# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0114
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0114?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 57, page id 1815201908:0114
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=114
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000114.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.
# 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.

PROGRPSSIONV COMLTAEBARVM
A
Procreptones constacrat indeterminatas.
PROPOSFTIO PRIMA.
Ontinuc proporcionalium diferentix sunc in continua analo-
duldem racionis luorum intesrorum
Anemasnirudines continuae proxortionales AG, BG, C, EC
C. Ollendendum est AB, BC, CD, DF, F. F differencias in conti
nua elle analogia luorum inccororum; e concra (IAB, BC, CD, 8C. Fue-
rinc continux, e F C addatur ve AC, BC, AB, BC sint proportionales;
DicO _ AG, BC, CC, ec. essein concinua analogia.
Demonstratio.
e
roniam AC est ad BG, ve BG ad CO: eric diuidendo ve AB ad BC, sC
LBC ad CC: ee permurando AB 2d, BC, ve B C ad C C, (AuC (VE A C+ ad
BO. Similiret B C elt ad CG, ve CG ad DC: _ dividendo B C ad CG VECD
ad D C e permucando B C es ad CD, Ve CC ad DG, id cAt ve BC ad C 6,
id est vE A C ad B G. aEqUi CFAE VE A C ad B C SC AB ad BC, ergo BC est ad
CD vE AB ad BC. Conrinuxe lunc igitur proporrionales AB, BC. CD, ex qui-
dem in analosla luorum incesrorum AG, BC. Simili ratione oltendam reliquas
cum histribus esse concinuas: quod erac primum.
Sinc iam AB, BC, CD, ecc. Concinux, quibus ad dica sE FG, SIC DE A C Sic 2d
BC DE AB ad BC. DicoOmneS AC, BC, CC, DC, dc. esle in concinuranalo-
sia differentiorum. Duia ve AB ad BC, SiC AC ad B C, ergo permutando ex di-
videndo, _e rursum permucando ve A B ad BC; hoc est ex daris ve AC ad BG, SIC
BC ad C C. quoniam aucem iam B C est 2d CD, ve A G ad B G, hoc est ex da-
eis vE AB ad BC, hoc est rursum ex daris ve B C ad CD, eodem plane discurtu
osendemus B C C Cs D C ese concinnas, ex quidem in rarione BC ad CD, hoC
est AB ad B C. Juare cum eriam AC, B C. CD Unc in eadem rarione concinux,
OmNeS QUAEUOE A C, BC+, C Ci, D Ci crune in racione AH ad B C continux. Simi-
lirer ollendemus ex reliquas cumildem esse concinurs. P’acetisicur rericas propoli-
ionis.
PROFOSL1O 1I.
quatuor Fuerine quanticares in continuata analogia, cruneaggregaca
exprimaceccunad, ex secunda d Ferria, ex cerria e quarra, in conet
nuaproporrione.
Demonstra
Vneo quaruor in coninua analosia AB, BC, CD, DP. DIcOCTiaM AC, B D,
DCF, CNC concinue proxorcionales. cum enim sic ve AB ad BC, ita BC ad C D,
ei