# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0323
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0323?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 266, page id 1815201908:0323
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=323
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000323.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.85
# 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.

S. huit
SI
Desectoribus s enis Fllipseos
e
iunsanturque ABC.
ABC inCcribi poNunE.
42. primi.
VHa
PROPOSIIIO XLII.
ABC ellipscos diameter BD, ad quam ordinatim PONAEUE A P. C:
a
Dico ABC criangutu maximum esse illorum qua segmento
S
Demonstratio.
Eca p et B concinvente B F, ex A recta ducdeur quae-
Luis AF, Occurrens ellipa in C ee contingenti in F.
iungancurque GC; FC: Ononiam FC concingens
Cadic suPFa C, igirur eriangulum AF C maius est crian-
sulo AOC; sed AF C triangulo sequale est triangulum
ABC ob AC, BF aequidistancesiisitur _ AB C crian-
sulum maius est criansulo AGC: unde cum idem de
aliis omnibus criangulis ostendacur; pacec AB C crian.
sulum, maxitmum corum esse quae legimentO ABC in-
scribipossunt. Quoderae demonstrandum.
Coril
Corollarium.
Inc Facilis praxis elicirox ad inscribendum cuivis se.
smenco criansulum maximum: crigendo iinirum
dialectum L B, ulgendoque AB, BC. puncta. demonstratio patet expriori.
PROPOSITIO XLIII.
Riangulum maximum segmento cuiuis
non maiori lemicllipliinscripeum, maius
est dimidio eiuldem Segmenti.
Demonstratio.
spcum eriangulum maximum AB C. Dicoillud ma-
ins esse dimidio segmenri AB C: ducta enim diametro
BF, qua AC subcensam diuidac bitariam in D, eriy 2
CAF Cx A e C linCR AF, C C Parallelae diamecrO BF,
qux FC concingenti per B actxe occurranein F e 6)
iungancurque AB, C B: criangulum AB CD dimidium
est parallelogrammi AC. AEguI AC paraIlelooram.
mum maius est (OGIeNEO AB C, Cum AF, C G, F G li.
nex cadane exera elliplim; igitur ex criangulum ABC,
maius est dimidio ciuldem segmenti. Ouod fuit de.
monstrandum.
PRC
EiSto ABC segmento, non maiori semielliph inseri-
q   p   . e 1 e  1 1 e  1  e e 1   e      B   . 1 1 A e  p .   p B B a  s     Bus . p  B  e  t per 1    1      vr