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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1085, page id 1815201908:1142
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GONOTDES HYBERBOLLOVM.
essenormales. vnde rectangulis OR Z, A DC, Euantur quadrata R Y,  f. Fect u-
gulis inluper Z. R X, I. D M quadrata R S, D. C, _ quia FTM, FTL alympeoci lune
sectionis AB C, etiam Z. O Z L. A M rectangula incer (e lunc a Xqualia; vnde exc eNuS 2 1S. bypetB.
quadtari R V quO lUPETAE quadeAEUM R Y ae qualiS est excestui quo quadeatum D gesu
excedie D F B quadracum: _ quia POalympeoros est sectionis FD G, CxCCNuS AUX;
drati R S Super R V quadraco aequalis elt excestuic quo d. Aert quadratum DO 2̀ c179. Bu-
quadraco D O, ac proinde quadracum R S excedic quadtacum R Y eodem excopi, ius.
quo DO quadracum luperac quadeacum D F. limcisirue B P F. ad hyperbolam cu-
ius d(ympcocos est P9. Duarecum duarum hy perbolaruin FV G, BY F alcera (IC
in luperAcie coni, alcera in superticie conoidis; quae superticies nunquaM dCONCUF d 175. hu-
ruNE, nec ip (a sectioneS CONCUETenE. Duod erat demonstranlum.
PROPOSITIO OLXKEVI
NEcecur conoicet c us planis parallelis que eltip (ES FOrMENEB NL,
1085
IL
viconaepes C CMHC.
demonstratio.
exhubens communes incerlectiones BF, DII.
eric isicur ABC hyperbola. Ponatur aucem
diameter MI, qua diuidac B F, D HI bitariam
in R _ I, ex sectio Aac per MI P. Iquae recta sIE
ad planum ABC exhibens communes incer.
sectiones, K N, IO, qua pet 19. 1I. ex detin. 3. IX.
erunt rectae ad lincas P B, FT D, ac proinde P. B.
XN, IID, IO sunc axes elliplium; erie aurem
per ea que demonstrara luncc L. N Ohyperbo-
la cuinslacus cransuersum MI, commune cum
hyperbola AB C. quare verectangulum MKI.
adMII rectangulum, ica eA quadratum RN
ad IO, ee quadracum KB, 2d quadratum ID.
ac proinde guadracum RE NN ad quadracum IO,
requadrarum RB ad quadrarum ID, vndeve
EB ad KN, ica FID ad IO. Cune igieur sum
les elliples BNE. DOH.
Gatur ABC planum pet akem conoidis
quod sic rectum ad sectiones BF F, DGII
i
ABPOSTTIO, CLXZXVII
dlimiles erumc hyperbola.
lsectiones parallelae conoideos hyperbolici hyperbolas produxerine,
demon-
a