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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 649, page id 1815201908:0706
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Decur.
tea
dues
1
DE
erichae
depa
nstrai
dracue
rut
linean
lineal
d
50lu
6012
cuili
H6
AIC
A2.
e18
ON
R0.
E Y P L R BO
PROPOSTKTOdC
Vver recta AB consti-
cuantur quocuis parabo.
aequidilter C F ponantur C,
DF aequales laceribus rectis
lingularum parabolaram.
DicO FF. puncta esse ad
eandem hyperbolam cuius
apraptori AD, AB.
Demonstratio.
Ectangulum enim C F, DP, aquale eA semper eidem : quadtato AF, inde,
omnia rectangula AD P incer se luncaqualia. quare F P puncta lunc ad can. b Ex con
dembhyperbolam, cums asymproci lunE AD, AB. Ouod tuic demonstrandum.
PR OPOSITIO CCXXVI
Eperbolae ABC sic diameter eransuerta BD ductaG; AC. ordina-
lrim ad DB, Cincillis parallele F. L. FIanE aUTeM F O ad F C, ve lunE
FF ad F F.
Dico GC esse ad candem hyperbolam.
Demonstratio.
IIaL VEEF ad FG, iId BD AIMETEK NanIVeT-
Cahyperbole A, BC adLR. DE PONANEUE P I
e CH quae aequidutene AC. quoniam PF ad
cric quoque MI ad M B, VEM HI ad ML. aC pTO-
QuEnECED MI Ad NFI, ica IB ad HL. SCdML
ad LR. ergo reccansutum DIB eA ad roctangu
reccansalum. nam cecrangulum BID ad BID.
reerangulum habel Caciohem compoltam ex ra.
cione BI ad BL, Hoc cst LII ad L. H; e ex
ratione LIad bL, Hoc est R HI ad RTT. est au-
cem quadracum lF, ad PR quadratum vereccan-
sulum DTB ad DFB reccangulum, quoniam supponitur D B erantuerla diame-
cet hyperbolae ABC: igirur etiam recrangUIUM RHIL. ad KFTL, rectangulum
est requadracum IF. ad PE, quadrarum, hoc est quadratum FIL ad HII, quocirca
LG6, cA hyperbola. Quodtuir demonstrandum.
huiius.
Ix ACB, ad eunde aXCM
CF: crectâ deinde AD que
CXXV
FB eam racionem habene quam M B ad M L
inde re MIad IB, ica M EI ad HL. e consc.
eAt ad MHI hoc CA F F 2d F G, VE BD adL R.
ex construccionesigitur ve IB ad HIL, ica cA BD
lum DIB, ve es recranGUIUM KHIL. ad XHI.
dens
otet te u u  e u    s  te t e ste e   e ee   t  t e  e      se i    t e  te  t    e       e i  et    ) t