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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 240, page id 1815201908:0297
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=297
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240 PR OL E GO MI E N A AD SFCIIONESCOH
ostendam puncta quoquo F D, OC esse ad circulum: quare rectangula DIC, HTIK
xqualia lunc, rrid rectangula F F C, _ DF C: ac proinde aequalia criam quadra-
eis TM ex FI. perpendicularium ad D C. Isirur puncta DM L C, circulus cAcu
ius recta DC est diamereri isicur de c.
PVR OPOS
clit
03
e
ad 
condendum modo elt in quontscne eese ce axes esse.
Demonstratio.
Onus itaque scalenuS AB C secetur plano peraxem BF, quae ex vertice B ad
cenerum circuli ACC balcosprocendicur: criangulum productum ABC sC.
cetur recta CD, gux angulum BCD aequalem exhibeat angulo B A C: X diuida-
cur DC bitariam in F, de iungacur BF. Dico illam esse axem secundum huius
coni: quodica parebic, praecedenti propolicione ostensum est sectionem Factam pet
rectam D C, comodo quo illic praeceptum fuie, circulum producere: igirur recta
exapice B ad punctum F quod huius circuli est demissa axis nomen obrinere de-
bet exipla axeos detinicione; restar igicur ostendere P P P rectam non estelincam
sine BF productam non incidere in P. cencrum bals, sc proinde B L axem esc
alium ab axc BF. quod inde pacet, quod E I recta tc aequidistans linex AB, cum
lecec duas rectas CD, C A Bitariam. Igirur A recta cA linea R FB, sequetur duas
parallelas se le incersecare, quod est ablurdum. Constacigitur omnem conum scase.
num duOSaXCS admICEFC. Quod demonsrandum fuic.