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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 346, page id 1815201908:0403
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=403
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.83
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40
P R OPOSITIO OXCILI
EL L. IDStS
Dicotucus AC ABF in C d II, limilicer diultas ehe.
Demonstratio.
NIE CemiellipAS AB C CUTAS ALIS IIL RC, LCLIILHICOTOS AUILCMI DEE.
Temiellipsi A B C aqualis po; MMICrBANEE cn lemiellipsi
de Pemicireulo criangula ABC, DLF intet IC a GUaIIA. IL CAD _ F, nOr.
males ad balim demicraneur BG, F FI.
ipsum P. A: led requadrarum L. I ad quadrarum BG, ita est rectangulum AIC
ad rectangulum AC C: ex re quadtacum MK a F FI, quadracum, ita CA DRP
rectangulum ad rectangulum DHF, ergo ve AI quadracum ad rectangulum
AC C, ica est quadrarum D R ad rectangulum D HF: e permurando ve qua-
deacum AY ad ipsum DK quadratum, sive ve quadracum AC ad DF ira cRFC-
atangulum ACC ad rectangulum DFTF, constacipirur ex Sereni l. L. prOP. 12. li-
neaS AC, D F in C e H, proporcionalicer esse divilas. Ovod erac demonlteandum.
PROPOSITIO CZCIV.
FCenE A BC elliplim diametri guxuis coniugate AC, BD iunctis
punctis AB, C B, diuidantur AB, C B linca bitariam in F e C: du
CANTUTGS ex P. CenerOlinCK P F, P. G: dein tam pet
puncta AEB, quam C F B ellipses describantur
quarui coniugaca sinc diametri A B, E. F, C B, F. 61
Dico ABC elliplim aqualem esse duabus cel.
ipsIbuS AEB, C EB.
ik Cenris T eC K, ad diaMCerOS AC, D FnormaleS CriBANEOFTL, RM iungAn
Lxurg; AC, F C, _ DM, MF: quoniam semiellipss ABC semicirculO DMF
aqualis eA, crun de maxima criangula illis inscripea nem pe AI C, DM F incer (0
190. hu. xqualia 5 a erie ixicur ve criangulum AI. C, ad criangulum ABC id cA vi
bea
ed
FI ad B C, ica criangulum DM F 2d criangulum DF F, id est ica linCA NTK ad
F FI, adeoque re quadracum I. I ad BC quadtacum, ita eric quadratum MK ad
cCorol. 191.
isus.
Etbns dbtbo
Voniam eam ABFF, CR L.G, HC BF Blameert
LIUNECONIUGREX, CrUNEB ABC, AF, B, C F. B ctiangu
la maxima que suis semiellipsibus inscribi postune: est
aurem AB C criangulum duplum crianouli CF B, igi
rur ex cllipsis ABC c dupla est ellipsis C F. B. Similiret
osendamelliplm ABC, auplatu ellC elliplIS B L. A. 2.
GLanEUE
qu et et eui uepues et e t et pt t t es te e  Me   t s tit at uet e e e e  ti e st   st te e  e  e    u ete   et tu e te e  e  a  pe ste  si stu