lincam CR: puncca isitur A, K, B ad P 2-
rabolam sunc. Ouodcrarostendendum.
PR01061111 1BCC 1.
De bo e3i3 cmr
Nlcripcum sic icerum roctangulum AB CD
Lcirculo AB C, ductag; laceri B C paraHetaFF,
quae circulum concingac, ponantur recta OHI
aequidistantes laceri AB: hancque Ca lL. rectan-
oulis, aequalia rectangula FVIAI. L LWVABS SI
Dico A, M, D plncta esse ad pacabolam.
et HC sacit tor sost et 1L 31.LL. P c
d
ec reit 
RFF 
dE
avq eL
Demon.
e ttute et   te te  te e t  t t et    tee    et se   e  e tt  t  e d      tt tt de tut      t