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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 516, page id 1815201908:0573
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P AR A BOL A.
PROPOSTTIO OCCZLVIII.
Oncingens parabolis paral.
lelis mcercepea in conractu
vsecacut.
emonstia
DOnaturper P punctum quoduis in
perimeero parabolx DF F altum-
prum contingens AC; dico AC iv
F bissecari, Polica per F, diamerro
BC, Ponacur quaenis D F, aquidistans
AC; occurrens paraboIX ABC in
FT _ K. quoniam igitur FD, aequi-
auc +. hu. diamello in P biACCAEUT.
eROPOSITIO CCCXL1X.
ctuins, distat contingenci AC; recta F D in G, abissecta est; sune aucem a quales H D
Defin. . F K: COraigItur FTK in G bissecta est: quarC _E A C b xequidistanS FTR, ab eadem
Pris, e diamerris per contactuunt buncta ductis; inter se x qualia
Demonstratio.
IHE ABC, TTTK parabolx Parallelae: e
DTHK parabolam COnTINBAHE AC, DF.
FC: ponancuraurem per FI, I, K, contactus
diamerri; BFI, L. I. MK. incelligancurque iun-
Si FNO, CBA, DLF: dico criangula
LMG, CBA, DL P incer CC eAe xqualia
quoniam enim parabola parallela lune, dia-
MCEri LT. B FI, MR aequales Cun: Cunc au-
Eem AC, DB, F C concingentes in FI, I, R
cbilariam diuilae; ae qualia ixirur lune s crian-
P R O P OSITIO CCC. L.
Adem polita ASura: sinE in AB C parabOla linCXETCS AC, DF, FC,
saequata aleleres sesmenca: lecencur aurem AC, D F., F. C bita-
tam in FI, I, H.
Dicopuncta HI, I, K essc ad parabolam parallelam parabolae ABC.
e iL .1C
Demonstratio.
+RiGAHC CA LEse L punctis diamecri HB, MK, L. P: quoniam equalia Lunc se-
emENTA D AF, ABC, OMF, criangula quOqUCDLB, ABC, FMG, aqu2
lia sune: quare ex diamerri L. I, BFI, MK aequales lunE, de puncta I, L,K ad paTa.
bolam pac allctam ABC.
Riangula qua hunc a continsentibus, parabolis parallelis interce
lLnE.
:3+ 8. Beb
1218bu. BuIa ABC, FMG, DEE.
Nottete e pe  e e st e t  e e t te te tut  t t e  tte e  e  ste et e e et e et et   te  e t  te           et   t      
PRO.