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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 437, page id 1815201908:0494
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=494
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

et
V
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de
C
a
10
2d
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1at
p.
11
D A R A BO L A.
proporeionales. lune aurem de ATT, A T, 2. A C linex criam in CONFINUAtRFACIONC; 151- 2F
67
cur A C AFI, AL. A C eandem concinuan analogiam. Quod etac demonAtrandum. huius.
PROPOSITIO, CLXXILI.
Ildem posiris ponatur ordinarim C. D.
Dico AC ad A C criplicatam habere rationem eius quam habet
Demonstratio
DVontam A G, H H, AI, AC lines per praecedencem continiix proportionales
LsunE, ratio AC+ ad A CD criplicata eAt eius cuius A FL 2d R C eIFADPHCaL: Sed bEr27. de
AHI ad AC, id est AF adt AD, racionem habet duplicatam BL a CD: isi propressioni-
cur A C ad AC rarionem haber criplicaram ehus quam habet B L linea aue
CId. Duod erat demonstrandum.
eRO POSI FIO CLXXI
darabolam ABC cuius diameter AD COnFinGAE II A AIACA AL,
Politilq; ordinacim CD, F C7, per D d A parabola describatur AHI F
cuiuscangens AB, diamerer AC: ductaque AF, ponatur AC, SCCANS
AIIF parabolam in I, rectam FC in HC puncto, ex quo crect a diametro
IEB, ducacur ordinatim linea BL, occurrens A F. linex in MI, rectae AC
in N, e parabolae ATIF in II.
DicoCD, FO; BL, M L, NL, HL lincas in concinur esse allatogia.
Demonstracio.
FRivatur Ex F diamerex FF. Ouoniam B K equidi.
LstaE diamerro AD, recta C D, F C, B L proportiO-
nales sune: Sed _ F C; B L, M P. quoquo TUNEPFOPOr-
cionales; candem isitur concinuane racionem CD.
FOG, BL, HL. Rursum cum racio NL ad K C, id cR
2d BE, id estracio AP ad AC,, duplicaca Ecracionis
BE ad F C, id es LM ad L B, rectX GUOqUCBL, NI
NVE proporcionales lunc. Pottremo quia FC li-
nea ad lineam FTL duplicacam habet racionem AV
ad R C, id est quadruplicatam L. B ad C+F, id cst L L
adCM, linca L HI, T. I, L M, L B, I Fproportiona
les lunes isitur concinvane eandem racionem linex
CD, FC BL, M L, NL, HIL. Duod erar demon-
strandum.
Pxopostit
ZV
BLdd CD.
Dltabolas aquales ABC, LLVC, W
leslateribus rectis, lecent aurem selepa-
rabolae in C, _ ex C ordinatim ducan-
eux CBs C F, demissisgueoxiA lineis, 27
Qualibus AB, AC; quarum alcera A R3. 1 1 C
quidem ccci AB C patabolair In B, lcavi 0  id   ett . 1B
NT B.3
communem habentes verricem,
ContinganE in A lInCXAFC, AF xqua-
AC Ve
3