# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0179
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0179?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 122, page id 1815201908:0179
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=179
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000179.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.
# 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.

ROGRESSTON E S
1
1O CZX
TE magnicudo aliqua AD, Secta in ErES parceS AB, BC, CV. ablata
+  media BC vel alEErUETA CxCICMTatU, reliduis AB, CD Hal aGuas
E HI, quae diuidatur in crespultes L F, Fb b H in cadem ratione quu
Dicorclinqui candem ninicudinem daca minorem.
Demonstratio.
niam AB eAt ad BC, H LF ad F C e BC au C D, VE HC 1a , IL. 181
axpermucando AB ad F F, VE BC ad F C, _ CD ad GTI: CrBO = VE AB
ad E F, sCA D, ad F FI: d permutando AB ad AD, VE FF ad F FI. Cmilicce
624 Guin- demonstrabimus DC esse ad D A, VE FIC: ad HTF: ergo AB b cum CD, ad AD
Ht cum GFI ad R HI. d invercendo AD ad AB cum CD, id est ex hyporhesi
FFT, ve L.TI ad FF cum C LB id est ex hypochesi IM. Cuncigitur AD, F FI, IM in
concinua ratione minoris ina qualicaris. non alicer demonstrabimus NT 9, CaerCra-
que relidua in infinicum cum prioribus eandem proporcionem minoris inaequalica-
Cug sin cis concinuare. Duare crelinquecur cundem magnicudo daca minor. Oyod exat de
monstrandum.
eRordstrIO CXAI
F
Cta cst AD: Si hoc concinuetuT;
d
115.
Aca SIE A B magnicita vrcum que secta in C, ac inFeF A B, C B me-
dia proporrionalis Pbhacur D B; rurlum inter DB, C B media (IC
Dico ex AC. relinqut lan demmagnicudinem dacd minoret.
Demonstratio
L ehocconcindecu.
Exprimam huius; AD est ad DC H AB ad D B. LCgu AB Mdior est quam DB.
erxocriam AD eAmaior quan BC: ergo AD maior est quam dimidia AC:
quare DL. Macet en Guau P.C, laeoque e maior quam dimidia D C. Podemmo-
do probabicur F F ese Pes atlo F C. aeque ica in infinicum semper plus dimi-
S. Ao ab A C, eluq; Feltans auterecur. Quare d relinquerur randem magnicudo dara
minor. Ouod erar demonstrandum. 1.
P R O
  e pet  . o  s s  p e  e i    p t  .    i .  1  . .  s  1   1      e   t           1      t ue as  l