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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1044, page id 1815201908:1101
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PA A 1
5
ROPOSTTIO CXVI.
Anislinca in quouis plano posica
quod per cenrrum spheroideos
transiebilecatur a ceurro sphaeroidis.
Demonstratio.
lesphaeroides AB C sectum plano BDF.
per centrum F, ducta vero sic in plano
BDF recta BF per cenerum F. Dicoillam
bilectam esse in puncto F. Agatur enim pla-
num per AC axem sphaeroideos AB C quod
rectum sic ad planum BD F, erie BF. ho-
rum planorum communis incerscecio, quâm
ex 114. huius perspicuum est bileccam esse in
CCHETO P. DUOd CTAEPrOPOSITUI.
PROPOSITIO CXVII
Ectio sectioni per axem Factxe (I X-
quidistans fueric, eidem similis crie.
Demonstratio.
Donancur in sphaeroide AB C duo plana
Farallela POB, BID. Vnum scilicCt
per cenerum BID, alcerum eidem aequi-
distans. Dicoillas sectionesinter se similes
esc. Agacur planum AB C per axem sphX-
roideos rectum ad plana parallela, Occur-
rens illis secunduim lincas PF, B D; CrUNE
isituE PE, BB axes a sectionum pec
cenerum sphaeroideos _ sectionis POF,
crigaturnormalicer ad planum ABC rC-
eta L I, divisa deinde P F, BiFariam in R,
agacur planum per K quod cranscacper L. I
lincam nimirum FOTII, exhibens KC
communem incerlectionem cum plano
PC F, cum plano aurem per axem ducto
ABC, incerlectionem FFL, que ceric axis
Cllipseos FOFI, cric icaque RO normalis
2d P R, cum sc aequidistans I. I. vndere-
ctangulum FK II, est ad rectanguluF L. II
VEd PKF rectangulum ad rectangulum
BI D. Sed ve rectangulum F R HI ad
FIFI, ica est quadracum K C ad L. Iqua-
dracum, cum sectio F G FI Sc elliprica cu-
ius axis est FFI. Igicur ve rectangulum
PK R ad BE D; ita eAt quadratum KC
ad FL quadracum, igiEUE DE P F ad BD,
ica eA KC ad P L, sunE aucem L L, K C et BD, L. L axes ellipscon. Ouare limi-
ded ta telllonbo. Addderdnale exoteltl.
LRO.
2215. huicus.
Cros. tnino
d 4. elips.