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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1059, page id 1815201908:1116
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la
LONOIDES PARABOLTCNM.
hormales erunc ad planum ABC,
acproinde per detinic. 3. vndec. nOr.
males ad AC. PEF PEZ
cdencet
RFG, BD IparabOlX TUnC _ aXCS
earu, E F, B D. AAF rCCtX F F Xqua-
dis BK, _ ordinatim ponaeur FIK
que crit parallela DI, cum sIc B D I
parabela; isicur vea BK ad BD, IId
est qualttacum FTK adD I quadei-
tum. quia similicer ABC parabola
est, rectanguluM BA F C ad AD C.
El, velinca F. F ad BD lineam, hoc est ex constructione ve B R ABD. Sednle-
ctangulum A F. C ad rectangulum A D C, ica quadrarum F. C ad quaat a D L. (C u
enim F C, DI sincnormales ad AC quadrara rectangulis sunexequalia.) IsICEFC
quadratum est ad quadracum D I, ve linca BR ad BD lincat, HOC eIER HL quala
cum ad D Iquadeatum. Igicur F C linea aequalis eA linex KHI. Scd _ linca R F X-
qualis est ex constructione recta B K, igitur sunc xquales ee similes parabola F L
ee BR FI. ex xquale habene lacus rectum quod axibus BRu L F MMCrIC. Lodem
discursu octendam quam libec aliam parabolam ant pal altetum aequalem cse ac simi
1059
22 parat
b47. Parab
lemparabola per axem. Omnes isicur parabole axi conoideos parallele sune x qua-
les acumiles, nc lacus  ECHBAADCHE COmMUnC. Quod erac de-
monstrandum.
PR OPOSITIO CXLIII
dei conoidisparabolici axem praebere.
Constructio e demonstratio.
Icconoides parabolicum AB C curs Daus H L. C. Invenro cenero balcos D, et
codem erisarurnormalirer ad planum baseos recta DB. DicoBD FOrC AXCM. AL
sumpeo enim quonis puncto I in linca DB, hacsectio F TC: FI quae aequidister bali
AF C. Deinde sccundum lincam BD sectio alcera Faciens communes Ccettones
FGDR, qua r6. vndecimi erunc parallelx. itaque IFI, TG, TF xquales sune, e simi-
licer DC, D F, D A: Sed eriam IE aequalis est IC, quemadmodum e K D aequalis
DE. Isitur quia DB secat omnes lincas in plano F C HI plano ba(cos A L. C. PA12s-
selas alam, axis eri con p C alS Gua P.
e   pe  i p t se it  e  t e tte  e e et   te te at est t t  et  ta   st  e   si   t t  et at       u 1    t e t     t pel 1