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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 442, page id 1815201908:0499
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6. secundi.
neam R F.
artuim.
 A R AB O L A.
PROPOSDTIOCLZXAIV.
Idem policis; producta
Aea GFI, GOCCUTraE CR
lineae in HI, DE AF produera
Dico IMt El rectanguli
esc ad leclangulum F NA,
c Te lectangulum est
eectangulum FO AI
11.
Demonstratio.
Scensui est praecedenci pro-
polcione, quadracum HC
ad CF, candem habere rario-
nem quam DC quadracum ad
quadracum CF, ac proinde, qua
M: SCd quadratum R C HOC eA D N XGUaEuF D F qua.
IOTT ad FO A rectansulum. quod sorruit demonstrare.
PROPOSITIO CEXRE
Sto AB C parabolxe aris C D, aqualis laterirecto, actaque per D Or.
salnarim linea D A, prOduCATUTHHL, VE AD, D P. lincae aquales sine
uo
litiex L. C in N. I cl 1903CuNiI
draco, una cum rectangulo F. N A; Similiter quadracum CP hoc est P. M, X quale
eAtquadeaco E P, una cum rectansulo TM FT. cumigitur sic quadracum P. MI ad DN,
sicue quadratum F L ad D F, rectangulum quoque LM FI est ad rectangulum F N A,
rEguadratum F I ad D F gnadratum, hoc est per pracedencem ve rectangulum
bensverricem in C. e concinhrem C D; ducancurq; B G parallele AD,
occurrences parabolis in B de F, de iungantur B C.
Dico ese ve quadratum BC, ad quadracum BC, Sic R F lincam ad lin
IAnGAnEUEGUE AC, E. C: dein per C de E parabola describatur C F F, ha-
Demonstratio.
S Risatur ex A diameter AB
occurrens B Clincis in L. qua.
quadraro COc huc O FI, lcun
CD, DF adeoque  CC, C
linex RquenEuT) aquale est rella
sulum FC:T; quadrarum igicul
BC aequale est rectangulis FO
R CTitioc est rectangulo IOKF:
sed TGK E rectangulum est ad rectangulum PC K F, DE FR linca ad lineam RB
quadracumixitur C B est ad quadracum CB, ve K F linea est ad lineam R P. Ouod
erat demonstrandum.
PROPO51Y1O CLLaaI
Dico lCadB CpCalaabete alte es Ga  B
ad AV.
Denoi
dracum CB aquale est quadraris
BO, CC: est aurem b qu’adracum
BC aquale rectangulo ROI, d
ildemipolicis:
Ba