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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 504, page id 1815201908:0561
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
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2
L. ALL 1DL 11.
L. HESSEALOECCCNVII.
ildem posris. Gunc B, . C. L, DL. quadracis, ae qualia rectangula B. F RV,
ofelle, ad parabo la.
4
1
Demonstratio.
Ectangulum GFR V ad rectangulum
TITSX est vE R V. linca ad lineam
SX: igicur X quadearum C B cst ad qua-
dracum PT, ve R. V, linca ad lincam SX:
sedre BG quadracum ad quadeacum PI,
Gc AOC rectangulum, est ad a rectangu.
lum ATC, igicur rE R. V ad E X lincam,
sic AOC rectansulum. ad rectangulum
ATC, id CA DM C rectangulum ad re-
ccangulum DN C, id eA M R b linca ad
lincam, SNV, quia RST. oAensa eAt para-
bolasisitur _ ML V. est ad XN, VEDMC
rectangulum ad rectangulum DNC.
similicer octendam oNc X N ad Z O, ve
DNC reccangulum ad reccangulum
DOC; punccacixirur N, X, L. ad Pat2
bolam lunF.
. (11
PROPOSTFIO CCCZHHIE
IIdem posicis: iuneaneur AB, AP, NO: tancq receangula E, F. N.
LIHTX, L. IEZ aequalia quadraris AB, A P, AO
Dico V, X, Z punctarurtum esse ad parabolam.
Demonstratio. IC dEit
ol
Voniam BC, PL,O L, normales sunend AO, quadracum A B (2 qualc est qua-
dracis AC, CB: sed C B quadracum aequale posrum est rectangulo Cr Fi RV.
ex A Ci quadratum aequale reccansulo C F R: igicur quadratum A B id est rCCTAN-
sulum G F V, aequalo est recrangulis OFK, CF RV: Smilicer oRtehdirur
receangulum IHIZ, aequale esse reccangulis ITIS, TIISZ: _E LRZ reccanou.
lum aequarireccangulis V.KC P, P. R T. Z. Ced cum (C FR, G, FR V recrangula x
qualia ponebancur quadraris A C, CB; _ THIS, IFTSX, aequalia quadracis AI,
316. e IP, XC. Octenta Cunc V, X, L ellc d ad Barabotam; isicur ee iam 28 parabolam (un.
PROPOSITIO CCCXIX.
NIE, AB C parabola diametet A D: de ordinarim ad illam posirxe DB:
Dhac aurem ve DB adt DB, AC D F. ad.  F...
3: FI2. t
DICOAF. F esse ad parabolam.
t 37
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BF lis St sta B92 III.
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ap. 3 X. AIE eY S . Bit nop, HROi SaIBMO.S E LeI MB AA CL HC etC
.3e11d cc2 F. l  c t 2L. F1. 1. 1 L. P3 11.2
A.
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Oocton
dico puncla +4.
4.
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