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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 193, page id 1815201908:0250
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n (Ic
incet
CI
Onet
onstrain
uo
e licaqt
Cicpe
BC
delerie
Concin
10
qual
p
E Ait
JUm.
CIR CV LYS.
e R OPOSIFFO XLV.
Dem praectare a puncto inera aream circuli posito. Oportet aurem dat2
hoc calu non minorem esse rectaillâ, quxe per P. polica ad diame-
rum, per L quoque cran lcuncemnormalis (II.
Demonstratio.
Aex A veprilis, accommodetur in cir-
culo, equalis BD: cenerogue F circu.
Ius delcribatur concingens BD in HL, EFaN-
sibic ille per punctum dacum F, vel infra
illud cader: cum enim ex hyporhesinorma-
lis per E ducta 2d diamerrum, Det P, quo-
que ductam, maior essenon posie daca li.
nea A, id cA D B: PatCE _ P F diameerum,
qua rectam per R ductam sccat orthogona.
licer, maiorem non esse diamerro, quxe li-
neam D B daca A Xqualem orthoxona-
licer diuidercc. vnde circulus radio F II deCoriprus, vel cransic per F, vel intra cadet.
veraque calis agacur per P concingens circulumradio F.HI delcriprum, parecillam
requari recta DB, id est dacae A: quare Fecimus quod poltulabaEUT.
PROPOSITIO XLVI.
Dato extra circulum puncto lineam educere quae in data ratione à
Laperimerro dividacur: oportet aucem rarionem daram, maiorem
non esse illa que repericur incerparces linexe quae a dato puncto per cen.
erum ducicMI.
Constructio e demonstratio.
Ec dacum punctum A ec circulus BCD:
daca quoque ratio AIE B ad Li, quae minoe
sic racionis AB dd BD, parrium diamerris
Aac rectis P, F aequalis CTT, e CIquidem
ApAE: intentaque K media inter IG, CFI)
POnAEUT Ex A COnTinSCNS AC, _ VE R ad
GIsiC AC AaC ad AL: Pacoe ex datis
AL minorem ese A C, e non minorem
AB, adengue punctum T in perimecdcl.
se circuli: ducatur igirur per L ex A linca
AM occurrens circulo in P _ M, dico
AM Cacistacere pecicioni; cum enim L AM
rectangulum aequale sc quadratO AC e
TOTI rectangulum quadraTO R, POnacuE
aliem e I. A 2d AC ve IC ad K. crune
CI. R, CII linex proportionales ciuldem
ACELHS EUM ALS AC, AM; vndo vePrI.
in2 OI ad excessum FII, id est per con- 
Aructionem DE E ad F, SiC ,A F. quarra ad
excessum L. M. eduximus igicur à dato punrc
40, _c. Quoderartaciendum.