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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 629, page id 1815201908:0686
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=686
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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 0.78
# 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.

pun.
1
alleta
CDCO.
mpTO.
sulum
CCTIo.
CCTID.
C.
VI.
Demt.
Coni
qui
ecris
in
malIS
inD,
reuli
AIP.
ana
Fb
1
1
2
2d
Vi
1a
l
WIHIIIIII
AYP ER BOL
eRODOSITIO CLXXXVI
Lin cuiuscunque sectionis diametre ptoCa, Pucuuur aumatur,
ctuum puncta:
Dico in parabola parre diametri a verrice eiuldem _ contingente inFer-
ee ab illo ad sectionem concusemes a, uG aCHIq; CoACa-
iungenre incercipicur linea. empaeMalorem, inhyperbolami-
ceptam xequalem esse illi, quae ab ciuldem vertice e linea contactus con-
ROreMI.
est au
Demonsrato.
IE A B C conus, sectuS erianouIO peFareM A B C, diameter aurem BAlEoS AOB
SE A B in qua assumpeo quonis puncto R; ponacur B ET aquidictans AC, X F I
normalis ad AB, cum per FIE, e PB, hac sectio exhibens in superticie conilineam
CFTT: Cric illa parabola: ponatur exinde axis coni C D, pertciaturque parallelo-aL. Depa
Srammum CDB, cuius laceri BMI OCCUEraE FFY producta in F, iunctaque C F, dia- rabola
MCErO AF prorractae occurrat in K. ponatur aurem per P concingens circulum
AlB in l: convemer illa cum AR. CR MMeisin K, vripropolrZ. de pacabola
octendi: vicerius, h lecundum TK e per C relccem coni, planum incellioaeur du-
ci, continger illud superticiem coni secundum lineam CI: vei propolic. 17. de para-
bola oltendi: eadem quoque propolicione oltemum est iunctam IF, parabolam in
lcontingero, e L. II, IIF lincas elle aequalesiquod etac primum.
Rursum inEeF F _ R in F K linea punctum Matur quodcunque G; iunctilq;
F, C, TC secundum YF, F. C liire as pranaasacur, exhibens in coni superticie li-
neam L. I: Crit YF L bellipES; oporter aurem ostendere TC, eandem contingere br. vol2
In  _ CL maiorem esse L P. Ponacur per L linea FN, ae quidictans BC in pI2- De cllipsa
cum L C maior sic PN, recta quoque L C maior est P. F. deinde cum verumque parabola
Pranum CTK. in sed CLe Colteltisic luperticiem coni, ec F IP elliplis in vnocan- c Ibid.
cu puncto occurrie C I linex Mmirum in L. planum CTK, in Ladcoque e OY
linea invno cahe picto occurrit ellipsi, adeoque in P concingit. Ouo crac se.
nO ErIaNgULI pEF AXEM OCCUEEeNS F G, linex in NT: quoniam igicur punctum +
TUMIEUT INECE F _ R, Eper C, recta incelligacur duci, paraIlela CB, cadecc illa CEX ele-
vlera F N, adeoque i punctum incer C_ L est: quia vero F NI, IT L aequidistane mentis.
_e dPFI, TIF ostensa sunc aequaleS, reatxe F P, L N quoque ae quales TUNE: Quare + 17. D
punctum I e G, in plano lic CTK, recta FC in eodem existic plano: quia vero
cundum.
ue LL Ll haclecundum L. L. P. P lineas planum YF. O: Paret IFO esse hyper-
bolam
Sumatur denigue inter C _ F, in CF linea punctum quodcumque P; iunctis-