# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0364
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0364?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 307, page id 1815201908:0364
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=364
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000364.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.86
# 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.

el
pat
LL Y
Voniam eam P. B linea aequidistac
recta AD quam P C+ 2 ipA BD,
CTUNE F, C, BD lincae xquales: CA
aurem AC,C rectangulum aquale
quadrato B C, quodrecta FC ducta
sic ad diametrum circuli norma-
lis; isicur ex quadraco BD aequale est
rectangulum ACC. eodem modo
est F EI quadrato, hoc eA quadraro BD aequale rectangulum AHIC. led BV
quadratum estx quale quarex parci hgurx, igicur cam A C C quam ATIC rectan-
sulum est aquale quarre parri fisurx. Ouod erar demonstrandum.
Corollarium.
INCPATCE AC HTC lineas eNe aequales de G HI bitariam ese divisam in D.
PROPOSITTOCXXI
Idem posicis ducancur rectxe BC, BFI.
Dico BC, B HLlincas limul sum pras axi A C este xquales.
Demonstratio.
Voniam aqualeS sunE B A G, FF C, quadratum A C Xquacur rectangulO ex AC
L_ TIC. Icerum quia aequales lune GD, DII, aquabitur rectangulum AC DvCoroIl.
bislumprum rectangulo A G FT. Ouare cum cquadracum AD aequa le sE quadra- n2o huimii
eis DC, AC de rectangulo AC D bis, idem quadracum A D aequabitur quadracoc+. secundi.
DO _ rectangulo ex AC, HIC rna cum rectangulo AOFI. Acqui rectanoula
AC, HIC, e ACFhAxquantur rectangulo AC, C. Ergo quadracum AD aequate
est quadraro D C una cum rectangulo AC C; hoc cAt quadraris D O CF F, hoc est d r. sceunat:
quadratis DC, DB. Sediildem aquacur quadracum CB, equancur ixicur quadraca
AD, GB, ac proinde rectae AD, C+ B xqualessunc. Fodem modo detmonstrabitur
rectas CD, HIB aquales esse. Ambe igieur CB, B HE Cimul sumpex axi lunc x qua-
1es. Quoderac demonstrandum.
Corollarium.
Tincsequicur: A ABC cllipsis axeS Fuerine A C, BD, d ex B vertice minoris mmii..1
LPaxis rectae dimictaneur BC, BFI, aequales lineis AD, D C, lCCanTeS aXem AC
in C e H. Ouodcam AC, C quam AHIC rectangulum, aequale s quarea parri
tixurae. adeo que C e H lectionis poli sune.
k01031I1O CXXII.
Demonstratio.
plm ABC, cuius
sclanet Comzala
C, DE contingane in A
e C; e alio puncto quo-
uiSBTreslinCX AF, CO,
F6: _ FC Quidem Oc-
CUITTAE AF, C C rectis in
F e C. productacue E D L
occurrat FC linex in l, 8
ex B, recta demirtatur BHI ordinarim ad A C diametrumm.
42
Dico