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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1076, page id 1815201908:1133
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2076
CONOTDES HIYPBRBOLLEVU.
Demonstratio.
Ccurrac planum DF F ad angulos obli-
quos axi BC. Dicolectionem D F F et
lipeicam esse. Donacur planum. A B C per aXeM
BC quod sic rectum ad planum DB F, exti.
bens communem incersectionem D F, qux oc.
currac axi in puncto quonis FI, crectâ deinde
normalicet IIF ad planum ABC hac sectio
per HF parallela bali ATO, SCIlICCE RFL
quae erie circulus. deinde ponatur planum
MNO, bali quognexquidistans produces cir.
culum MNO ac Signanscommunem incerse-
ctionem cum plano DF F rectam PN. crie
aigicur PN parallela IIF, ac proinde b recto
C plano AB C. quia ergoram FIB, quam PP
lunc rectae plano ABC, deknic. 3. vndec. crie
TTE normalis ad DF, RL; _ P N normalis ad
DF, MO; 2c proinde HIF, PN sunc ordina.
c158. H EIm POLICE ad axem D F, SCCLIOHIS DE F, _E quadEAEA HIB, PN rectangulis RHIL.
MPO aqualia: sunE. Deinde ostensum eAtc rectangulum R HI L. ad M PO, candem
habere racionem, quam rectangulum DHI F ad D P F rectangulum. igitur, cum
rectansalis RHIL, M PO Paria sinc Guadraca ITB, PN, eriam quadracum FIF ad
PN quadracum eandem habet carionem quam rectangulum D IIF ad D P P rC.
ctangulum. Ouare lectio DE F elliplis est, cum linea HIB aequalis siICHIK, recta
verO HF maioc H L, Gvc HIL.
v
inc..
peraxem conoideos. ls pelbolam exhibet.
RODOSIEIO CLZZII
Mnis sectio consideos qua cran (eacper cenitum hyperbolae Facta
Demonstratio.
le conoides ABC, cuius sectia peraxem
habeac pro cenero punctum D, Per quod
adacur planum DBC. Dico BF. C esle hy-
perbolam. Hac enim per axem DH sectio
quae lic rectaad planum BP C, Eeque id pla-
num AB C, cric isicur DI communis inter-
sectioplanorum ABC, X BF C, diamerer in
lectione ABC: assumpeis aurem punctis R
SE L in dIAMEEEO D I, CrIGANEUERP, LF nOr-
maliter ad planum AB C. crunc ixicur bX li
nex in plano BE F quod orchogonalicer pla-
no ABC insistic; posicis deinde in sectione
ABC ordinacim rectis OLP, M K N ad cI-
mecrum DI, hanclectiones per R P, L. Li qua
baA ACC aquidistenE occurrences plano
ABC, secundum rectas O R R, TLS. cun
ipicur defin. Z. vndec. rectL R L, L F HOTImales
linc diamerris circulorum OE R, LF S, CrUnE
quadraca R L, L E rectangulis RK O, SLL
xqualia. cririgitur re rectangulum RI il
S, ITa quadEATUI R E ad L F quadra-
cum