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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1084, page id 1815201908:1141
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CBAOIDES HSEERBOLTOYM.
EKOTOSIIIO CEXXZIN.
Mnestectiones cemens ls perbolici axi aquidistantes, (i inter se
quoquexequidistene, cenera habene in linea qux à cenero hyperbo-
lx per axem conoidis producte, normalis ad parallela hyperbolarum
Plana ducieur.
Demonstratio.
Tcigitur planum ABC per axem conoi-
deosinclusi cono D R F alymprorico, od
quod aliud ponaene B CFT ad rectos ansU-
Jos, quod aequidister axi conoideos. Dien
sectionis B GFT cencrum eAe in P. I, quX a
ceriero hrperbolae AB C ducirur normalis
ad planum BCTI. planum enim BC.HI.
productum lecer conum, e exhibeat hy-
perbolati RGF; huius centrum erir in
recta FI. Acqui hyperbola PCrTI, ijidem
asempeocis claudirue quibus hyperbola
R GL, VEPATCE CK 176. ex 177. huIUS. ergO&
cenerum cum ca habee commune in recta
E I. Similicer ostendam omnes hyperbolas
ipsi BCFFT parallelas habere cenerum in re-
eta PI. LiguEFerBO prOPOSiTUM.
PROPOSITIO CLZZZV.
Ececur conoides hyperbolicu ABC.
lectione per axem _ altera BDF,
qua recta (IEad planU pCFAXCI, CON-
curracque cum laceribus crianguli per
axem COnIA(YM PEOTICI CKETA CONUIM.
Dico secrionem B DF. ese hyper-
bolam que cum lectione coni FDC,
non concurret, qua in eodem plano
exictic.
Demonstratio.
CM CK 19. PI. _ CICHHIC. 3. TI. PALCE R FV
LBA L, aCDE C rectis L. M, PL
Voniam planum BDP. rectum est ad
INUM PCF EXCM AB C, _ concurrit
cum laceribus criansuli peF aXCMI CXEra CO-
num, isicur sectio FDO coni HIMOL.
hyperbola est, CUIUS CCHErUM SIPPONACUE
punctum P. ex quo a (yMPEOTOS dUCATUEPO.
Dohcaigitur diametro P D, aNumproque in
ea puncto quonis R crissAnEuE R S. D, 7 que
Eine normales ad planum crianguli ABC
peraxem, ex secundum R S, DO lectiones
hancbasi conoidis parallela, exhribebunc hae
sectiones circulosOTV, AF C _ ZV X
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