# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1043
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1043?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 986, page id 1815201908:1043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1043
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.89
# 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.

NGVLA CXLENDRIC
Demonstratio.
Sc enim per PrXCCdenCeM
rectanoulum EBD, aqua
le A C, F K rectangulo. sed re-
clangulum C.BD Per candem
aequacur aCLC ECclaliu
10. lgicur rectansao  etill
aequale est BD. L C rectane-
lum. Duod Fuie demortata.
dum.
Onatur in lemicirculeACca Moendens arcum C F, ex cuins
cerminis perpertu utes Hane P. F, CD ad diamerrum AB.
Dico rectangulum quod continerur
veraquesimulCD EF, _ C F aqualcel-
Ccrectangulo contento rect a linca DF, et
rectâ P. HI subrendente circumferenciam
E BII, quae una cum circumterencia C F
Semicirculum CBHI perticic. F.A Pappi
ibidem propol. 23.
Demonstratio.
Omplero circulo, sicipsius diameter CHI,
e producta CD in K, ad ipsam perpendi-
cularis dUCAEUE E. C, _ FFI, FK tunganeuT.
Duoniam igitur diameter AB (CCAE C K ad re-
a05 angulos, aequalis est CD ipA DR. Scd _
ED eA aequalis B F. ergo OK aequatur dua
bus CD, e RF: est aurem G F. requalis eriam
DE; que vero reliquam semicirculi C F. HI cir-
cumferentiam lubrendie est F FI. Itaque quo-
niam angulus K cA ae qualis anguloTI, _ IIFC
angulus in semicirculo rectus, aqualis recto
RC F; crunc eriangula HF C, K F G xquian-
gula. ergove IIF, ad E C, ita R C ad +F, e
ob id rectansulum concentum HE, P C, hoc est HI B, D P, aequale cA ei quod OK,
CE hoc est ei quod veraque simut CD, PF, e C P continetur.
EROPOSTTIO ZZZIX.
IIdem politis demitratur perpendicularis P. I ad diamerrum HC.
LDicorectangulo CF, P. lX quale esse HIF, C Prectangulum.
Demonstratio.
2B.a. VnEenim aerIanSUIZ CFT, C F HT Similia, ac proinde laFerA CP, FP sunE lateri-
bus CB, P. FL proporcionalia. un de rectansulum CB, PHL rectangulO PP, C P. est
aequale.
PkC.
ROPOSITIO ZZEVIII