# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0565
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0565?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 508, page id 1815201908:0565
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=565
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000565.jpg
# 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.
# 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.

con
versa 47.
aius.
ad B, TII.
A R A BOL 1
PROPOSETIOCCCXXVII.
Sco ABC parabolX diameter AD: astaC per A ContingentE AF,
demictantur diamerri F. B occurrences parabolx in B, X AC in C:
ponantur aucem ordinacim linox, HB: Hacq ve FCi ad F C, sicB, HL
Dico puncta A, I, l esse ad parabolam.
Demonstratio.
(7T FG ad FC, sic AP est ad AF.
id CA IIB ad HIB: igitur de FII est
ad FTL, ve BHI ad BH: X HII quadra.
cum ad quadracum TII, ve ITB quadra
cu ad quadracum FIB id eA VE AHI linca
ad lineam AEI: puncta igicur A. L, I 2d
Parabolam lunE.
PROPSSITIO CCCXKVII.
C parabolx diametet AD aequalis laceri recto: ductaque or-
punctis B, B, erigantur ex B diametti BF Occurrentes A P. linexe in C:
hancque rectis AC aequales liex BF.
DICOA, P, F puncta ese ad parabolam.
adinacim C D perficiacur quadracum C A: Cumprilque in peripheria
Demonstracio.
VCaTE reCtA A C OCCUErCNS F B lineis in FTI:
quoniam A D laceri recto x qualis eH, _ C. D OF-
dinacim posita ad AD, reCtX AD, CD, aequaleS (UME:
onde e rectae AO, EH quoque aequales sunC: e FL C
linex aequales iplis F B: dempris isirur communibus.
BC, manene ITB, FC linex aequales. Guare Li C est
ad F G, DE BFI ad BFT; id CH vE AFIC a rectangu
lum ad rectangulum AFFC, id cA A C: F rectangulum
ad rectangulum AC F. puncta isicus A, P, F. ad pa
rabolam Cunc.
PROPOSITIO CCCXZIX.
DArabolam AB C Subrendat recta AC,
quar in D secent quorcunque diame
cri BD: Franc aurem BD lincis prOPOT.
tionales DI.
Dicopuncta A, F, C esse ad varabolam.
Demonstraio.
L bD ad BD, H V. D elt ad. L. D, led cl
ve BD ad BD s. Sic AD C b reccangulun
ad receangulum A B C: ioitu d F, D Cstad R D.
vE AD C reccangulum ad rcCEangUIUM ADC
Quare AP C PUNCFA Cad parabOLAM CUME. OisEY
Ce. sq B_ D R O.
u i s e   us se  p    t.   e .  e    et    s .  t    s  1   e    e   i e   s  e  it se e   e e ue   e  it