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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 398, page id 1815201908:0455
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=455
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

AR L
eROPOSITIO LAKL
Iead AB C parabolx diametrum et Domnarim polea linea C B: Fa
caqu AE xquali ipsi AD ponacur per L linca F H parallela recte BC.
dein ex C. ducarur linea C P, occurrens parabole in C Duncto, per quod ex
B agatur linca OCCurrenS axi AD iitEL, X F F linex in l;
DicoFE, BD, Ellincas in contiluta esse analogia.
Demonstratio.
Inca CF occurraE diameero in R.
Ouoniam A F linca aequalis ponirur
lince AD, d TTA; AK linex quoque
inter seaquaneur, cric P H reliqua X-
qualis relique R D. Rurlum criangulum
FX F ad criangulum D K C duplicacam
habet racionem F. K linex ad lineam
RD, Id est HID ad F IT. es aurem e
60. huiur.
criangulum B ED, adcriangulum F FL P in duplicaca ratione FTD ad FX F; isitur
vecriangulum FR F. adcriangulum DRC, sic BFID criangulum; ad criangulum
culum DKC, est compolica ex rarione LL a D C, id cA B D; X CK F K ad R D, id
NECFAEO F F ad B B, eadem cum rarionc B D ad P. I. quare F B, B D, F. I linex sunt
eROPOSITIO LAKLL.
F FFF adcoq; rariones exiisdem habenc coposicas, sed rario erianguli F R R ad crian-
CA DEI ad HE: e racio crianguli B EFD, ad criangulum FHL est compolica ex
ITD ad HIE,  ex BD ad E I, ablacatur communi racione HID ad FTF, ma
CONFINUX propOrtIOMalCS. uod erar demonstrandum.
t, A tuerint plopoconateo, eL. B, sectionem contingere.
Demonstratio.
DOnuntur ex A _C C ordinatimtA.
NCX A D, C G ad B D, di amCErUM.
quoniam ipituFB F, C C linex equi.
distane, eric ve B ad FB, AIC CF
ad FF; _ VE FB ad DB, ACFB
ad AF. (cd B C, B F, BD linec sun
proportionales; igicur d F C, EP,
F. A lince in concinua lunc analosia.
Duod eracprimum.
cruncigitur HC, HlF. HA concinua proportonales, alF ad FA, ve HCadHI.
sed _ C F cA ad F A, ve F C ad PF (cum F C, F P, P A sinc proporcionales) ixitur
VeFTC ad FTF, SCF C ad F F: _ dividendo ve HIC ad C F, ACF C 3d CF, quod ab.
Curdum, cum FTC exhypochelmaior sic velminor rect a F. C. quare FTBnon CAtcan.
BEHS, REC qux uis AlIa PTXTCT F. B. Quodera dem.
DArabolam AB C cuius diamerer B D concingac in B linea BF; de
missaqi ex P. linea F. A occurrat parabola in C e A, diametro vero
DD IM F.
DiCOE C, EF, E. A lineas in continua esse analogia, de COntra(I FC,
nem in B concingere. Sin verosagatur pet B cangens, quxe A F linex occurracin H.
Sineiam E. C, E. F, E. A proportionales, iunsancurque P. B, dico F. B lineam, sectio-
 e  tit   i. .   .  1 .       1  1)     .   e 1u      1e t u    s 1. s.  ut     t e t   t . e  t 1   1e