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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1030, page id 1815201908:1087
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.90
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NGVLA P ARABOLICA
rum communes incersecriones Cunt Bali rngulari sINE FCCLE AC, C D et
1030
Cam vngule F. FC. L, candeabete lalloem quam ongula ABC L ad
Demonstratio.
Scentum acA rnoulam A BCD ad vI
sutam EF CL quincuplicatam habere
racionent etus quam habec linca AFT ad P, C.
sed eriam prramis ABC D ad prramidem
CD quincuplicacam habecracione AFY
ad F. C. Quod sc demonstroeriangulum AB D
quodchemaximu coru b quae parabole inleri.
Bt Ponacae criangulum F F L, quod iremaxi-
mum est, eandem haberrationem, quam cpa-
rabola ABD ad B. F I. parabolam. sed dpara-
bola ABD ad R F. L, eriplicaca habecracio-
nE AHI ad F C. ergo e criangulum ABD ad
crians. P F.E, criplicaca habec rarione AIT ad
FC. Deinde BC alcicudo prramidis AD BC
est ad FC alcicudinem prramidis RFL C
VETTC ad G: C, hoc est ve quadracum A FTad
quadrarum P C, hoc est in duplicara racionis
ATI ad F. C. Ouare cum racio prramidum
ABD C, E FI C compolica lic ex racione ba-
Aum ABD, F FL, ec racione alcicudinum
BC, FC, perspicuum est eam esse quincupli-
cacam racionis AHI ad F. C, 2c proinde can-
dem cum rarione vrgularum quibus inlcris
buncur. Ouod cracpropolicum.
Corollarium.
Mnelcgurendua quoque ongularum quae supertune ablacis prramidibus in-
Lseripeis aux inclu(IS, inTeF SC CandE FATIONEM CONFIHUAEE qUX FeperTA CA InFEK
iptalmet rngulas aucprramides.
PR OPOSTTIO XCV.
lE AB axis parabole THLB, quae balisestrngule parabolicxe ABDII.
Facd aurem sectione per dae B, que alsignet in superticie cxlindri-
careeram BD ale bngulae, sIE F. D quarta PAESFCCTE BD, POnatur-
queplanum M E. C parallelum balI LB HI, cum plano LD HI sectionem co.
munem Faciens MC.
Dicolbaria BCad VS Clata AZL. D G, CAI HabEFC pFO.
porcionem quam crisinca duo adrnum.
CE, CL.
Dico prramidem ongulae ABCD in scripeam ad prramidem inclu-
EFC L bugulam.
Demon-