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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 510, page id 1815201908:0567
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P AR ABBLA.
Dicopuncta E, I, K, _c. ad candemt cleparabolam: _ li series conri-
nUatUM AE, P. F, F C, _c. maioris tuer inxqualicaris; dico parabolas
in aligu puto conuogireils vero muotistucrir inae qualicaris dico nul.
15
Demonstratio.
Voniaim AE, E F, FO, XCC. pro-
Lporrionales (IME, F F est ad F C,
vE AF ad AF; id cst vE F B qua
rdarum ad quadracum FB; id cstFI
quadracum ad quadracum ER. B-
milicer ostenditur esse FF quadra-
cum ad quadrAEUM FIL VE PF, di-
nea ad lineam F FI: punctaisitur B,
T, K, T, _c. ad parabolam CUNE.
Quod erac primum.
PONAnEUE aUTCM SeTICS AF, P. F,
EC, dC. Maioris inaqualicatis: di-
co parabolas convenire in aliquo
puncto. sc enim AB C parabolx
xquale rectangulum E AN, _ LLQuadearo xequale rectangulum F F. O: unde cum
E B, FTguadraca aequalia Cinc, LCangula quoone P ANY, F F O sunc x qualia: qua-
et recum A L maior pOMALBL L L, Crit A N lacuS rectum minUS IACCTC FCCTO F O:
C3) L e. CLD A mulum Sit iam A F, L. F, F C: de c. termi-
Aoden hs. . D, s norum concinuatiomrinoris inxqua-
1DD FD I
licacis: dico parabolas nusquam sibi
Occurrere ponacur enim L A lacuS
rectum parabole ABC, _E NTF, 12-
A 19, cus reccum parabola F LII, quiaigi
Bcil eren
Tur F B, FET quadraca equalia suHE.
recrangula quoque P A F, MFF X.
qualia TUINE: e Cum R F minOE pO-
RAEuIE FF, erit L A maior quam
cloclisqME ondenulquam sconuenicuele.
CTioneS.
O CCCXXZIII
darabola axis AN, in quo lumpea
iparA D demiccantus aequales diameci
BRSF erBBP BC smerhuD 1D sit. C1
DicOD, E, P. plincta esse ad parabotam aqualem
parabola L.BC.
demoptratio.
(_ LB etS s SLACIMN
Cris ordinatim BL, PONAHEuE E.G, paralletX. Ouoniam
isitur AD linCa, aqualis es BF id estF C, demptaves
addira commun F D, reCtE A F Xqualisest D G. vnde DC
eA ad D Gi VE A E Ad A F, id e vE F. B quadearum ad qua
drarum BB, ANCH F. et quadracum ad quadeacum F C. pun-
craixicur D, CiL dt parabolam Cunc, quiu vezo cam AF, DC
quat
quam lectiores convenire.
 C
latus rectum AN, d F YK parabOIX lacus rectum F. O: erie isieur quadrAEO F B
Ds e eLe ASSNS
167. Hm. 2deo que parabolx in aliquo puncro J conuenient: , YI s.
  e  se  s    e  ute uet e at . ue e s.  e  te  t ate  t te ti ete ete  t tt      et st e  s at  i  it te  t t    et e t  s