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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 856, page id 1815201908:0913
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OYCTVSSL
Uarium.
xegtalem magnicudinem subminutare Aliquancicari quae extursir ex ductu pla-
ni SO insuxorticiem F R. Cuncenim SO. _c TR, linex xqualesrectis AV, et
Odem prortus discursu parebirbauim OV, ductam in alcicudinem diametri BD.
P. V. ve ex ipla constructione, d prxecedencium cenore laris manifestum est.
RC
OSITIO CCXXXIII.
TIrculum AB C, sccet linca per cen-
ilrum acta BD, qua diuisa bitariam
in F _ F, crectisq; ex ijs normalirer ad
diamedum rectis EO, FC, deseribatur
L. L parabolaaxem habens BD. Deinde
hanc concinux proporrionales HIN, KH,
corpusresultans ex plano R NI, in
cudinem BE, aequari magnicudini
Da(i IL, ee alcicudine BF.
Demonstratio.
Voniam concinuane eandem rationem li.
LBCX FIN, RN, MN ex constructione igi-
cur quam habebicracionem YTN ad R VP, CaH.
demhabebie HIK ad RMI. rectangulum ergo
FIN, RM XquaEuTHTKN rectangulo. demon-
Aracum est aucem rectangulum FIK O, hoc eM
FIK N, aequale eNe HP, KP rectangulo, pro
politione scilicernong ehmalecunda huius libris ibitur rectansulo FIP, FL L. Xquale
est cectangulum HN. KM. lsicur per quadraselimam quincam huius constat pro
bocrum.
u
alE
Corollarium.
Ine manifestum est lineam NM, non ese parabolam, nisi Forre quis eam etiam
rircualis nomenclatura dignari relie, ed quod ad Formalem aut veram Facile pos-
sic reduci. E enim fuerine IPI, rectxe consticuex dupla rectarum RN, eric R R el
lipsis, De exlib. de Flliph constac. posicis aucem eunc rectis IR, aequalibuS RMI; crit
RR, vera parabola, cum eandem rarionem sint habicurae rectae INI, ad NR, lineas
quam habene R D ad OF, rectas, quare PaTeE R R, non minus Fore parabolam
quam sr ex constructione facta L. L. par abola.
PROPOSITIO CCXXXIV
mis diamerri AC oCcuens LL, Contingenet qua agaer
diamerro AC, e perpuncta AB C descripra sic parabola cuius apex B;
_ per punctâ AC delcribacur parabola habens verricem in concurlit: lin
nex BD cum circulo ABC, qua producta occurrar contingenei EP
in punctis e e R.
Dico
VIrculum ABC CUIISCCNETUMD, COnEINGAnEAF, CF eductX Cter