# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0281
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0281?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 224, page id 1815201908:0281
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=281
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000281.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 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.

DROLR GOM F N A
Corollarium.
TInc colligere licet Facilem praxim cohno(cen-
di lacera criangulorum quae per axem sectio.
ne facta emergune, d proportionem illorum incer
Cc. Ponacur enim Cemicirculus AB C: cui ABC
criangulum scinscripcum habenslacera AB, BC
aequalia laceribus maximi crianguli alicuius coni
Per axem secti: Juoniam ergo quadraca larerum
minimi crianguli per axem eiusdem coni xquan-
cur quadrarislacerum maximi AB, B C, (hoc est
quadraco AC) Pocerunt de minimi lacera inAecti
in Comicirculo, quae snE AD, DC. quod s cerria
quedam lectio hac per cundem axem, proporcio
lacerum illiuscrianguli, reperietur neceslario in
aliquo criangulorum quodhabebic balm AC, e
vercice in rno punctorum que lunc in parceperi
mecri BD. cum enim aqualia  quadrata lacerum vnius criansuli quadracislace.
rum alcerius; quod per axem Lacta lectione relulcae, sincque ABC crianguli qua-
drata AB, BC aequalia quadraris lacerum maximii quadeata vero AD, I C aqua.
lia sinc quadraris lacerum minimi; sequicur lacera cuiuscunque alcerius, quod per
axem coni producieur, in aliquo criangulorum reperiri debere quod balim habeac
AC. ee lacera reliqua se sc in aliquo punctorum decussantia que in arcu B D, assignari
porsunt, quod ex decursu sequencium propolicionum maxis clucidabitur.
eROPOSIT1O
1V
Nconoscaleno à cuius vertice demissa perpendicularis in perimerrum
baleoscadic, si quoduisum per axem sectione facta exhibeaeur:
Dicoquodnormalis a tetetee coni ducta ad balim crianguli cader in
cilcun perca gu ucscribetur diameero incercepta incer perpendi.
cularel a verrice ad balim ducta e cenrrum baleoseiuldem.
Demonstratio.
mista perpendiculariter, cadac in B
punctum perimeeri bascos BF C,
descripeo deinde circulo BCD,
supec diametro BD, agarur planum
per axem quodcumque AR L, exhi-
benscriangulum AF F; cuius balis
primo secec circulu in punctis DC:
ad Ci ex A puncto verricis, demic
catur AC. Dico illam esse qua bali
PF normalicer insistie; duCaTUF
enim recta linea B C, iunoncurque
BF. Ouoniam ixitur ex liyporhiele
AB recta cA plano balIS BP, C F
angulus ABF rectus cAt: ad coque
quadrarum AF aequale quadratis
AB, BF; hoc est, quoniam angu-
lus BC F in semicirculo eciam re-
Aus
CleigimE ABC conus cerrubaleOS
D. 2 coni verrice A recta AB de-
 ue s   te is pit tat a  su  t ut  . u u   pa a e et  e et  e p et ut  t t p sa   t   a  se     e        l el