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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1052, page id 1815201908:1109
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amrtur
BCollixiru
e2 40Ba
d 12 9. hu-.
s
tunc demonuctandum.
SP H A R O1D CS
Demonstratio.
PhaeroideS ADC seCAPeF BF, axemin
norem plano ad axem AC recto, lectio
B FC circulus a eric. inscribatur super circulo
C=B, lempata DBFC. ducto aurem Pee
axem AC plano, exhibeacur lectiones AHIB.
DK B, _ inscribacur cuique sectioni lua para.
Bola ABF, DBF. Oltensum b est ABF
ductum in sc 2d D BF ductum in sc cam ha-
bere racionem quam parabola in(cripta A BF
ad inscripeam DBF. sed parabola ABF ad
DBF Parabolam, (quoniam axes B R COM-
muneslunc) estc VE AE ad D Bi igicur eciam
ABF. ellipricum ductum in (c ad D BF, cir-
culare ductum in (c Cst vE AF ad DF, sed vE
ABP ellipricum ductum in sc ad DBF, cir
culare ductum in se, ita eA AB B, ellipricum
ductum in orbem ad DBF circulare ductum
in orbem; cum dquadraca IIIad K Iquadra-
ca cam racionem contincane quam circulira-
diis FTI descripci ad circulos radiis RI de-
Scripeos.igItUE ve AP ad DF, ita CE sphxrOides AB F ad spHxram DB F. Quod
quae tieper cenerum incer se luncequales.
Demonstratio.
Ine auo maximi coni ABOC, DECB in-
Ccripci splixroidi, insistences sectionibus BC C,
E CF per cenerum Factis. Dico illos inter le 2-
quales ese. criangulum peraxem coni FD F est
aequale criangulo per axem coni ABC; Per en
que libro de clliphdemonstrata clunc. isicur F est
HC ad HIF, ve reciproce DI ad AHI. sed ve
HIC ad HIF, Sc g elliprica basis BCC ad balim
ellipricam B GF. ergODE BGC 2d R G F, ic
reciproce
a
I ad AEI. erBOHCOnIEDF, BAC
PROPOSITIO CXXXII
nes coni maximi pa cetur eci insictenres alicui sectioni
PROPOSITIO CXXKIII.
IE conus ABCD MCCOIaI MMICripruS
_e per F centrum d verricem coniA du-
ctum planum exhibeaceriangulum ABD,
cui inscripea sic parabola A F B verricem
habens A, alrera vero inscripea sic ellips
AHIB F. caiusvertex B.
Dico