# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0238
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0238?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 181, page id 1815201908:0238
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=238
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000238.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.85
# 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.

et
EC
bu
cen
CCUIIE
iament
ItaB
icuei
RI
XVI.
iM ct
nA;
dia
F.
CIR CVF VS
Demonstrario.
VAaTAFUMENIM A C, ad AD quadratum est
E AB rectangulum ad rectagulum ITAB
elemenca: hoc estve C A linca a ad lincam
LLL. lcd ve C A ad FIA, Sc C+ AI rectangulum
dd rectangulum IT AI, id est quadracum A F,
ad AF quadratum; ergo ve quadratum AC, 2d
AD quadracum, ica es A F quadrarum ad qua-
deacum AF, quare ve A C linea ad AD lincam,
ita AI, 2d A F. Ouod erar demonstrandum.
PRO POSITIO XIX
InE ContInuX proportionales AB, AC, AD, diamerri circulorum
leincus in eodem punctocontingentium, crectaque ex B normalit
Ter BO occurrence perimeeris in HI de G, iungANEUE AG, AFI.
Dico AB, AHI, AC, esse in continuaanalogia.
Demonstratio.
VnCeNIM IN CONCIMUAEA TaTIONC AB, ATI, AC.
veluri eriam AB, ACi, AD per elemenca.
quare AC media cA incer AB, AD; Ced exhy-
Pocheli ipla quoq; AC media ponitur incer AB.
AD. Igicur AC, A C linex (unc aequales; adc0-
que in concinua lunc rarione AB; AHI, AO.
Ouod tuic demonstrandum.
eROPOSITIO XX.
Ldurta fueric dtAMIELET AB in COTIHUC PFOPOHIONAleSAC, AD, AF,
DAL, _c. Potlamurque normalirer ad diametru, _HI, EI, FL.
Dicoinetas LFB, AHI, AI, AK, in continua quoque ccanalogia.
Demonseratio.
Vncenim quadrata AC, AH, AI, AR intex sC vE
rectat ta B AC, B A D, BAF, B AF VE ex cle-
Henas pater; se d rectangula ilIa sUINE VE A C, A D, AF.
AF; igituE e quadEATA AC, AHI, AL, AK CunC
vElineX AC, AD, A B, AF: quae cumponantur con-
einux proportionales, patet e quadrata AC, AII
a AR. adeoque de lineas, in continua essc 2
Bia. Ouod crat demonstrandum.
eR. O POSIIIO XXI.
Veenicuio ABC recta collocara lic BB perpendiculatis ad ala-
metrum AC, qua dinila bitariam in HI: centro HI, inceruallo HTB, de-
Ecriba