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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1088, page id 1815201908:1145
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1088
GONOIDES AEDERBOLLENM.
Demonstratio.
i Scenim spatium coniresciltum TBCDL.
xequale conoidisimul cum lpacio quod co-
noidesambic: rursus idem spatium coni Xqua-
lc elt corpori cxlindrico simul cum spacio soli-
doquod crlindrum circundat; elt aurema de-
monstracum spacium quod conoides cingit x-
quari cylindeo IMNOL, ivicur ablacis X
qualibus reman ene conoides e spacium quod
Cslindrum ambic aequalia incer lc. Quod de-
monstrandum fuic.
PROPOSITIO CXCII.
IIdem poltis:
Dicoconum abscissum AIK L. ad
spatiu quod circundat conoides E FOHI
habere rarionem compolicam exrario-
ne alticudinis AF ad alcicudinem E P,
e ex ratione IL. ad criplam rectx IL.
Demonstrario:
Scentum CHur eum lic, exlindrum LMIN OE equari spacio Colido quod ambis
conoides hrperbolicum, isicur quam racionem habehie conus AIKL. ad cy-
lindrom TMNOL, eondem quoque habebic ad corpus cingens ipsum conoides.
Pedracio coni AIR P ad cxlindrum LM NOL, compomtur exracione AF ad R P.
e exrarione VP. ad criplam II: ixicur etiam conus AIK L. ad corpus ambiens co.
noides habet rationem ex ijdem compolcam.
PR OPOSITIO CZOTII.
Ecto conoidi incluSIS SIECONUS ABD C FaCTAGs Per axeM AF. secrio.
Lenerriangulari AB C ee hyperbolica BR AOC, dinisisq; AB, AC
bitariam in F _ C: duccaque FC que secrioni hyperbolicx occurrat in
II _ I, harrectangulo HIFI aequale quadracum KL, _ per A C axem,
_ LK semiaxem deleribacurelliplis. Deinde hac recrangulum (ub F. B d
MK aequale quadraro L K, _ describatur parabola AMF, cuius axis
MK Facco denique recrangulo sub F. B _ K N, aequali quadrato HC
Icu FIE describatur parabola ANB, cuIUS VCTECX A.
Dico conoides hyperbolicum ad conum inclusum eam obcinere pro.
porrionem quam Luperticies AME BN A ad CuperAICIEM ANBE. HE A.
Denon
audus tuvius