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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 760, page id 1815201908:0817
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.89
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TVS FL AN.
eROPOSTTIO EZZVIII.
960
ABC: Paret per ea quae in lib. de patabola ostendi, C. C eNe ad parabolam.
BF ad B A
Dico C D planum ductum
in planum BF. xquale corpuS
proterreilliquod oritur exdu-
ctu BC in F. A.
Demonstratio.
Veancur infinice parallelae BC
DF. A. Duoniam DBE rC.
etangula aqualia ponuntur rectan-
gulis ABC, eA vE BC adBD, EC
dendem BCAd C. D, sicBF. 2d F A; rectangula igicuTBC P A
ae qualia sunc rectansulis CDB P. quare BC planum ductum in planum B. A ae qua.
cur CD dudo in BP. Ouod fuic demonstrandum.
eROPOSITIO LXXIX.
TTeicerutm AB rectangulo in scripeus circulus DE, ita vE AD, BF linex
cinc requales e circulus eandem habeat cum recransulo alcicudinem;
hane aurem proxortionales AB, AF, F F, _ FD rectis aequales IE F.
Dicoplanumi AP duccum in le, xquale corpus proterre illi quod ori-
FDF Cx F D ducto in DK.
Demonsirat.
Seo AB rectansulum, intra quod circulusponatur D E candemha-
bens alticudinem, dein D B P rectangulis a qualia tianc rectangula
Voniam AB, AP, F. F, proporrionalestuIII, MLD ad ILL. prima ad secundam
Lhocest exhyporhesive AP ad P F, SIC P B   I POTheS AD excestu
quancur, recrangulo F. D K. planum ipicur A F ductum in sciplum CA _e quale plano
ED duceo in planum D R. Quo dtuir demonstrandum.
ad excessum A F. ergO COnNerEendO DE P A ad F A, sic D A ad F D: dividendo;
igicur re F dd LA, IC LA al L . Guare lestam Proporonaes L. L, lHC
s AF quadracum equale recrangulo F F D, id est, quia exhryporhesi FD, RP X