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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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p
EL L IPS1S.
Demonstratio.
Incin AB C ellips diameeri dux coniusatae AB, CD.
dicoillas elliplim quadritariam diridere; de _ AB, CD
diameeri ellipum quadritariam diuidane, dieo iIlas esle con-
rugatas. Ouoniam AB, C. D diamecri lunc coniusaex, cric
AB ordinacim polica ad diameerum D C, vnde a FaM AF. C,
CFB quam AF D, B F. D sectores lunt xquales; sunc au-
tem eE AF. C, AF. D sectores ob eandem racionem xqua-
les; leCtoreS igIEUE QUaTLIOE AF C, CF B, BFD, DF A, lunE
incer se xquales, et AB, CD linca quadritariam dividune
elliplim: Quod erac primum.
Siciam ellipes quadritariam dinisa, dico AB, CD dia-
metros esle coniuxacas. sin vero ducarur ipsi CD, coniu-
Paca FC, igirur fi F C, lector quadrans ellipleos est per priorem partem huius. AF.
qui seclor AF C ex hypocheh eriam quarra ellipleos pars cAt, ereo lectores FP C,
AF C aequales lunC, pars ex cocum. quod heri nequiciigitur F C diamerer non est
coniuxaca iptius CD, nec guaeuis alia prXTCE AB. Ouod erar demonstrandum.
Corollarium.
Inepatet lectores quarum cum que conturararum, equales esse sectoribus eu
juscunque alcerius coniugacionis lingulos lingulis: linguli enim quadrances
Cunc ellipseos, e s sectores lint xequales ac larera vuius sine coniusaex, alcerius
eriam lacera este ConiusaTaS.
PROPOSITIO XLVII
Eclores ad verticem oppoliri lunc incer sc aequales.
Demonstratio.
ECenE ABC ellipsm diametri quacunque
AC, BD. dico sectores ad verricem oppolicos
eNc incer (c aequales. ducancur enim ex F centro
diameeri dux PF, F. Ci _ F F quidem coniusata
iph FB: F C vero coniugaca ipl AF. Ouoniam
ibirur sectores BF F, AF. C, b aequales luncdem-
pro communi AF F, eric sectOr AF B, aqualis
Ccdtori F F C: rursum cum sCCtOTES FF. D, GPC
nc equales, dempro communi DF C cric lectoF
DF C aequalis sectori F F G, id est A F B ad ver-
cicem oppotico. eodem modoostendunEUr AF. D.
BF C sectores aequales. isicur, etc. Duod fuic de.
monstrandum.
LLOcLI
IE in AD C empit IcCt Guca ADB, OpOTTCL ex B rectam
ad peripheriam duccte, qua cun b nca lccloreoa a
10 abC a Glae.
Con