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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 339, page id 1815201908:0396
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Demonstratio.
EL L IDSF
Vata O FT linea parallela rectae CF, quae
circulum in E conringac, ducatur ex G li-
nea CT Parallela rectae AC, occurrens lincis
CF, A F in K _ L, ellipli vero in I: actaque
Per I linea IM, qua AF lincae aequidictar, iun.
sancur puncta AL, FL, CG, FO: Duoniam
IMI linca aequidistat secanci AF, Crit = IMrC-
ctacangens, ideoque AIF criangulum beorum
maximum quae AIF segmento pollune inscri.
.F tot
bi: quod aucem C GF CriangUIII COTUM SIE maximUM qu_ C G F lCBIEHEO CIE- p eauus ex
culi inscribuncur manifectum est, verumque ergo criangulum Eplus est quam dimi-3. en +2.
dium lui scomenci. Deinde, quia PI, K C sunc requales, ve facile ex r7 4. huius dedu- huius.
CerUT, sunEque LG, A C parallelX, criangula TAL, CCK sunE ae qualIa: SUINE VErO C+3: huius
ob candem causam aequalia criangula IF L, GF R. cocaigituE AIF, C GF aequalia
Turic. Similicer demonstrabimus segmentis reliquis ellipeicis ac circularibus intcribi
Polle, sive cerminorriansula maiora dimidiis segmencorum es Equalla incer lcixqua.
lia igicur lunc scxmenca ALF, C CrF. Ouod erac demonstrandum.
PROPOSITIOCLZZKII
AbeanE ABC ellipsis e circulus AD C cundem axem AC, duca-
Lcurque recta guaeuis P. F normalis ad axem AC, occurrens ellipt
in C1.
Dico esse ve E. C ad F F, Sic ABC elliplim ad circulum ADC.
Demonstratio.
EiX centro EI normalis CFIEAEUF ETB D: OECUTTeNS
ellips in B ec circulo in D. ve FB ad HD, RC
F.C elt ad B F: sed ve FTB 2d FTD, ACd ABC ct
liplis est adcirculum AD C: IgITUEVE E C ad F, F, (IC
ellipsis ABC est ad circulum AD C. Quod erae de.
monstrandum.
PRDBOSTFIO CLRKKILE
AbeanEA B C ellipsis de circulus AD C cundem axem AC ad quem
Lordinacim polica lic recta P. F. occurrens ellipsiin O d circulo in F:
Dicoleomentum ADFF. esse ad scomenrum ABC F. vE ADC cir.
culus est ad elliplim ABC.
Demonstratio.
i
oroil. 4.
auu aenab. alcacuique Eecla
El aequidictans ipsi A F, concingens
circulum in puncto D: ex quo ordinacim
demictatur adaxem recta D I, OcCurrenS
Mllipli in B _ AF, AC lincisin I _ M,
asacurque pet Brecta BR parallela ad
A G, quae per 154. ellipsim tanget. dein
linex duCANEUT A D, D F, AB, B G, VEF F
ad F, C, HCFL CA ad TMI, Sed es VE F F ad
F C, EcID adIB. isicur ve ID adTB, GIC
CE ad TM. ergo e reliqua DE ad reliquam BM, retota ID ad cocam IB. eAt
autetu