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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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CONOIDES HYPERBOLLCYM.
Demonstratio.
int communes incersectiones batis AFC, de
Oplanorum DL. F, FIC Y rectx D F. C I, qua
erunc normales ad diametrum AC ex 19. rndec.
d detin. 3. Ciuldem, dueta vero GB, OCCUErAETC=
Atx DB in R, ponacurque per punctum R
planum ML N. Parallelum baC extibenS L K,
communem incerlectionem cum plano EDFs
quae normalis eAt ad MVI. rectangulum igitur
NRM aequale est quadrATO LK, de rectangu-
Ium CC A xqualc quadraro GI. Igicur ve est
rectangulum MIK N ad ACC, ica est quadra-
cum RL ad quadracum GI. sed quia ratio N K
ad CG, eadem cs Cum ratiONC R MI ad C+ A, EC-
ctangulum MKN est ad rectangulum CO A,
in duplicata ratione NK ad C G, hoc eA BK ac
BG, hoc est RF ad C TI. Isitur criam quadea-
cum RI ad quadracum GI, est in duplicata
racione R E ad (+ TI. ergo ve quadrarum RL. ad
CI quadrarum, iea eA quadeaEUM K F. ad qua-
deacum CFFT. Cune icaque similes portiones pa-
rabolicx P K L _ GFF I. Sed lacus rectu porrionis FT C: T, maius es latere recto por-
cionis BKL, cum rectangulum IICI maius sic rectangulo FKI. Tgirur verum
elt quodremocior a verrice maior sc parabola quam qua propinquior elt.
PROPOSITIO CLXXZIII
DOnatur conoides hyperbolicum ABC
Lsectum planis paralselis exhribentibus
parabolas BDF, F CFI; ostendendum est
lectionem BD F minorem esse sectione
FOH.
Demonstratio.
PErticiatut Conus alymptoricus L IK, e planU
peraxem ductum. exhibeachyperbolam ABC
eiusque alymPEOEOS L I, IR, quarum TK aequidi-
Aabie parabolis, ve Pacec ex 180. huius: plana vero
DBE, OF FI producta producac HgUFAS MDN,
OOP, dua veigue parabole existent cu plana illa
alymproro TK xequidistent. Ostensum est a para.
bolas ADN, BDF aeguales esse; similicer et
OOP, FOFI. Igirur cum ostensum criam sE
bparabolam DM N viciniorem LK, minorem
esse parabola OG P remoriore, criam BD F
parabola minor erie parabola FGHI, gux remo-
cior est ab alymmPEOTO LH. Quod fucrac demon.
Arandum.
108Z
82. huius.
hi