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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 505, page id 1815201908:0562
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.84
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FIII.
9ua
CTaH
idieue
ane
ula
P A R A BOL A.
Demenscrarto
EScenim F. D quadratum ad quacatum F. LHL
quadearum ad quadracum D P ex hypochen ld clt
ve AD linca ad lineam AD; puncca igiEUE F, F aC
ParabOlam TUInE.
eR OP OSLFLO CCCXX
VIE ABC parabolae diameter AD, d ordi
nacim poliex CD, BF: ductaqe linca AC
qua BE rCCEIS OCCUTEAEIN FF, FaE VE FB ad
FB, SC BC ad BC.
Dico O, C puncta esse ad parabolam.
Demonstratio.
oti
atac vE BF adt BG, SIC F L. 3d F H: quoniam est ve F B ad F B, ita BC ad BC
eric permucando ve FB ad BC, sic FB ad BC: se Del construc, DF cA ad
EFI, ve EB ad BC, ergO F F CA ad B IT, vE F F ad L FT; igicur cum puncta F F
in directum sinc, puneta quoque IIFI in directum lunc, re paret ex clemenris: de
_ide quia est ve FB ad B G, siC F F ad F II, erir componendo, connerrendo O F
ad BF, VEFH ad FB, ∞ permutando CF ad FHL, VE BF ad E F, ee compo-
nendo GTT ad ETT, VE B E ad FF, iccrumque permulando CrTT ad BR; VE LFI
ad FF; sed cum anre ostenderim eNe FF ad FFI, v E P CM ad FHI; crie quo-
que ve F FI ad FB, siC F HI ad F R, crgo ve GHI ad LH, lic GHI ad BF, e per-
mucando CTI ad C TI, ve BP 2d BB: igirur ex quadcatum C FI 2d GHI qua-
deacum est, requadrarum BP. ad quadrarum B t, hoc eAt ve F. A ad F. A, hocCIC,
ve AEI ad AHI, punctaisicur C. C ad parabolam lunc, cuius diameter A IL.
PROPOSITIO CCCXXI.
Donancur eadem qua prius, et
tanc F F lineis aquales rectae
BO.
Dicoicerum A, C, C esse ad para-
bolam.
Demonstratio.
Vm enim P B lineis aquales p0-
naneur B, addicis communibus
BF, rectae FC aquales luncF P, dCFG
quadraca aequalia quadracis B F: igitur quadracum F G ad quadrarum F C es ve BF.
quadrarum adquadracum B E, id eA ve AF linea adlincam AB, id eA AF ad AF.
puncta
ttttttt
138