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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 451, page id 1815201908:0508
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D.
lI
1C2.
me.
C II.
ren
lum
D;
lum
AC
eet
icuE
aM
et
ea
D.
0.
D
AC
c.
2.
P A R ABOL A.
PROPOSTTIO CCK
NInC ABC cmpleos vel circuli diamett contugat AC, BD; du-
Oetaque quanis C. F parallela AC, secanre BD productam in F, RanE
ED, BD, CD continue, provorcionaless descriptaguc per ACC pun-
cta, parabola, Culus diamerer CD, P0-
naneur linex quocelinque FHI paralle-
la L B, seccances emplim in I, parabo-
DICOFH, IE, LH lineas eAsC PrO
portionales.
Demonstratio.
(VE AEI C rectangulum ad rectangulum
ADC, SIC FIK linca ad lineam DC
a III quadracum ad quadracum BD; igi-
cuE FTK linca ad lincam D C duplicacaha-
becrationem eius, quam habec PFI linca ad
lincam BD. inde cam E D, BD, CD pO-
Sicione Encproporrionales, es ED, FHI pri
meincer se xequales, sic aurem d racio DC
ad K FI, cerrie adcerciam; duplicaca racionis
DB 2d HII; secundae ad secundam; crunt
FH TF KH in concinua analoxia. Quod
erac demonstrandum.
PR OPOSITTO CCVII
NTemicirculo AB C decussene sese orthiogonaMet II DMaeM auX
LAC, BD, quarum alcera B D bitariam in F divisa, delCrIDAEUT PEF A, L3
C parabola, cuius axis E. D, ductaq diametro F C, quae lemicirculooc
curratin H, Ponatur HIC.
Dico F C ad C. C. duplicacam habere rationem eius, quam habet H1C
ad HC.
Noniam AC dupla elt BD, ec illa du-
LplaFD, reCtX AC, BD, ED pTODOF.
cionales tunr. estaurem F. D ad FC, in du-
plicaca racione DB ad GTI, cum sIC vE
AD C rectangulum ad rectangulum AC C,
id est BD quadcatum ad quadeatum HC;
rectxe ivicur CFo bHEr, AC in concinua
Tunc analogia, sed ee AC, IIC, CC c linex
proporrionales sunc; igicur FC ad GC, certia ad rerciam, auplicatam  HaBex sionibus.
rationem cius, quam haber HC 2d HIC, secunda ad secundam. Ouod erat de-moncu
montrandum.
60051210CC
ma
onibus
lam in IL, _ AC lineam in FI.
monsoraio.
ocresiont
atabolas aequales ABC, OL. L MIuelSC Ad CMm axem AD, qui x-
qualis sit lateri recto consticuras, conrinsancin a  , lne bt,
HIC: d