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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1058, page id 1815201908:1115
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1056
arS ondec. rectam O PD. exie denuo DF R O circuES, ex quia 2 D R parallela est ad TF, ac rectd
Ostl. 3.
CON OTDES PAR ABOLTCVH.
Duare sectio DF R F ellipa CH. Quod crardemonstrandum.
ROrOSIII CALI
Mnis sectio ari conoidis palabolici equidistans patabolam exhibet.
Demonstrario.
Seo conoideos ABC, cuius axis BD, Cectio
F F C aquidistans B D. Dico sectiOneM PFC
esse parabolam. apacur per axem BD planum
CB A, quod rectum sic ad sectionem B F C, CX-
hubens communem incersectionem F F. Deinde
agacur aliud planum FT R L quod aequidister bas
AGC, cuius communis intersectio cum plano
F F G sic linea TK, linea vero FC sic communis
eiusdem incerleccio cum plano A C: C. Duoniam
plano ABC, Plana P FC, de FIK L orrtiogonali
Ter inACUnE, eriE RI communis corum sectiOCTC.
Cta plano ABC. Similicer _ FC Fecta est plano
ABC. ergo rectangulum TIIL aequale cA qua
dratoIK; _e rectangulum AF C quadraco FC
est aegualc. quia vero eciam AB C planum per
axem BD Policum cA, parabola CcA. ABC secrio
demonstracum vero eAtlibro de parabola  quod
cectangulum quoque HITL ad A E C FCCEaNOU
Ium eam racionem obcincac quam linea R L 2d
E F lineam, igicur eriam quadracum IR ad F C
quadracum, eam rationem habet quam linca P Iad
E F lincam. quaro h parabola eA sectio P. F C aXi
F ex construct. normalis ad planum AB C, eric e recta P R bnorinalis ad planumi
ondec:
B A C, ac proindenormalis adrectas, D F, c ON. Isitur rectangulum FTIK est ad
NPO rectangulum requadeacum PF ad P R quadracum: led verect ingulum FIIK
ad rectansulum NP O, ica rectangulum D IFi, ad rectangulum :D P F. ergOre
ctangulum DIF estad rectangulum D D F, ve quadeacum PF. ad quadracum P R
2. parab.
BD aquidistans. Oudu am.
eROPOSITIO CXLII
Arabola omnes qua generaur  Conorde parabolico lectionous
exiparallelis, aequale lacus seccum habent quod omnium axibusin
lerui: liue a quales ac limiles lunt omnes parabolae axi aquidittantes.
Letonslatie
N conoide ABC PONANEUF eres
secciones; altera per axem BD,
cemeet x BCi reliquae dux cidem
ad angulos feclos, vila Guidemnem.
DCCCF, PacaCa dXt, alceraverO
ne5 F Gun per 19. vndecimi
MOE=
DBI etiam per axem: Facientes
cum planobaleos communeslecrio-