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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 388, page id 1815201908:0445
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.88
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Perele
venea
AR ABC
Demonstratio.
Eccarbulum B DC ad recrangulum F DFE a Facio-
nem habet compolicam ex B F ad F: D, d GF 20
ATD, id est AF ad AD: Sed rario A F ad AD duplicata
eA rationis BF ad F D: reccangulum isitur BF C adre.
ceansulum FD FEcriplicacam habec rarionem eius quam
habec BF ad F. D. Ouod erac demonstrandum.
tROeOSITIO LIV.
Darabolam A BC cujus diameter AD con-
tingar in A linea AE; ductaque quavis AC
quE parabOlE IFCTUM OCCUTEAEIM C, Lumantur in A C lincapuncta qux
plicacam eius quam habec btL ad LiL.
Demonstratio.
2 Eccangulum BOFT ad recrangulum PF F, racionem
haber compolicam ex BC adIF, _ Cx GTI ad H F,
id elt A C ad A F: sed racio B C b ad TF duplicaca cAt
rarionis AC+ ad AE, ixitur receangulum BC+ FTad re-
ctangulum PF. F rationem habec criplicaram ejus quam
habec GHI ad F. F. Ouod crar demonstrandum.
eROEOSITIO LV.
Seo ABC parabola diamerer AD, quam in
D secer ordinarim linea C D: divilaq; AD
in F _ F, VE AE, DF sinc aequales, ponancur
ordinarim EB, FC.
DicoFB, FC quadrata limul sumpra, x quari
quadrato C D.
Vcta AC OccurraE L BIIHCX in FI, _ F C in I, eri.
Sacurque ex C diamerer CR, (CCanS P C in R
Duoniam AF per hyporhesim aequalis eAt FD, id
CA C R, angulus A H F. aequalis angulo AIF id est an-
suIOKIC (ObFTF, CF aquidistances) et angulus APH
angulo aqualis CKI, erit AFIP. c criangulum aequale
criangulo CKI; _ FTE linex aequalis RI. Rursumcum
eam C D, GF, dTF; quam CD, BF, HL F linCC proPOr-
tionales sinc, quadraca FC, B R mediarum, aequalialune
recrangulis CDTF, CDHL; HOCCR recrangulis IFR, TRF, quia HIK, RIlinca
22. sccunai. X quales lunc, sed F. R quactacn dequale cA c recrangulis IF R, TRF, igitur et
contingenti in F. e C parabole vero in B, _ l.
cunque F, HI. ex quibus eriganeur diamerri F F, FTG, OCCUrreNECS AC,
Educieur
exprima
WIHS
Per
DICOB CHrectansulum ad rellangulum LF. F rarionem habere eri-
Semonsttatie
d +2. 1
Ducterac demonstranu.
quadraca F C, BP simul sumpra xquaa sudE quadraro L K, id est quadraco CD.
vorona
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