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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1022, page id 1815201908:1079
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ENCVLA PAR ABOZ TCA.
Demonstratio.
Enero R, spacio FT, describacur semicireulus, ouia axis FK Xquaeur lacerire.
at0, erit YIR equalis K F. unde semicirculus cransibit per F, ec C. Super hoc
Temicirculo rebasi incelligacur heri rngula FFTIO, a Cylindro recto abscista guX
Si. Buins. alcicudinem parem habeac diametro baseos F G: productaque M L in O, sCCCTUE
ingula planO peF MCO ducto. ORensum enim a CA PArECM VnSULArEM FFLOMN
ad reliduam, eam racionem obcinere quam parahola F FL. M tegmentum, ad par-
677. huius. cem L MC: Sed ve vngulae pars ad vsulx parrem, ica quoque sesmencum b spHXrX
2d sphaeex Cegmencum; isicur eam Cortiuneur parces sphaerx incer se rationem quam
parcesparabolx habenrincer (c. Duod tur demonstrandum.
PRODOSITIO LXZXIV.
Zhis alicer quam Archimedes prox. 4. lib. 2. de sphaera e cylindro
lpheram lecundum datam rarionem diuidemus, hunc in modum.
DArabolam F FTC, cuius axis HIR, par Ordinatim POSIEX FR, per dIAMeTrOM M L.
seca in dara ratione: reque secta FC in M, ica axem sphaera seca in F. planum
ductum per F rectum adaxem, sphaeram secundum dacam rationem parcieeur; ve
pacet ex propolicione iam demonstrata.
PROPOSITTO LXXXV.
exlindrus parabolicus, (cuius axis F P, balis parabola ABC, at1
Labaleos BF, ordinarim ad axem potITa AF. C,) Secetur planO per
AC, exhibence in exlindri superticie lincam ACD.
Dicolincam AC D esc parabolam.
Demon-