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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1067, page id 1815201908:1124
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CONOTDES BARABOLTOTM.
criplus est, conoides rerd ciuldem selquialcer. igieur l contus Pertacue, L. CHCCOnOI
desq. cslindrus aurem 6. F. X quo PATeC propOlicum.
PROPOSITIO CLV
Ionoidi AB C inscribatur quicun-
sque cxlindrus DOHIF.
Oporteat rationem conoidis ad cy-
lindrum in(cripcum nocum Facere.
Demonstratio.
Scensum est cylindrum cui conoidesin-
scribitur, duplu esse conoideos infcripri
lgicur racio cylindri super bali AIC, ee alci-
rudinc R B ad cylindru, cuius basIs CA D OFI.
de alcicudo FHI. dupla a est eius quaim habce
ratio conoideos ABC ad cundem crlindrum
inlcriptum; noca igitur est racio conoidis ad
inscripcum exlindrum, cum noca sicracio cu-
iusuis eylindri ad quemuis exlindrum.
PROPOSITIO CLIX.
IE conoides AB C cylindro ADCF.
Dinscripeum, _ plano F HIG POLIEO,
quod aequidistet basi AD C, AaC Cy-
lindrus FHOI, continens conoides
FBC, e haclectio AB C per commu-
DEM AXCIM.
Dico cylindrum ADCF ad c
drum FHCL habere quadruplicatan
rationem AC ad C+ F lincam.
Demonstratio.
1067
cylindrum AD C F. ad cylindrum F FTGF
quadruplicacam quoque habere rationem eius quat  C AabeC dd LC.
xiindrus enim ADCF 2d FHIGT, r2.
tionem habet composicam exbal ADC
ad Balm FFT C, guxe duplicaca est racionis
AC 2d FO, e ex racione alcicudinis C P. ad
OI hoc eAt R B ad BL, que est paricer du-lA
plicara b rarionis AC ad FC, cum sectio
per BK, axem conoidis exhibeat parabolam
ABC. unde cum racio BR ad BL, ducta in
racionem dupticaram AC adG F, producar
quadruplicatam A C ad CF, manifectum Ac
1a
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