# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0372
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0372?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 315, page id 1815201908:0372
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=372
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000372.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

eH1
E L L T. PIS IS.
extra ellixum: ergo ille omnium inera elliplim, cangencium, mannus ell. LI dat 2
igicur ellips, e c. Quod crat faciendum.
Corollarium.
GHuus propontionis discurtu clare constac circulos omni inceruaste clepios
quodminus estincervallo. FA ellipum ipera concingere in puncto A. (CenErO
inCOr I _ A consticuro perringane vlque ad A. verricem axeos. Illi crenimcir-
culi concingent cum qui radio F A descripcus est, cogue minores crunciquare eriam
elliplm incra concinsene cuius axis AC.
PRODOSITIO CXXLV.
IIE AB C ellipleosaris maior A C e in illo poli D, E, RaEGUEVECD
Dad DA SICEF adF D, e DG ad GF.
Dico ex quonis puncto rectae FC circulos posse describi qui elliplim
incus in duobus punctis concinsane: cetiera vero illorum conlistere inter
F e C exclusis terminis.
Demonstratio.
Vmacur enim quoduis in FC recta punctum FI, ex ex
DH linea ducacur II B, breuissima illaru a guXe ex FT ad
peripheriam duci porerume; dein ex B ordinatim ad axem
POnatur BLR, X iunse FTK, TTB, pater per elementa
TIK iunctam aequari FIB, adeoque circulum cenero II
incernallo HIB descripeum eran(IrC Per R ee B: e cum
FIK, HIB linca sincbreuissimae per constructionem, pa-
tet circulum BD R, corum cadere inera ellipsim ac prO-
inde eam in B e K, punctis concingere. Duod aurem
cenera circulorum ellipsm in duobus punctis continsen-
cium consistancincer Fes C exclusis terminis, ex copa-
rec quod PA, GC linex breuistimae sine illarum qux Cx
F. X G, ad peripheriam duci porerune, adeoque circu-
li cenero F vel C, e inceruallo quouis maiore quam AC
F A vel CC deseripei ellipum secene: radiis vero F A
vel C. C deseripei omaximi sine, illorum qui ellipsimin-
cus in vno cantum puneto concingune.
EROPOSIIIO CX LXVI
Adem manence figura: propolicum sic in axe punctum delignare
squo cenrro circulus deleribatur, qui elliplim in daro puncto intus
Continsat.
Consttncoid e acthondetalto.
6. 134. hc
Ic dacumin peciphecia punctum B, pec quod l acta incelligaeur concingens, demIE-
cacur ex B linca BFI, normalis ad tangentem, occurrens axi in FT. ManiFeCUM CCEC YZL. hu-
Fipunctum lacistacere pericioni. nam cum c FIB linea breuissima sIc Carum qux Cx ius.
FIad peripheriam duci pollune, concinset circulus cenero FI inceruallo ILB de- dr3s. huius.
scripcus clliplimin d puncto B; isicuc, e c. Duoderac taciendum.