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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 555, page id 1815201908:0612
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=612
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
# Lines: 78 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.
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# After the first blank line: the recognised lines in reading order, one per line.

XH
etan
n
uN
dea.
11
aCUI
13
dem
60
un
um
eres
c
10
C.
C.
IX
im
2
(1t 11. 11
H Z P FR BO
IX M FAT, X ad diamocros communes constidura aueoque _ a OPPOLI:X hyper bO.  En 1.
lae ABC; cohdicuimusigicys. ducx hyp erbgla gceram oxpolcam, quod TUCFAErC. m
I
PROEOSFTIO XXXI
la
Et A 21I
ABC, DFF opposicarum lectionum alae cranuersa AE.
L cenerum C actaque peri L. conringente Hlls qua C, l alrm
procisoccurrar in HI eI, Ponancurper l’e VI parallelae aamecto L,
quae DF. F hyperbolX OcCurranc in D _F, e pet C BONaCuL. Z C aqui
distans HII, deinde F.D occurrar alymproro lC in l. ae Pet L dlucacur
LMN aequidistans A F, occurrens IdiFtirperbola in L Paelo, Per.
quoc acta Ordinacim L. D Occurrar I. G in P. 1 ex quo AP. aequidistans
ponatur P RS: productae aueem P. P, DP, F l occurranc lincis CO, KN,
 e I: SidEBIL SBMBIL
ZiiI
13 1111 , 3318
Dico puncta illa esse ad hyperbolam
coniugicaip(I DEF, quam in X contim
Demonstratio.
eie
FIanE MK, CO lincis aequales N Y, S V. quo-
niam LG, KO, LG parallelogramma lune
quadracum YF ad quadracum YL, id es qua-
dearum F I adquadcacum YR, est vequadeacum
Z l adquadracum OR, id est Ont quadracum ad
quadrarum R O. sedrequadracum XF ad qua-
dearum YL, lic b AY F rectangulum cA ad rc-
crangulum A Y F. in F D, FD contingenti x-
quidittene, id est ZRM recrangulum ad re-
crangulum TLM id eA FKD rectansu-
tum ad recrangulum FOD, id est rectangu-
Ium Z. OX ad recrangulum Z. R X, quadracum
1395.9: 243 L. l. 513SAO eit 3IIEZBCI
idicur MO ad quadracum R O eA vereccangulum Z O Z ad rectangulum Z R X,
punccaisitur c, OM X ad lxperbolam lunc, cuius diamerer Z. X de ordinacim ap- c rbid
plicacae MO, Guibus cum aequidister Z L, erir ZId contingens ex quia diamerri d27. hn
AL, L. X, libi meclb parallelas bisecane, coniugacae sunc diameeri A F, L.X, et ini
DEF, OMX clecctehes quoque coniugata.
Corollarium primum.
cDeS.
dotitus.
Flnc patet concingelles per verrices diamerrorum coniusacarum ductas ly.
peorisoccurrer in vnO COdCHGUC pUnCTO.
Corollarium secundum.
X diccis quosu lequicur coniugatassecriones, communes habere alymPTOTOS.
lROCO51IIO LL
o
quilicum.
PR In XM O.
rEctiones comusala M AIBC DBS, GHI KLH Quatum ce
Derum O: Per uod ducta sic diameter BF, ad quam ordinatim appli.
lco
 u e a set ett e   t st e ete et      ita  et    esti ta  e a  t A     et t t   t    e
Sac A l.
CeTUL AC.