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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 261, page id 1815201908:0318
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ELLIPSISE
PROPOSITTO XZXIII
Sco ABC. clip (CoSaxIs A C, Super quo ve diameero Pem lCirculus ac
cribatur AD C, alsumproq; in axe puncto F quod non sIECenEruM,
erigatur ex F. orchosona FD occurrens ellipsiinB.
Dico conringences per B et D actas, axi AC in vno eodemque puncto
OcCurrerE.
Demonstratio.
Ciaturper B concingens BF, conveniens cum axe
CLin F, iungancurque P. D. quoniam FB ordinarim
Polica ecadaxem de BF. sectionem concingie, CrIC = C F
ad F A, ve CF. ad B A: unde e iuncta F D circulum
contingie isitur contingences per B _ D actx, con-
veniune cum axc inruo eodemque puncto. Quodtuir
demonstrandum.
Corellarium.
Inc facile eriam demoncrahimus E dux rangeures
in eodem puncto diamerro occurrane normalem
O. quae liperrnum conractum D cranscac, cransire
etiam per alcerum.
PROPOSTTIO XXXIV.
Sto ABC ellip liIS diamerer BD, ad quam ordinatim pOnAtuF AC
LsaGAnEUTG Per A _ C contingences.
Dico illas diametro in rno codemq puInCEO OCCUrreTE.
Demonstratio.
DEriS huius pacet singulaS ConringenteS pet A d C ductas
cum diameero convenire: A isitur non convemane in co-
dem punctos occurrat A F concinsens diameero in F, _ C IY
in H: Ouoniam cansens AF concurrir cum diamerro in F,
CrIECVEDF ad EB, lic D F2d F B. cursum quoniam cangens
CHI concurrie cum diameero in HI, cric veD F. ad FB; hOC
estDE DF ad EB; sic D FI ad HI Bs ex dividendore DB ad
BF, Sc DB ad B II, quod fierinon pocest. quare cangences
non occurrune diamecro in diuersis punctis. ergo in codemi
Quoderar demonstrandum.
eAOIOSILIO RZEV
102
a30. huius.
b de circulo
vel perc
a. 10 tut
suins
denua in cctortemtcos alea.
eorunetam AC, ordinacim elle policam ad diamerrum BD.
Sco ABC elliplis, diantelet  proucla iue L dCk
1E H Z
Demon