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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 544, page id 1815201908:0601
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.81
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ATZ PER BOL A.
Constructio es demonstratio.
obla Cuius alymprotos exhibere oporret: diamerer sectionis H
GB, qua in Z bitariam diuila ordinacim ad illam posicx sinc AD C: deinde AaC
rectangulo CDB, aliud amile FIF. M. quod aequale, quoque sc quadraco DA,
cum RIM, diuis2 bitariam in NY, AAnED F, D F, aequales, NEI dimidix HIM. PO.
nanturque ex centro lineE ZF, ZF. Dicoillas esse alymproros hyperbolx ABC.
Posica enim B R, quae x quidistet DP, ponacur K O, Parallela BD, ex P, S aequidi-
saris RB. Erie ereO vE F L ad TR, id est BD, sc KB ad BZ, siuic R V, id eAI Y
dupla XB ad CB duplam Z B, ex permurando ve H I ad IX, sic BD ad BC, _ F. I
ad TF, VeBV) ad D G: vnde BIF recrangulum simile est rectaneuto eDB a
deoque ec mile rectanoulo HILMi e cum F D, HN ex constructione aquales
tinc, aequalia quoque sunc rectansula P Y F, FI I. M: quare ex PIF, rectangulum x.
quale quoque est quadraro AD. codem modo ostendicur P OS reccangulum cimi-
le rectansulo C PB ex aequale quadraco  Y. Rursum cum quadratum F. D, tam
aequale ra quadrato AB, una cum rectangulo P. AF, quam F l F. receangulo cum
quadraro TD, quadracum AD vna cum rectangulo E A F aequale est quadraco ID
una cum reccangulo F PF: dempris igitur aequalibus, AD quadraco e receangulo
ETP, manCE F A F recrangulum xequale quadraco ID, id est R B: codem modo
oltenditur POS receangulum aequari quadraco RB; ae qualia isitur lune recrangu.
b15. hains. la B AF, P O S: vide Z F
Z E alsmpcorib sune hispecbola ABC. Extribuirus
isIeuT, e C. Dubd erac Laciendlim.
12 l.O2.
17 h1EC
(IF
etrit eoroqcaite ha cL e Ct ABee EnI. ( 13
Corollarium..
10.
IE A BC hrp
inclequicur Pous aolto L. L LL. pea ABC ex F AF, otonu
cim ad diamerrum C B, ecc. ve ance rectansula CDB lmisa ee lecransulis
E.PF: manifecta es demonstracio, ex discursu in priori demonstratione adhibito.
ae ee eeo eesra ese oooease