# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0492
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0492?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 435, page id 1815201908:0492
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=492
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000492.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.84
# 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.

C
eri.
M
PI
MM
2d
e
at
P A R ABC
erac democutatdum.
quoque est rectangulo C KHI. L C K, F K. H R dnex inconrinua analogia. Ouod
PROPOSITIO CEXVIIL
Sto ABC Dparallelosrammum; delcHIpCaG; DEF A d C, parabol
scuius dianerer A D, ee concinsens AB, dclevatur d alicta pet
B _ D, cuius diamecet sic BC _ concingeits D. Occutrat AueM para-
bolae AFC in F. deimdeper A, E, C puncta cerria de Ccribatur parabola
communeshrabens Cum aliis aiaecros.
Dicoiunctas AC, BB, parabolam AF. C conlhetei AaC.
Demonstratio.
quadracum ad quactacum AB: lunc au-
adquadracum AB, H AI quadracu ad
xqualia lunc, e linca AB dupla A F, vei
A D dupIa F C: quaEC E F etiam AC
lineae occurrie in C puncto, quobitariam a DB, alcera paralleloorammi dia-
meeroO seCaTUE. Rurlum quia AB quadratum quadruplum est quadrati FB, crie
_ BC linca, quadrupla linex F Fs est aucem AD id est BC, ostensa dupla FC
igicur F C dupla est F L, X F F, F. C linex aequales. vnde BD linea a est concin:
sens; limilicer oltendicur A C lincam, parabolam AF. B concingerc. OuOd CTAE
Corollarium.
Tinepatet AO, B DIincas, I Mo puncto se incersceare, vbi P C est Xqu alIS FE-
Ax F P: quod singularim ec explicire annocare verbo placuie.
PR OP OSITIO CLXIX.
Ildem postis. Molcet E punctum incerlectionis exhibera
Constructio e3 demonstratio.
GaCUE PEF F, diaMCTCE P F sCCAHS
LDB lineam In G. VE F F ad AD, AC
FB quadratum ad= quadrarum AB, d
VE FF linca, ad lineam BC, sC AF,
cem AD, BC linea per hypochelim
xquales, isicur ec FB quadracum est
quadracu A B: guadFAFA IBICHE AF. FB
demonstrandum.
Tuisa AB bitariam in F, deMIETATUE ex F diameEeF F R, dequaliS QUAEEE ParEI
Iinex BC: dico F, erminume F F, delignare punctum incerlectionis. Sic
enim P punctum interlectionis indelcum _ per R dinmerer agaTUFF. Fi, CrIE B F, ve
in pracedenei propolitione ocessamus, aequalis quareae parri linex BC; isitur per
compolicionemcum PP Mlameter decur ae qualis quarrae parri linex BC, PacCE F.
punctum esse incersectionis, Xc. Ouoderar exhibendum.
LKOTOSIIIOBUZE
IIdem policis ducacur quaeuis diameter tL L Pecans parabolas in H, L, M.
Dico tt, tit. ttMlitend i concinua este analosia.
Demon.