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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 847, page id 1815201908:0904
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=904
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

AC
ia
A PL A N V M
847
Dolam. FISH. Mlaperlineis A, F O (id Cs lineis F G que sune partes linearum AC)
aequales NYM, HP. cruncrurtum punctA MM, C PP ad Paaa. G_IL vCrO FTL
lince Equales Tunc AB, _ ITT ipAS AF xquates, sccla Llaguales lune rectis
A, CF. id eC Conltr. NM; ac proinde IIrecta, Cuspse spatum LL aeuares la
rectis MP, duplis MNI: igicur cum II lictea aistale MM MP, Vetati producane
Darabolam MP; eric TI, Parabola rircualis, cuius axis est linca FT, quam osten-
dimus supea veram esse parabolam.
PROPOSITIO CCXXIK
Virculum ABC Pecec recta pet Cset AC, d Altetaton per illud
AAL, e policis D F ordinacim ad diametrum AC. tancrectis AD.
aequales lincx D, E. G, _D, F. II.
Dico CHI esse paraboral Cullo lalus leclu el AB.
Demonstracto
andoquidem quadrac AD, est ad quadracum AD, in racione A F linex
Ladlincam AF. Cum GE F AC, rectansulum aquale AD, quadraco. quia verd
exelemencis constat AF ad AF, candem habereproporcionem, quam habcclinca
AF ad A F. Igicur quam racionem habebic quadeacum AD ad AD quadracum.
candem quoque recta A P. habebie ad rectaI AR: TUNE aUTeM F. G XqualeS Cx
constructione rectis A D. Igitur quam proporcionem HaBCFFCCTA AF 2d A F, rC.
ctam, candem quoque habebie F. G quadratum, ad quadratum FG; estigitur C
velHIHI Parabola. quod vero recca AB, aequalis sic lareri recto ciuldem, sic costabit:
rCEca AB est ex constructione linex B C, aqualissisicur B C: qua dratum ad P. C.
quadracum ealem habecracionem quam habet linca B A ad F A lincam: hoc eAt
quam habet BC, linea ad lincam P A. quociica paret B Cr, hoc est B A, esC latuS
reccum parabole O HT. Ouod exar demonstrandum.
EOPOSTTIO CCKKIV
NIc in ABC circuli perimetro astumprum quoduis punctum A, ex
 satoela ponaneur quorcunque AB delenles cculi ABC pe
rimeeroin BB punctis, per quae tecca ponaucut L. L, lIOrmales ad CD
siametrum circuli ABC3 Lncal LL, aguates pito B, de Mt Id
AC. ue diamerro lemicireu  ece AB lneIS In MM:
diametro DC bilariam dinisae: iunetâ deinde AC, describatur super
t
AAME
    es  pa s te te e e tat  t t   e  te   a e ete tit  st t  tte te te ei pe e te  tes ti s e e e e e us t  e e tu  t t    t. p e t t    t    et  r. 1