# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1173
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1173?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1116, page id 1815201908:1173
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1173
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001173.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.86
# 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.

2uC
QYADR A FYR A CTRCVEF
Demonstratio.
huic
uius e5
inter Ce vibales quare cum bales pelamu ene proporcionales, crians patalle
lepipeca proporcionalia lune, quorum ille bales lunc. Pari quoque modo ostendieur
PROPOSITIO XXX I.
Scensum acam lineaS PO, P R, P F quam Z K, Z a, X O proportionales el
(C, hoc est P d3P P; PM. indeb rectangula quoque proporcionalia lunc O P d
RP ∞, L PMI, sunc aurem parallelepipeda communem habencia alcicudinem P X
Parallelepipeda habencia bales, rectangula R P P; F P ∞s I. PM ec conimunem alcis
Ex29. Fudinem PX, proporcionalia esse, cum eriam bales illorum proporcionales sIMEs
roeres.quare conctarvericas proposicionis.
Vper AB constructis quadratis ABC, AB D, descripeis preterea pa-
rabolis AF C, B FIL quarum verriceS LInE A _ B, AXES VeTO AB, B A;
item parabolis A F C, B OI, quarum verrices etiam (InE A eE B, AZCS VerO
AK, BD; Policis in TUPCFF G, F FI que aequidistent CD, de sectionibusoc-
currant in E, L, C, M _ N, F, O, HI, diagonalibus quoque AC, BL, in pun-
Ctis P, Q, R2, 5.
Dico rectangulum L. ZG ad F x O, rectangulum duplicatam habere
rationem eius, quam habet rectangulum PZ Q ad RNS rectangulum.
Demonstratio.
Le tuiu)Scensum est supIa Lam rectangula L. Z. G, P Z O, F Z. Z GVIaII FCCLAHSIIA L AO.
R x S, V a Y eandem continuare racionem. Ouarc cum extrema rectangula
gmmns. L L, VX sunexqualia, cric crario rectanguli L. Z G4, ad FCCFAHBATAM L NOdu
plicara racioris quam haber rectangulum PZ.  ad rectangulum R a S. Ouoderat
demonstrandum.
tROPOSITIO XXAII
Ella Cllalheltoo.
Dieo recrangulum PZ Q ad R aS, duplicaram habere rectatglu
E. Z. M ad Na H recransulum.
Demon