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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 421, page id 1815201908:0478
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Primorecta BD non hc maioe dimi-
dio laceris recti. dico BD lineam ese
quaelicam: delcribatur enim cenero D in-
teruallo D B circuIUS; CONEIHOEE IS PeF
praecedencem parabolam incerius in pun-
eto solo B: iitur reliquae omnes lineae ex
D ad peripheriam ductx maiores suneli-
nca BD.
Sccundo BD maiorhedimidio laceris
recti: cenero D circulus deleribatur2 CO-
cingens ABC Parabolam in duobus
punctis A. C. ducarurque recta D C: crie
IIIA MINIIMA (VE PAECE) illarum que exD
duci pocerune ad peripheriam parabole:
ex daco igirur puncto D, lineam duxi-
mus, dec. Quoderac faciendum.
eROPOSIFIO CAXXVIII.
(VICABC parabolae aris AD ma-
L.ior latere recto; ductague ex D
ordinatim linea D B, cenero D, interuallo D B circulus delcribatur BHC.
Dico illum incer lecare parabolam in quacuor punctis.
Demonstratio.
Vmacur F D aequalis dimidio laceris rectii
poscaue ordinacim P F, AGAEUFPCF F COn
tingens F C, conveniens cum axc in G. Ouo-
niam F C est contingens, de PD aqualis di-
midio laceris recti, angulus b DF Ct rectus elt.
quia vero AD linea maior est dimidio laceris
recti, ED minima eAt CarUI C GUIX CX D ad
peripheriam duci poltune: adeoque de minor
BD ordlinacim posicai clreulus isiEuF CCHEIO
D inceruallo DB, descriprus cader rlera F,
ex secundum aliquam lui partem extra Para-
bolam. Rurlum cum DB, minor dsic rectd
AD, (cu D A maior sic larere recto,) cader cir-
culus BHI C intra punctum A: ex sccundum
aliquam lui parcem inera parabolam: Ouare
ee in alio puncto quam A parabolam incerse-
cabic. Similirer ostendicur circulu BHC, ver-
sus parcem AC occurrere parabola in alio puncto quam in C; circulus igitur centrO
D. inceruallo DB descriprus, parabolam se car in quaruor punctis. Ouod erae de
monstrandum.
LD. R O POISIT FOACZXXIX.
CIEA BC parabolX axis AD maior lacere
Drecto; poliraq; ad illum ordinarim DC,
centro D inceruallo DC circulus delcriba-
EuFCBF; Occurteeille parabolae in quaruor
punctis C, B, F, G, d ex Bpuncto interlectio.
nis ducarur B F ordinartr sd axcr: 1CWP cit 0d
Dico F. D lineam aequale esse lateri recto.
D A R A
32 Daiuo.
brs. buirio
5117. ba
d10. huindo
11I
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