# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0268
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0268?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 211, page id 1815201908:0268
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=268
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000268.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.91
# 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.

C. TR CV L. V S.
PROPOSITIO LXXXII
DEx extrema diamerri A B circuli A B C, circulus deferibatur ADB,
POlicaque AC, quXOCCUTEaE AD B perimetro in D, demittatuF
hormalicer D F ad diametrum AB, iungancurque DB, C B.
Dico rectangulum ex AB, DE, ad rectangulum ADB, cam rario-
nem habere qua eA incer rectas CB, DB.
Demonstratio.
Voniam ansulus AC B in semicirculo rectus cR
adeoque aequalis angulo AF D; _E AF D, ACB
criangulis COnUNIS ANGUIUS D AF. CTUNC AD F, AC F
riangula limilia. rule ve AB adt C B siC AD ad DF.
_C ABD F. rectangulum aquale rectangulo AD CB:
Ced rectanguluns AD CB est ad rectangulum ADB v
CB ad DB, igicur de rectangulum AB D F ad rectan-
sulum ADB csrc C B ad D F. Duod erac demon-
ctrandum.
PROPOSITIO EXXXIII.
Ceurrat circuli ABC dIAMeEEO FG In F.
orchosona AC, quam in D Scceenormali-
Ter BD, iUngANCuEqUC AB, BC.
Dico rectangulum ABC ad rectangulum AC BD rarionem obci.
nerceandem, quam FC diamerer ad A C lincam.
Demonstratio.
VnganEuE AFC. quoniam AC liner in F bitariam
adeoque ad rectos est divisa, CrUNE AF, F C linCX X-
quales, de AFC rectangulum xquale quadraro AF id
eAt2 rectanogulo E I CT: quia F E, E A, E C TUNC PEOPOE-
tionales. Sed E F C reccangulum est ad receangulum
AC. F E VE F C ad AC; igicur ee rectangulum AFC
2d A C F E reccangulum id estb parallelopramum AFC.
VE F C ad A C; quis vero est AFC receanoulu ad recE2.
sulu ABCVE AFC parallelooramum in angulo AFC.
ad parallelogrammum ABC, in eodem angulo ABC
cu ex iidem rariones habeane composiras) eric permucando AB C recrangulum
a Parallelorramum AB C, id est ad rectangulum ACBD VE A F C recrangulum
ad parallelogrammu AF C id est ad c A C F P. recrangulum, id cA ex demonstraris cibia
eFC ad AC. Duod erac demonstrandum,
eR, OP OSITIO LXXXIV.
cenelc vicunque circuli ABC, AD C in punctis AC, iunet aque AC.
OHanEuF C F. HI, C BC, Occurrences perimerris circulorum in B, F, 6,
IUNGANEUEGVE AB, AF.
Dicorectansulum ABC, ad AF. C rectangulum cam racionem obri-
are, quam C BC, ad rectangulum HE. C.
D
47. prim
5
b69. huin
Detn