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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1047, page id 1815201908:1104
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APH X R OFDE S.
LROBOSTTIO CXXITI
atnes sectiones Pel ceuum sphaerodeos Cladseunces eam incer se
Srciunet rationem quam continent aesaes t 1C.
Demonstratio.
IHE sphxroideos A B C. dux sectiones BDL.
DF D Eper centrum HI ductE. Dico illas cam
inter se habere rarionem quam duo axesmaio
resincer se si sphaeroides sic oblongum. agaeur
enim planum ABC. per arem AC, quod re-
ctum sic ad planum BD F exhibens commune
incerlectionem lineam BP. crit aigicur B R axis
maior sectionis BDF; recta verO HID qua
communis estincerlectio plani BD P cum pla-
noperaxem AC, axis minor est b cum sectionis
BDEcum AB C vel ADC. Cmilicer commu-
nis incersectio plani FD C, cum plano quod per
aXCM A C. hec eric axis minor cum lectionis
EDC, cum sectionis peraxem Facta cum igitur
sectiones percentrum omnes, eoldem habeane
axesminores, eam incer le rationem habebune
quam ares maiores, cum elliplium ratio exra.
TIONIBUS AXIUI COMPONAEUF.
Alicer e breuius propolicum sic concludo.
per Corollarium 120. huius elliples Omnes per
cenerum cranseuntes, axem minorem habene
communem cum sphaeroide. Guare cumratio
ellixlium ex axium rationibus componatur, c.
FTUNECIIPIES PET CCMEEUM ETANLCUNTES, YEaXES MaIOTES.
PROPOSITTOCXXIN
et daro sphaerosue eMplim exhibere,
que ad ellipiu petaxem rationem ha-
beac dalanoris ina qualicaris sicq. illi
requidictans.
Consirucio umonpratio.
Ae spHaeroides A B C cuinS eCtIO PeF AXCHII
ABC. SPOEECAE aucem CAMNCKCCMIPUM i
sectionis per axem ABC; sectioni aurem ABC
ad rectos angulos consticura sic quadam secticr
per BD. dico hanc sectionem esse quairam.
nam similis es sectioni quae illi heree parallela
per axem sphaeroideos AC, e consequenteF
similis sectioni AB C, acqui aimiles lectiones
sune in duplicaca rarione lacerum homologo.
rum, hoc elt AC ad BD, hoc est F. ad F. Isi-
cur exhibuimus quod pecebatUE.
ratione duplicaca L alF, qua a Guet a Xl
AC. Rat VE F, ad F, ita A C ad BD, in plano
2047
212s. huvius
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