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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 414, page id 1815201908:0471
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im
b 2bid.
cIbidi
P AR ABO L A.
DArabolam AB C cuius axis AD contingarin 
linea quanis C F, conveniens cum axe in F. diu
uilaque bitariam C F. in F, ducatur F D normalis ad
E. C contingenrem occurrens axi in D.
Dico AD lineam, quarta esse parcem lateris recti.
L. 5. 5d 5d eC . 1S C 1 2IS. II
Demonstratio. 1ISVP S
Vngancur puncta CD. Ouoniam FD normalis eAt ad CaB:
genEEM F. C, anguli F. F D, C F D aequales LuME; Sune aurem
e recte F F, F C ex hypocheh aquales, SC FD communis,
criangula isitur E DF, CDF, _ E. D, CD lacera aqualia
sunc. QualC _ anguli CF D, F CD aequaneur; e AD a linea
es aequalis qllarre pactilaceris recti. Quod erat demonsteam.
al.
PROPOSITIO CXXIII.
Darabolam AB C cuius axis AD, contingac in B recta quaeuis BF
conveniens cum axe in E, demistaq; ex B linca BF parallela axi, hat
Dico AH lincam aequalem esse quarex parri
laceris recti: _ si AHI tueric quarta pars laceris
recti, e BF, parallela ari, dico angulos F. BLI
FBC ese xquales.
Demonstratio.
Voniam FB xequidistac E D, angulus AR B Xqua.
lis, est ansulo FB Chocest anguloFTBR: vnde AH
linea bxequalis est quarrae parri lareris recti. Oyod erat
primum.
Rursum cum AFI linca sic quarra pars laceris recti, an.
sulus HBF aequalis est anguloc AF B, hoc eA FBC,
cum FB, F, D aequidistenE. roCCtuF aurem puncum H
tocusparabolae.
R OPOSITIO CXXIV.
Constructio ex demonstratio.
PROPOSITIO CXXII
2DC auat ag ctuS F BF1.
AEx parabolx Focum exhibere.
U dacae parabolae AB C, aris B D, cui quoruis ponaneur e quidictantes, A P CD
DASAEUF aureM per C contingens GFI; duct aquC ex C recta CD, hat angulo
qualis hac aleitus cehexionis, raclli rehexi omnes convenienc in D puncto quod
quartam laceris rectiparrem designac. dacx isitur parabola focum exhibuimus.
Porro focum indisitamus punctum D, quod in illo fiat combustio, es radii restexi practil
FC C, aequalis angulus ITC D: constat per praecedentem propolicionem punctum
D, ese Focum parabola, adeoque BD quarram esse parrem laceris recti. de quoniam
CF Inea est quaecunque parallela dus, Hin religuis quoque angulo incidentia a