# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0353
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0353?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 296, page id 1815201908:0353
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=353
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000353.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 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.

L. L. IPSIS.
R O POSITIOC
Ine AB, B C diamerri conius Alx inxquales, et ex A recta guauis
ducatur AD Sccans elliplim  D; cui ex C porallela ducatur C F
Demonstratio.
DRimo cadane parallelx ad eandeni partem ellip (eos: Du-
cancur rectx linex P. A; D C. Ouoniam AD, F. C linca
Sibimucuo aequidistanE, CruINC = lEGIENEA P AS D C in-
cer se aequalia, adeoqueb AB F; DB C sectores aquales.
addito igicur communi ABD; crunt F BD; ABC sC
ctores incer se aequales. quare cum virius sectoris larera
B A, B C sincdiameeri coniusacx, cciam alcerius laFeTA F B,
BD sunc coniugacX
Sccundo cadant AD, CF parallelae ad parres elliptis
opposicas: producancur semidiametri AB, D B in HI e
T iunganturque puncta HIT. Ouoniam AB; BC TUnECOn-
ugaca eric csectot A B C quarca pars elliplcos, led AFI dia.
merro dbisecar elliplim, adeoque porrio ACII, dimi
eium est ellipscos. Freo AB C sector dimidius est lemi
ellipseos AC FT. ac proinde aequalis sectori C BII. quie
durem YFT per rg: huius est parallela ad D A. cui exhy-
Pocheheciam C P est Parallela, crune IFI. C P incer (o
Parallele. ergo setimenta c CI, F FI adcoque de lecto.
resFC B I, (sB F. xquancuriaddico isicur communi LBH.
sector IBF aequalis est sectori C. B FI, hoc est, re iam
ance octendi, sectori AB C. quare cum sector ABCS AF
quarca pars ellipleos, sive dimidium lemiellipleos; eriam
sector PB F erir dimidium semiellipleos, hoc est portionis
TF D, quam esse semielliphim pacec ex C oroll. a5. huius.
Eroosector TBF hoc est lector ABC eqvalis elt lecto-
ri EBD. Duare cum AB, BC sinc coniusatae, ctam
DB, E B erunc coniugaca.
Sintiam AB, C B, icem, F B, DB diamerri coniugata iunganEUrGUE AD, F. C.
dico AD, P C lineas ese parallelas. Sin vero; ducacur ex A ipA F C paraHlela AF
innoancurque F B: cricisitur IB diameter consupara ipli F P persecundam pais
cemhuius: Ccd DB per constructionem coniugara est diamecro F B, ergo cidem FB
plures diamerri unc coniusarx. Quod herinon porest. isirur AF non a quidistacipu
P. C. idem ostenditur de quauis alia. ergo AD sola parallela eAt recta F. C. Quod
crac demonstrandum.
eR0P051I1O Ct
le in AD C empCasasCetum B guauis diamectorum Contugalio
AB, BC: iunetisque punctis AC, lecer AC lineam in L Mlaierer
quaecunque BD, cui coniugata ducatur BF, ductâque linca FD secet
AB diamerrum vecunque in 6.
divilas.
LUNGANEUFE C B, DB.
5I. huit
huin
C46. huius
1Coroll. 45.
huius
BicO E B, DB diametros eAc conivsardS _ CONETA.
Dico AC, FD lineas, vei ec BD, AB in F. et C proporcionalicer esse
Demon-
o