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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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Dcct.
teM
SPYR A L +8
Demonstratio.
Vcacur diameTer AK, et CI, F K ad diamé.
erum ordinacim applicarx. Ouoniamigieurper
24. Acchim. de quad. parab. parabola D AK, C AV
selquicerciae sunc criangulorum D AR, C AI. Para-
bola est ad parabolam re criangulum ad criangu.
lum, hioc est, cocum cs ad corum re ablacum ad ab-
lacum. Erso reliquum lesmentum DC A est ad
reliquum lesmencum CC A, ve corum ad eorum
sive ablacum ad ablatum. sed (ve demonstrac C la=
ujus ex Commandino id 23. 6.) provorrio ablaci
crianguli D AK ad ablacum criansulum C AI
componitur ex proporcionibus D K ad CI, _ K A
2d TA, hioc est ex duplicara racionis DK ad C I
Per 20. I. Conicorum. Ergo proporcio scgmenci
DE A adscemencum C C A componicur ex proporrionibus DR 2d C l, _ au
plicacaracionis DK ad C I. Ergo proporcio sermenri DC A ad segmencum CC A
eriplicaca estracionis DK ad C T, hoc est racionis B A ad F A, vel D A ad F A.
Firco proporrio semenri DC A ad sesmentum C C A eadem est qua cubi B A ad
cubum F. A, alirer aurem plecaque in libro de pacabola demonstrara invenies, (cd
noluimeis demonstracionibus propoliciones Archimedaas concinsere.
Conveniune isicur eriam in hiac cam eximin propriecare spiralis et parabola.
Duoderat demonstrandum.
Scholion.
Actenus parabola applicanimus quiaquid nosaru dignum de siralibus vel Archimenes
Lvet Pappus demonstrauis. F.L quidem ista sufficiebant vr me promissione mea ex soluisse vi-
deri possem. Sed cum non exiruum similicudinis campum superesse viderem; statui alias non
nullas parabola proprictates vicissim Birali applicare; omnino tamen pauea e multis; ne dum
appendix excrescis in librum, prolixitas lectori molestiam afferas.
PROPOSITIO ZIX.
Cresia es parabola proprietas
quam prop. 5. de quadratura pa-
rabole Archimedes demonstrac, nolq
in hoc libro non semel cicauimus. Pa-
Fabolam TanGAE A D, e Secet diametet
cius D B, iungaturqVe AB. DuCanEUT
deinde quoruis F C F parallele diame
ETO. EFIE PErPCTUO AE ad EB, VEFC
ad C B.
Verum, quod Archimedes alL H
elexic autno aduercic, eadem proprie-
eas reperitur exera parabolam. Nam (I
producatur AB ducancurque diame.
ero parallele FF. C, Temper A F est ad
E B VE FC ad CF.
Demonstratio.
ia Aan punctorum Cdlatut aC.
cui DB OCCUETAEIn C. F P eAt ad FE. C, vF
a  e ete se ee are ro oo a setion