# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0688
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0688?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 631, page id 1815201908:0688
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=688
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000688.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.88
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

UtemM
acigitu
Proc.
nette
unctur
aqua
qu
alle
es le
ettu
301.
Eperbolam D F C inter alymptoros rectum angulum tormances
l.Aconsticuram, Cecec ih D parabola B D E habens axem BC. policae
ex B quanis linea BK HI5 gux hyperbola occurracin K de parabolx in
HI, deleribatur per LThrperbola HO habens AB, B C alympEOTOS; _
ex B quauis alia ducatur BL. O t, occurrens hyperbolisin L, e O D2
rabolx in F.
Dico BK esse ad BFT, ve BL est ad BO.
Propositionem hanc, vri es duas sequentes, quo d suis locis exciderint, huic parti apponere
visum est.
Demonstratio.
DONANEUE KM, LN, IIL, OO:
aequidistances AB. Friangula
2ISIEUE BKM, BLN aqualia lunE,
ver ex crianoula BFTI, BOO: unde
BK MI criansulum est ad B L N, VE
BTTT ad BOQ criangulum, et
permorando B K M ad BHL, vi
BL N ad BOO: sEdBKMErian-
adtrianoulum BOO in duplicaca estrarione L. A ad OO; igituE VE RM adFTY mensii
in est BK ad BH, sic L. N est ad OO, id est BL 2d B0.
Nota vniversalem hanc esse propositionem: neque necessarium esse ve B LL linea incidat in
FT, communem hyperbola cum parabola intersectionem; sed BTI, B P quasuis pesse esse, vii
ex demonstratione iam posita manifestum est.
PROPOSITIO CAC.
TInE AB, BC rectum angulum Formances alympeori hyperbolarum
ADF, E C, quasin D e P. secet parabolahabens axem B C: pOnatur
aurem ex B guauis secanshyperbolasin F dc G, occurrens parabolx in
M. ee ex F, D, C, F. punctis rectx demirraneur D HI, Fl, F. IL, GL. paral-
lelae AB.
Dicorationem DHI ad FL, maiorem esleratione FR ad O L.
Demonstratio.
Ecta BD producta OCCUTTAE L. C
poperbolae in N. ponacurqueNO.
Parallela AB; cxic isitur DHL ad F 1
cve NO ad OL: Sed ratio NO 2d
OT. maioris ad cande, maior d est quà
racio F. K ad CL, minoris ad candem:
racio isieur DII ad FI. maior est ra
tione FK ad C L. Duodtuir demon.
Arandum.
Gulum ad bB FLI, in duplicata CsFAEIONC RM ad FFT; similicer B L. N eriangulum B Exele:
Me peri sat  tie a e   t  eu  eta  s  s t tat d d a    t t   e t st t te eta t e u  et  pe te e t ti    p   set