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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 301, page id 1815201908:0358
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=358
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.87
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A0
B
EL L IPSIS
30+
vecriangulum B HD ad eriansulum BFTO, eric quoque D F ad B G, verrianou-
lum BEC ad criangulum BIA. Vicerius cum criangulum BHIC sic ad criangulum
BFD, ve OHI ad LTD, hoc esta ve AI ad TC, hoc est ve KI ad LB (cum enim bili
C B sic coniugaca ip(i AB, _ AR, ex constructione tangenS, PatCE AK, CB esse
Parallelas) hoc est vecriangulum A TK ad criansulum AIB: eric componendo
criangulum BDC ad criangulum BITD, vecriangulum A KB adcriangulum A IB:
e permucando criangulum BD C ad criangulum A R B, vecriangulum BHTD, hoc
est sicur ance ostendi, vecriangulum BIC ad criangulum AIB. sed criangulum
ARB eAtberiangulum F. DB, ergo criangulum B D C est ad criangulum F DB, b7r. huins.
hoc est, quoniam E, D, B C sunc pacallelae, B C est ad F. D, ve criangulum BIC ad
criangulum AIB, hoc eAt sicur oltendi supra, ve D E ad B Cn. Luncisicur in ratione
Continua D F, B C, R D. Ouod erac demonstrandum.
PR OP OSITIO CX.
IINE AB, BC diametri quaecunque coniugatx, a sumproqi in peri-
pheria, incer A ex C puricto quovis D, agatur per D concingens,
occurrens AB, BC diamerris in F _ F, iunctaque A C occurrar diame.
ero DB in C.
Dico rectam DF ad DE, rarionem habere duplicacam, eius quam
hrabet CG ad C A.
Demonstratio.
)Veacur ex B linca BF parallela ipA B F, _ CX B
recta DII ocCurrenS FB linex in P. crunc igitur
Perpraecedencem, concinua FD, BFI, F. D. adeoguera-
cio FD ad E. D, duplicaca racionis FD ad BFI, id cA
DI ad IEI, quia DF, BFI per constructionem aequidi-
Ranc: rurlum cum FIB recta aequidister cangenti DF,
erune DB, BII diameeri coniuratae; Cunc aucem Cx CON.
Aructione criam AB; B C coniloaca, igitur c ve DY ad
TFT, AC C G ad G A: quare _ racio FD ad DF, dupli-
cata estracionis C C ad C A. Ouod erar demonstran-
dum.
eROEOSTLIO BAL
VIncAB, BC diametri coniugAEX _E per A _ C FANSenFES aUCANEuE
DE, FC. Cc aurem ex alia quaeuis diametrorum coniugacio fLI, I L
quae producta OCCUTaEtangentibUS DP, FO in F., F, D, e
Dicolincas D F, FC in A e C proporrionali-
cer esse diuisas, nimirum esse E A adt AD, VE GC
ad CF.
Demonstratm.
nis R M ad MHI, _ GC ad C F, duplicata est racio-
nis IN ad ER. Aequi ratio RM ad. MH aequalis clt
cracioni IN ad NYK. ergorationes F A ad AD, eCC
adC Faequalium cacionum duplicataes lunt aequales, pro-
porcionalirer ergo secta sunc DP, C F in punctis C A.
Duoderac demonstrandum.
rCaHTUE LinCX FIK, R T quae rectas AB, DC UCCM
In N ex DY. RaciO E A ad A D d duplicaca est ratiO.
hic