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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 651, page id 1815201908:0708
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Perbo.
nC
d
queC
EB. I
r0AB
dHI
e
IVE
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B, 11
101
1b
cim
Demonstratio.
FX P
Veacur linea A FTCccaS lineam B C,
ICVEHLC, C A Eincx quales; de AanC
eres quancicaces ill continur analogia
convertam propolic. 7. Uaius. Fiat
praeccrea rectis CElastates LK: crun
igicur rectangula ITC: R. X Gaa Gua
Otacis C C. IgicuE A C+ C+ estBypCIOO.
CTT, C B, CI: crir II linca recta per
a quodica parcbic. Pertacur Ml. L. Xqui
dictans AD. Isitiir per 192. huius
G, AanC quadrata C C aequalia rectan.
ulo FTCL, una cum rectangulo LL C L R, etir G G hyperbola: sed quadracum
ETC vna cum quadeaco C B, aquale est recranoulo HCK; hoc cs i
HCP. una cum quadrato XI, vel HIC. isitur AC. F sunc ad eandem hyverbolam.
Duod tuic demonstrandum.
ngulo
tA1TIO CC42_
IE AB axis tipperbolx B C D, cuius F cenerum, de aris coniugatus
FC, de axi patalsela
DFE, CcenErOvero F ductis diamerris E C POnanEuEC, CII, xquales
Dico BHH Core hyperbolam.
Demonstratio.
Donacur ordinatim C I_ HIR. quoniam BCD
hyperbola est eric AIB ad AI B; rectangulurt
vegnactatum CI ad C I quadtAcaM. Polca ica-
que BC; oux equidistet EF, et hyperbola op
POLITA AMMi CriE recrangUIUM M L C AdML C,
ve quadracum L B ad L B, hoc es CIad C l, qua-
dracum. Sed quadratum P.C aGuase est quadraris
PL e CI; hoceA quadrato F B e reccangulo
ATB; una cum quadeaco CI: est aucem quadra-
cum CHI illis iplis aquale; isicur ablaco commu-
crangulum FC O aequule quadraro C I, quoniam
niquadeato CI remanet L. HIN; aquale rectan-
sulo AIB iria cum guadraro CI. eric ergo re-
cionem hiabecquam quactacu Co L ddl. C haC csF HlR aa HL R. Quacalum Pacee
aixitur B H H esse ad candem hyperbolam. Quodtui demontet as ., 1. 11 a 3. huipi.
.  ta Bet
recransulo AIB RGUaEUE MN C reccangulum
quia vero est ve C I quadracum ad C I quadra-
ccatulum OMH ad OMHI. vereccangulum MC ad MHC, reccansului
cum; ita rectangulum A tB ad A TB, hoc est MEY C ad MINIC, erit quoque rC:
ergoeclam recransulum O fL. al, OIHI AOC CIC A AB a AKB; canidem rg
11.
epst
 (e 11134CAY15.
. L (113B5D e1t. Y X ios e AC
13t
RC
A    e    te  s qu te e te t e at s. t  p et    u  te e t. e te it  te e e e stet e   et s  s  e u e     e          t