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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 454, page id 1815201908:0511
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=511
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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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eAR ABOL1
eR OPOSTTIO COXIII.
s
sulo AIDI.
Emicirculum ABC, cuius diameter AC.
concingac in A linca AD; delcripraque per
A Parabola, cuius dals AC, & contingens AD,
Cumacur A E xqualts laceri recto; actaque perF.
ordinacim P. F, ducdcur in parabola diameret
quxcunq; DO occurrens circulo in B _ 6, pa.
rabola in HI, _ LE ordinatim politx in I.
Dico BDO rectangulum, aequari rectan-
Demonstratio.
Veacur per FE ordinarim linca HT K: OHOMIAm AD
aca in A circulu concingie, rectangulum BDC
aequalc cAa quadraco AD, id est quadraco HK; Sca
EHIK quadracum cl xqua le B rectans ulO K A F, 10
AF per hypochelum aequalis elt laceri recto) rectangulum ixicur
DAabolasduas ABC, DB L ac CucCMarem BF policas, _ Cm-
seses seleincerius in Mlticelecor in H e A diameter quaecun-
que CHs, iunetilque AB, LLB ducacur ordinarim linca LI, Cccans pa-
rabolas in, lK, L, ex M, rectas AB, HB, AH in C, N, O, e axem BF
in P.
DicoLL. K rectangulum xquari rectangulo C PNO.
Demonstratio.
Ectangulum O PN, xequale clC
LLc quadearo IP. Scd IP quadra-
cum est x quale quadraco L P. id elt
d rectanculo sFO cona cumrectan.
sulo IE. K redtangulum isicur C+ P D
xequalc eArectangulis CPO, IL. R
eAaurem C PM rectansulum, aequa
le rectangulis CPO, FGPNO.
dempeoixitur communi rectateo C PO, manec II. K rectangulum xquale rC.
clateulo  PHC. uod erar demonatrandum.
PROP651110C
BDC aequale est rectangulo HD L. Uouerat demonstrandum.
LROPOSITIO CCZIV.
CA HDYC
+2. bni
ix ole
meneir.
Acam lineam AB divilam in C, E, I, Ds denuo ita pareiriin F. VE Fe-
ctangulum AFC Cic 2d ca B  L Heu Gladestum
B1. :2
Constructio.
AE. C quauculum DB.
15L1
Eatis AC, BDbisectis in L. E L. NI, erise perpendidulares L. P. NV R aequaleS
Se, _ per puncca A, I, C, _ D. R, I ACCtBAnCI PalSBBI NV LMBIMMCHOOC-
CMB.SLI BC o
currences in C. Tum ex c dux C E. normales ad A B. Dico FaCcumL IUIBWH. ISIMCIM
B5.
 ti  e aii ut sits ete  e et  e e uet e u e e si s  pe u sue t et se e te te e ete t ti ete p  e  e e  t t e t t ute  i     1te  t  e e t s