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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 330, page id 1815201908:0387
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=387
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.87
# 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.

EL LIP S+5.
DC, DdF divise Punc in F _ 
Dico L. P. C M puceta esse ad elliplim.
StO ABC ellipsis diameter gexuis AB, diuila vecunque in D: 8
ex D ad peripheriam recta AUCANEuF DC, DF qua proporrionali-
ter diuidantur in E ee C: dein AD diuidatur in L, e DB in M, ve
Demonstratio.
VCANEUF ex C de F ordinarim linex
CTT,F. Pad AB, diameerum quibus ex
E d C paraIICLA duICANEuF P R, GN ve
DC ad D E, siCD F ad GD, igIEUEDEC HI
ad F, K, AC F Iad CFNY, _ FK ad ON.
DE CTT ad FI: isitur ex quadratum RR
ad quadrarum CNV, VE C HI quadratum ad
quadracum FiT. Deinde, quoniam D I
CAad DN, VE DI ad DG; _ D A est
ad D L, VEDF ad D C, cric ve DI ad
DN, SiC D A aAD L, CrSO VEVnA AntCCCE
dens DI ad vnum consequens DN, (hoc
eAVEDF ad DC, hoc CAVED C ad DF.
hoc cstvE DFI ad D R) ita ambae antece.
denres, hoc est eora A I ad ambas conse-
ad coram DMI. Similicer inferemus L B CHCdd KM, vE DB ad DM. ErgoLBad
rectangulum ATB, e rectangusi ARB ad rectangulum ANTB, ex racionibus il.
lis aequalibus compolirx, exdem Crunc. Led rectangulum AIT B cA ad rectangulum
ATB, vequadratum C FI ad quaAcum FL, hoc cA per superius demonstrata ve
quadracum P K ad quaacum C NV. Ergorectangulum L. RM cA ad rectangulum
L. NM, vequadrac L.K ad quadrarum C HY. ergo puncta L, F, C. M lunc ad el.
PRC
10 CLXIIV
InE ABC clliplS areS AC, BD.
ductisque ex D semidiamerris
quibuluis DE, DE, AGAHEUEPCF F &
E linea IO, K H aequalesip(ISFD,
ED, Parallele verO axi AC, OcCur.
rentes axi BD in G _ II.
Dico puncta AIK esse ad elliplim
ODOSITLO CLX
quences, hoc est Eoram L. N. SimiliceF InFeremUS A FF cNC ad L K, ve D H ad DR
Vnde AI es ad L N, VE AEI ad DK, se permucando AT Cst 2d AFL, ve L. N ad
T K. Praecerca, quoniam cAve DF ad DC (hoc eAt. ve coc2 D B ad EOTaM DM)
sic ablaca DFY ad ablacam DN, crir ex reliqua IB ad reliquam NMI, VETOTA DB
NN, ve FTB ad KMI, permucando isicur ac inuerrendo HIB ad TB, VER M ad NH.
Cum igicur ostenderimasrariones AFI ad AI, X AR ad A N, icem raciones HB
2d TB, _ KM ad NM caldem esse, rariones quoque rectanguli AFTB ad
t LXIS.
Demonstratio
Der AC ve diametro describatur cil
culus AL C, _ DF, DF linea verim
que producaneur donec circuls pelaett
lipum. Duod erac demonstrandum.
oiteu  seu e e e  te t qes tet te te e t  e te s e e t ete e it eat et eta  e e te ite ta   e  e  tte tit e e   e e es   ei   t e e e   e e e t e  e     a    e