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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 496, page id 1815201908:0553
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# Lines: 54 recognised, mean confidence 0.83
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R ABC
d
DR OPOSITIO CCCI.
Sumpeum (ic in A B C Temicirculi diacero AC, punctum quod.
Lcunque D, quodcontrumnon sic, d ex Dad peripheriam, rectae
AlICANEUE DF: asanturqueper F, linex , Ahales ad diamerrum
AC, _ D F rectis aequales.
Dico CC puncta essc ad parabolam.
2 FX 17. h.
bFXI3I.
cl34. hu.
4.
F
primo
Demonstratio.
Rigatux ex D linea D B HOF.
Lmalis ad diametrum AC
aetaque per B concingencC, que
AC, diamerre dac  H.
sececur IID bilariam in I: e
per I_ B, describatur parabo-
la habens IC aXCH
DB, ordinacim polica est ad
2ZCM IC, QD L
Il li
quales, contingee HIB linca
Parabolam in B: quia vero in eodem puncto, eadem leca enculum concingic, con-
cinsene quoque Cele in eodem puncto b circulus ex parabola guare DF lineis cequa-
les luntrectae F C. Igicur cum P F. C: lince normales ad diamerrum A C, rectisDF.
ponantur aequales, puncta C, C ad d parabolam lunc: cuius apicem astignac punctum
in quo HID dividicur bitariam.
R O
1O CCCIr
arabolam priori propolirione productam in intinicum eademm praxi
extendere.
Constructio ex demonstratio.
un
Occurren(
querectis FF in G. Ouoniam
a X
lat C D, aqualis C F, Parallela BD: eric F ad parabolam MBEI, cum omnes
DH cransaEX Cin C F. FI ad parabolam linc. Fact a deinde CM, aequali MN, Epo.
e Coninedo Patabolam, e crisacu  Perpenaeuas dd HF Cons
encemi cenlbq; O inceruallo FO circulus describatur; contingec illeo parabo.
Jam, dL deam in F: cum parabola describatur, h gux ex descripio iam circulo
KF P, oritut; Hac quoque concinget circulum R F P _ NF, LInCam II F, Be in PHO-
eiproxoncione oltensum est; verrex igitur ejusdem estin MI, cum MC, C N linex X
quales linc: erg Palabbla Illx dux communem habenererticem M, e punctum li
vnaigitur cadem que tanc parabola, qux per verumque circulum cst delcripta: ergo
circulus LFs Paladoum priori praxi de scripcam producic: acque ita cadeM pata.
bola cadea praki i inthICum COnEMHaBIEuT. Quod eras proxolicum.
NaCUE
l RO
      s    o o u s le