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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 654, page id 1815201908:0711
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ATYPER BOL A.
Demonstratio.
Tarios AB aequalis B E, duecaque AP lineas ON secans in punctis L, KanE
quadratis C F aequalia rectanSua G L N, CrunE NNL in a recta lincas igicur
cum rectangula NL C, aequalia nquadraris CF, ad dico quadraco AG, hoc est
GL cocum rectans lum N C L, a quale cric quadracs AC, C F, hoc est quadrato
AH, Hoc est OFI quaatalo. ISiur cum C FF media proporcionalis sic incer N C, _
CL, adb Peroba eu AFlFI. Quod erar demonstrandum.
Corollarium.
Z constructione Facile parec, hyperbolam FTFT ortam ex cranstatione linea.
rum AP. ordinarim polcarum ad axem ellipleos, lacuscransuersum habere aqua-
PROPOSITIO COZZEMI.
IE ellipleos ABC diameter A C non aris
LIncerna exconiugatis aqualibus; sed incra
illas _ axem (ica Gir, ordinarim aure ad illam
Policis BE hanc quadraris rectarum AF, AB
limul lumpeis xqualia quadrara D Fi.i
Dico AFFCorC ad candem tyxerbolam.
Demonstratio.
HE enim quadraTa rectarUM AF, AB simul
cumpea aequalia quadraris AD, BD bis sumpris.
sed AD, DB quadraca, cranstaca in quadraca DF,
Producunc hyperbolam, rei ex praecedenci constaci
igitur A F F ad hyperbolam Cunc. Ouod fuit de.
monstrandum.
Scholion.
DRimo assumpsi in propositione, AC diametrum quae
inter axem maiorem ex diametros conueatas aequa
les sita est: quia tunc quadrata ordinatim positarum. pu-
EXIsO
ellepse
e aX1cllipICoS AB.