# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0611
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0611?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 554, page id 1815201908:0611
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=611
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000611.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.84
# 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.

AY P F. K b. OL 
MO. est aurem R OS: rectangulum aequale TRHI
reccangulo: igitur _ IK MI reciangulum, est ad reCran
sulum OF. O, ve rectangulum AK C ad RS qua-
dEAEUM. EFAE AUTEM R P S rectangulum ad quadtacum
verectangulum 9F. O ad quadracum MO. Igi.
CUEVE O EO rectansulum hoc est P OB ad quadra.
cum MO, ita est ROS rectangulum hoc est IKM,
ad A K C rectangulum. eodem discursis demonstratur
rectangulum OFTT ad AHI C, camdemrarionem ha
berc quam F N B rectangulun ad quadrarum N L. hoc
est quam rectangulum F. OB ad quadeatum MO. Igi-
cur rectangutum AKC ad IRM, camdem habeEra
tionem; quam AILC, 2d rectangulum CFTL, e
GFIL rectanoulum ad rectanoulum TKM camdem
habecrationem, quam rectansulum AHC ad ARC
rectatigulum. Ouod tuic demonstratidum.
ROLOSITIO XXXVII.
aneux iterum oppolICa fectiones AB C, DE F, d ad diametrum
EBcollocentur ordina HI, IK, AC. POnaTuTQ; BL. concin-
Bens _ AD, IO. CF aequiemunet B: denique GH, IH prorracta cum
Dico rectarigulum C.M HI Ad LNTK, camdem rationem obrinere,
quala et L. Lecratsutum ad roctangulum 109.
1A
ta moto Demonstratio.
SEDEEpracedencem, rectangulum F PC ad OOTFe
 nla ctangulum, eam habec racionem, quam APC roi
cransulum ad recrangulu AOC: sed rectangulo A P C,
aQUaEUE GMHI reccangulum, e recrangulum AO C.
reccanoulo IN K. recCangUuM igITUIr OTMHL ad TNK
camdem racionem obciner, quam 109 rectangulum
orsdrecraneulum CP R. Duod fuerac demonstrandum
A OeOSFFFO XXXVIII.
ACH verbola ABC; oporteat illi oppositam
nul conticuere. IlA
1
5.1 moei
Constructio es demonstratio.
FNuenro cenerob typerbole AB C, nimieum D,
eriehioc communeleciam alceri ic hyperboles qux
E. inguiricurs Vlceriuss CiasimpeoriDK; DIponancur
in IperboIx AB C, illa Similicor producra, non
minus quam diamectid communes erunt. Diuisdin.
 superA C ordinarim posica, ad quamlibet diame
tru D. B, Bifariam in I, s hao DB xqualiS D B, S
D PxGualis D Ch e Per GCOIIOCeruT MCN a
quidistans RCi tanEauTem _ NTC, CFN lincae
aqlales lineis AF, F C, _ per MI, F, N hyporbola
dolcribaturs parer illam laristacore pecirioni: erier
enim rectangulum EFB aequale BCF reccansi
Sulo, equadracr AP, EqualoOM quadracorqua
retimiliserir ex aequalis tiypertiolasB  hypOrbo
12
Or
AD concurrant in M e N.
1