# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0239
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0239?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 182, page id 1815201908:0239
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=239
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000239.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 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.

 . p. 1 1. 111.  1 1 . 1.
TR CVLVS
circuli B GD in G, rectA VerO DB, AIAMerTO A C in F.
Cb AD, DE, F. C, cres MCas, Caudem rationem continuare.
Demonstratio.
182
Ccribatur circulus BG D, Ponancurq; FI C, quidem occurrens perimetro
DOnacur PP, aequidistans BD,
iungancurque DC, CF, AB,
quoniam F F xequidistac BD qua
in FI divila eAt bitariam, cric P IX.
qualis IF: vnde ve F I ad BFI, id
est F I ad FTD, SC F C ad G B id
CA IC, ad CFI, e permurando ve
FI ad TC, ica DFI ad HIC. qua-
re cum anxuli DFTC, FTC laceri-
busproporcionalibus contenci sine
aquales (ob FTD, F I parallcla5)
crunt eriansula FTO, HIDC: Scu_ O IF, BHIO, ItCM FP G, BDO.
lunc ergo in directum D, G. F, puncta, veCL elementis parec. Vicerius quia similia sune
criangula BD C, DGF, eric BD ad BS VE BG, ad D G: id eA F C ad G F: sed
etanpulum BDEF, quadrato DF aGualc. (unc aucem similia quoque crianpula
ADB, E F C. IsITuEVE AD, ad D D, ita F F ad F C. unde rectangulo ADR C.
aequale est rectangulum BD L F, hoc est quadracum DF. Cunc igitur continux
proportionales AD, DE, F. C: quod tuic demonstrandum.
Emicirculo ABC inscriprum eno criangulum cujus alcerum lacus
Dico BC, AB, d agorcaum Cx A C, C. B, eres esse in continuaration.
Demonstratio.
Flac A D ECsquialECTA C D: iuNBACUEquC BD.
arcus AB duplus eAt arcus BC, quia C BI2.
cus hexagoni est; igitur e angulus BC A, du.
plus anguli B AC: scd angulus BC A, quoque
duplus estanguli= BD A cum AC BCD IIOICO.
lesper constructionemigitur angulus BD A x.
Oqualis est angulo B AD e AB, BD laTCTA X
qualiaincer se; unde similia Cunceriangula BDC.
BD A: _ veC D id eAt BC adDB, ita DB
hoc est AB L AD, hoc cA 2d AC, C B. Ouodtuic demonstrandum.
EROPOSITIO XXIII
scersecent sete ac ACos, diametri AC, BD; polIri (GUC AF C, APC,
ungatcur L LD.
Dico , adOF, candem habere rationem quam agereeatuu
auacum AL, F C, ad aBBCcgncum AF, FC.
similis
VEF C ad G F sIC DF est ad R F cum DOF, G F. F similia sincriangula, igitur
BD est ad D F VE D F ad R F; quare sunc proporrionales BD, DR, R F d rC
eROPOSITIO XXII.
DC, Penidiamerro MLa GualC.
Demot
sustt t os su  sate  ute t  te tt e  e a p ei e te e  e se tut pe   tet e e t te a ee te e e  pete e te  it te     il e