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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 413, page id 1815201908:0470
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P A R A BO L A
Demonstratio.
BOnacur ex C ordinarim C FI. qu adtarum A C aequale
est quadracis AFI, ITC: sed FI C quadeacum a quale est
tectansuloTIA D (quia AD per hypochelim est de quadis 12-
ceri redto) quadracumisitur AC aequale cR quadraco AHY
vira cum rectanoulo H A D, id est rectanvulo A FF D, id eA
rectansulo P OF; at aurem e PC I rectanoulo aquale
quadracum C C, quadraca igitur AC; C C adcoque ec li-
nex incer se xequaneur. Ouod erar demonstrandum.
unnta si BIR O. ROSITIO CX i.
oe rcil. 32cil 23lB C4
SEO AB CparabOlBaris AD: eE A F linea
Saequalis quarre parei lacetis recti: CCHETO F;
inceruallo quouls E. L. circulus describatur oocur
rens axiin F e D, Parabolae vero in B: IUInSan-.
curque FB.
Dico FB rectam contingere parabolam in
puncto B. 5
Demonstratio.
i
Venim nOn CONEIHSAES POnALIT Ex F contineens FC:
cadecilla incer B ex A: vel vlera B. Cadac primoincer
B ec A, iursaneurque BF, C F. Ouoniam FC linca
est continsens; _ A F quarta pars lareris rectis linea C P
aequalis est recta 2 F F, hoc est F. B. Quod ablurdum. igi-
EuE E C ConcinBeNSnON CAdCE INCEF B et R. Cmiliter
ostendicur F C non cadere vlera B. Ouarc F. B Cola p2-
rabolam concingic. Ouod crac demonstrandum.
1e s E. CS et
i
10H. PR OP OSIFIO CXZI
Sco AB C patabola aris AB, ee AF
Reslinca quorta pars latetis recti: CenErOF.
intervallo quonis P F circulus describatur, 
Occurrens axiinF ee D, parabolx autem in
B: _ ex B recta ducarur B C, ordinatim ad
AXCMIS
Dico DC lineam, dimidium esse lateris
recti.
Demonstratio.
LF BD in semicirculo rectus; est aUTeM PeF PEX-
cedenrem P B contingens, D C igicur dimidium
b est laceris recti. Quo d ex ac demonstrandum.
Vngancur puncta EB; BD. eric igitur angulus
  t     te t.  site e  t .   
115