# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0336
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0336?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 279, page id 1815201908:0336
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=336
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000336.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.73
# 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.

B
E L L IPSIS.
les, e iam ostendi aeguales oriam esse rectas D FI, FT C; isitur =CC F D, Xequales 226. Promi.
tunc. similirer octendemus BF, D E. aequales eAte. C onstac ergo vericas propolicionis.
PROPOSITIOLXIZ.
TIdem posiris producarur D G, donec AC linex occuratin I.
Dico A6h AGC, AFC criansula in conrinun esle analopia.
Demonstratio.
X superiori demonstratione, in eriangulis CFC, F HD, pacec omnia ense
equalia, adeoque latera eriam P FI, IT C lune xequalia. considereneur modo crian-
Sula DFTO, BIIC, in quibus cum duo lacera DEI. HIF, duobus laceribus CFI, HIF
equaliatine, angulusque DHIC aequalis angulo CHIF; ad baum criam aequales
crunc anguli HIGD, CFFI ac proinde DI, CF sunc parallele: adeoque ve A T ad
AC, SC AC, ad AF, sed eAt ve AI ad AC, sic ACT criangulum ad criangulum
AC C: _E VE. AC ad AF. siC A C C criangulum ad eriangulum A F Cs igieuF vE
AC Irriangulum adcriangulum AG, C: sic AC C criangulum adcriangulum AF. C.
Quoderac demonstrandum. ivs cbcu
AEC
i. PROBOSITIO LXX.
Eliplim lecenebinae diameeri AF, A F in punctiS E _E F, et QuIBUS
GdUICANTUL FC, E B cangences elliplim, occurrentes diametris in C
e B, IUNGAHEUTG; P F. LS8L 111
Dicorriangulum AC F erianigulo AB F. xqualccAo.
1292
onratioI.ari
31ISZBIT SI.
X puncto F. ad A F duc ordinatim L. K, eric hEcBCaH
Ldenei LParallelas ideoque criangula AF K, ACL
similis lunc, ac proinde duplicacam habenerarionem ra
cionis AR 2d AF: hoc est quia c AK, AF, A B CunE
eres concinuxe proparcionales, rarionem habene quam, oci
AR ad A B. scd etiam est vE A K ad AB, GC Friansy.
lum idem AF R ad eriangulum AF B. ergo criangu.
IUI A E K ad eriangula ACF; AF, B candem habeC
racionem, aequancus ixicur erianeula A C F, A F B: 940d
erae demonstrandum.
BGe
IaieA e op 403GMCI
C A 35 sAB CITEI 10221C19Y :5. IIpi 1
11be. 33I.
3E. HOC): CMIVEEBE
ed odil. I D Cesol
3o.la: ct 2) crimnon
:e p adtiil
139 ACCB N 5. 13~ G12C 1. 1 2
t
31 23BE 1H 3e29 BOVC.D E ISF Sla 2CC
 reser eti 2B de
1.
.et L. 3 31.D0 1013 3: a) 5.XHt d 1. Si L. N (15 19
sit. BBCB it tAI.
b 13. tviu 5.