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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 335, page id 1815201908:0392
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.83
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sene
de
+61
O
EL LIP(STS.
P R O POST F TOLC VIXIXLV di
TIrculum AB C cuius diamerri (c decullant ad recos, Contingat
sin B linca B F: dein per A e C puncta essiplis actloatur contin-
gensB F lineam in E, cuius una c diametris sic AC. intC L D, auca-
TUE Ex A SCCANS AL, X per FagacUT F FT; paFaIlela BF, OCCUTTCHS CIAPIE
in I. Tum per A X l ducaehir recta AI. eoncinsac aurem circulum recta
MIN in MI, parallela Secanti AF, _ ox M ducacur HI O, parallela tansen-
ei BE, occurrens ellipsiin P; Ponacurq; pex P, recex B F. a quidittans P R,
secans F H lineam in R VI
Dico PR lineam, concingere ellipsim in P.
Demonstratio
 ∞BIS
PFCanCeS A E A TipISD BDR
Doccurrane in G e L. Deinde  cui
FFI OcCuErAE ipE BC in T)5 ex
cangenci in N, _ rOCtADP. In R.
SIMILIECE NIO OCCUEEAE ipA AF
in V, _C AL in S, _ D F in O.
de CD in X. Omniam ACD,
AL D criangula, candem habenE
basim AD, SIINEqVC FT, KI
requales, crunceriangulab AC D.
AL. D incer caldem parallelaS.
ste
Rursum cum MO lincaxequidister FK, crune V X, S Mhex aequales; clt vero
d MX icerum c ipA P O aqualis; ergo e reliqua M V relique H S aequalis est: cClavins
ledrectae MV aequatur linea N F, et PS, est aequalis RI, isicur _ N F, R I lincC ad 40. 1.
sunc incer se aequales: CA vero _ FT ipsI RI aqualis, isicur NY, RR aquales
TunE. Sed, quia MIN cans enS CadicEOTa exera circulum, N P maior est quam FT.
hocest quam R I. ergo _ R R maior est quam R I. erso punctum R, cadic exera
ellipsm. eodem modo sicam suBra quam InEra MO, ParaIIC lE du caneur quorcuque.
octendentur omnia puncta rectae PR, cadere exera ellipum precer punctum P, re-
cta ixitur PR, tanget elliplim. Ouoderat demonstrandum.
P R O. POSITIO CLZZV.
Sco ABC ellipsisaris AC vecunque productus in D, ductaqu ex D
slinea D B, quae ellipsim contingat in B PonatuT SCCanS AlECTADF, Oc
currens ellipliin E. X F: demissis deinde F. F ex B, B, FnormalibusF C, BIL,
F. I ad axem AC; IUNGANEUF F HI, FTI.
DicOFOH, E. LHL criansula esse limilia.
Demonstratio.
aryrtuius
ponstra
AR C, occurrens rectis FC, BII, F Lin
RP MI, duCANEUFAUTeM FeCtR MIFT, KTI.
FFI, FHI: Cum isieuE SE d ve F C+ ad F I
(hoc est ve GD ad ID,) SIC RG ad MI,
DATCE MK productam convenire in D: est
aucemC D I contingens, igIEuF TIRO.
FTMT criangula Similia TUnC. quare vE
RC ad MT, sic HO ad HTT: led est ve
RG adNL, AIC F G ad FL, igItUFVE FO
2d P. P, Sic H C est ad F L: lunc aurem an.
pec e mantecio ceterau eucus