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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 452, page id 1815201908:0509
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.82
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D AR A BO L A
HIC: _ G F quidem parabola D L F, occuIat in F, FI C vero parabola
ABC in C; crecti(que ex C _ F, diametris qua L e, CII lineis occur-
ranc im C, _ II, ducatur quavis LIE, paralletaz , lecans parabolas in
B _ E, rectas C C, HIF in I_ IE, axem AD I L. dein luPET A D vE
diarmetro, de scribatur Lemicirculus AMD, OCCurrenS PR linex In NI.
Dico LL. Mt rectangulum aquari rectangut ELB.
Demonstratio.
Oala 22 dGllatio cl la
ncertrecto, linca LLC
icem AMI, LB, ITCM MD, LF
aguatestu. eclat Muisirur
AMD aquale elt rcclansulo
E. L. B: Ccd e AMD rectanou.
loquoque ct aquale rectangu.
um ADM L, La CA LL. MirC
PROPOSITIO BOIM
ctangula isitur IL DE, BP F aequalia CunE.
eer ele
enta.
Ex ele
Ildem politis:
Sicorectangulum II. BM ae quari rectanguto BL. F. R.
Demonstratio
roniam LL M rectangulum aequale est rectanouto L. L B, vE YE ad a L F, id
LeA L R ad L F, sIC L B est ad I M: _E permutando VE L R ad F B, sICFF.
Sulum BI LL D aGae en Cclatalo B L. F. R. Duod cracdemonstrandum.
aEBCX.
ex A, L,D puncta empS aelcribatur, cuiusaxis (IC AD. du-
cacurquerecta quaeuis L.  Patalletd BL, occurrens parabolis in R et L,
axi AD in MI, ellip_M IN, diametrO CH in O.
DicOLEMIL reccas Suum aequari rectangulo OMN.
Deorsranto.
mencis. CA ad LM: e F. K reliquum 2dMB, ve T. K ad I. B, id est IY. ad P. B: b rectan-
IIdem poltis qua prius: HaE B C F rectangulo aequale rectangulum
eur TO,AIN VE TC
ad quadratum NM
AMD: rectangulu igIEuF AOD
dd AMD rectangulum, rationem
Voniam AD axis est ellipICOS.
in ponun-
dratum
AGL
_ ad illam ordins
rectangulum est ad rectangulum
2
habet duplicacaM: LC, 20 N H
id est rectanguli FTCiTad d re
Excle
meneis.
et
OMN: _ quia rario rectansuli A C, V, Aa AND rectanoulum, com
polica elt exratione AC: ad c AM, id cA ex duplicacatlatione BC Id RM, d ex
tuius. ED ad M D, id est ex duplicara rarione CF. ad M L, LaLI A C D TectanGUH al
AMD rectansulum quoque duplieaca A euS, quam habet id C L. teclalisulum ad
ectam.
dE rse
atete e t e   et u te t e te e te ete e t  te e ete et   e a e aete s te st te te te t et e e e e  tut u  e  et  e te t te e     u e  t  te e l   t pa st titi se