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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 58, page id 1815201908:0115
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=115
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.83
# 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.

1 .  p2 1 A 1BL 1
DROGRFSSTOHLS
212. Quin- exita verague ancecedens A C, ad vEramquE COHICHInEem BD, ve AB ad BC,
CD ad DE, cri veraque ancecedens BD, u CP veramque consequencem, ve
BC ad CD, id est re AB ad BC, hoc est re AC ad B D. Suncisicur AC, BD,
C P. in concinua analogi2. 9u0d fuir demomerandum.
ina ancecedens, ad rnam consequencie. Umilimodo quia BC ad CD, cA ve
5LL L
A B dinisa In C, Q D. VEFa
O AB a RC aMPIICaCa IB
eius, quam habet BD ad DC.
DICOAC, AD; AB.
Demonstratio.
BOnatuE A F, media incet A B,  AC, IBIEUE Eres etune continux quanticates
EAC, AF; AB. quare per primam hurus cric racio A B ad A F, eadem Cum ra-
tionc BF ad F C. led rario AB ad ACs cuplicara est rarionis AB ad AF., igi
tuE e racio AB ad AC duplicara cM Facionis B F ad F C. quare divla eAt C B
in e rediuila est eadem CB in D: ac plonte punctum D, vnum idem q. est cum pun-
DC ad CB
DS
elle in concinuaratione.
erunc quoque in concinvataracione AC, AD, AB. Ouod demonstrandum tuic.
A0 F. VndC Cum AINEErES ContinUX propOrrionaleS A C, A F, AB, ex constructione,
T 1O IV
si AB, AC, AD, Cine quancieates proportionales
O AD ad AB, racionem cius abele aupcaa, quamtra
de
atio.
Acio enim A D ad AB, duplicata est rationIS AD ad A C, sed per primam
huius ve AD ad AC, ita quoque eAt D C Alt L. B, lBItur rario A D ad AB du
plicata estrarionis DC aus. Guelelat demonttrandum.
e
LHE ETES CONLIHAX PTOPOECIO-
habet D ad L: ratio quoque B
ed etttd tadtitu d detto
Onales A, B, C; Sic aurem ratio
A ad B, criplicaca eius, quam
Dico D, E, F quancitates, in continua fore analogia.
aosoblo.
Vm eaeio A ad B, sc eadem cum ratione B ad C: ioicur eriati ratio B ad C
eriplicaca est rarionis D ad F. est aucem _ rario B ad C CX IHPPOMEIOHC CIHI
caca eius quam habet F ad F; igicur racio D ad F, est eadem cum rarione P ad F.
Suncisitur in continuaca proporcione O. L, li. Cuod demonltrandum tuit.
P R O
 a           u n  e pe a         mm