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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 553, page id 1815201908:0610
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=610
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

dF.
senii
DEO.
DV.
eque
lune
rem
Tert
la-
ICuE
DP.
IHE,
RS
AX
AU-
TRi
ME
dem
B.
et.
IIIIIIII
HIY P E R BOL A.
PROPOSITIO XRXIY
HInE ABC, DL F oppolicx sectiones, quarum communis est diame.
cer BE: cuix quidiltantes ponantur quaeuls , Bccurrences cOn-
cingenri per  acta in Gs ponancurq; ordinarim A I:
Duo ACD ieclansula xquarirectan gulis BIF.
Demonstratio.
DOnanEUE ex D ordinarim DH ad diametrum
BF. cum isitur eam AD, IHI, quam AL, GB,
DH linex aequidistene, crune AI xquales DHI.
_DHI F. aequales IB; rectangula isicur HIBL id eAt
DOA, Equalia suncrectangulis F. IB. DuOd eTAE
demonstrandum.
eleOTOSITIO XXY
Dicd A C,D rectansula proportiona-
lin esse quadraris CB.
Demonstratio.
Sceniu DIC rectangulum ad rectangulum BTF, vEC AL quaaratum ad quA- CEVL HA.
deatum AI, id est B C. ad quadratum BG: scd AC D d reccngula aequalia
Cunc rectangulis BIP: quadraris ixicur B C, proporcionalia quoque sunc rectangu-
la AC,D; quod orac demonstrandum.
PROBOSITIO XXZVI
Int sectiones OppolIEX ABC, DE F; d diametro cururs L. B, PMMal
crparalleta C H, lK; occurrences AC ordinarim posiex ad FB,
Dico blC rectangulum adrectangulum IlM, candemhaberera-
rionem, quam rectangulum AHIC ad AK C rectangulum.
Demonstratio.
d34. buius:
Adem matience Agura:
in punctis I d FI.
DOT AD aquidistance B. B, constimaneur ordina
eim IO, GP, I. DBMIO, Id R ad diamerruF B: erit
CrROCR F S rectangulum, aequale rectangulis, RO5
vria cum recrangulo 9) RO. Similirer rectangulum
OFC) aquale rectangulis () PO, PF N: quadratum
Aee AS. aequale est reetangulo nA R C, vna cum RS
quadraco; quemadmodum eriam quadratum MO X.
quale cst rectansulo MZ P, ui cum Z O. quadracoi
est aurem rectangulum R R S. ad quadracum A S, EVE
DF O rectangulum ad quauacu S L ntOIL. R S. Igi
cur ee reliquum rectangulum. RO S, est ad reliquum
permucando le Srectanguium ad reccanoulu OF. O.
eArcrectangulum AK C, d XS quadrarum hoc est
222 3
AKC, VEO FO rectangulum ad quadracum. K S5 e
13
estet e  ute et e at te ta te   t ta e t p e   ui t t   . eet 1  a    t o e    t   et e   e te  e   ita