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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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ad ellipum IDE: dico ex sectorem AG C cNe ad sectorem DFTF, ve cs circu-
lus AB C ad ellipsim ID F: invenco enim ve ance ellipseos D F. F maiore axe IK.
arBg.h- Supex IK ve diameero describatur circulus NOK: ductaque ordinatim P. M quX
Termencum L. IM auteracaquale seomento DF F, hanc reliqua ut prius. segmencu
isicur NVIP estad Ccomentum L. IP, vea circulus NO K ad ellipum ID F. Icaq; (c.
ementum NTO ad sesmencum L IMI, ve circulus NOK ad ellipsim: de permu.
tando, circulus NOK ad Segmentum NTO, rcelliplis ad segmentum L. TH, hoc
est exhypochesi vecirculus ACV ad segmencum A B C. Cum ergo se ve circulus
NOK ad scomentum NITO, ita circulus A C V. ad sermentum AB C, CxiF CF
iamb re circulus NO K ad sectorem NFFO, ica circulus A C V ad scCOrO AOC.
Acquire circulus NOK adlectorem NET O, Sic clliplis ad lectorem L. TIM, hoc
est quoniaM segMENEA L TMI, D P. F sunt aequalia. ad sectOReM D FTF. CrgODE Cir-
culus AC. V ad lectorem AB C, ita ellipsis ad sectorem DFF. Ouod erat demon.
Arandum.
PROeOStITO CIMNa
Ao A D B circuli diametet AB divila vecunque in C, dE per CnOF
LIaLIS DOLITA DE, SIE aurem d FC, diamerer quacunque ellipseo
dinila in HI, ve AB est In C, _ per HI ordinacim ducta lR.
Dicoleomentum DBF. eNead segmentum LC: IE vr cA circulus ADB
ad clip(I FL C, dECONETA.
Demonstratio.
18.
rectangulum B C A est ad rectangulum L. NM, ve quadratum D C ad quadratum
ON, ledraciorectanguli BC A ad rectangulum I NM; componitur ex racioni-
bus BC ad L. N, _ C A ad NM. ergo rationes B C ad L N, _ C A ad NM
Cmul sumpex aequancur rarioni quadraroru D C, O NT, hoc est rationi ad D C, O Nbis
Cumpeae. Aequirariones BC 2d LIF, _ C A ad NM, sunc caedem siuc aequales,
cum sinc B A, IMI ex hypocheh proporcionalicer divilx; ergo carum vna B C ad L. V
eadem eAracioni DC ad O NV: Cod, cum sC ve BC ad I NV, SC C A ad NM, crie
quoqueve BC aa L H, lC B A ad L. M. Guare b A adt L. M, id ett SI ad0l.
Nuento ellip(eoSaxCMmBIOrE L MI, de LCHBACTMIPEL L H CHCUIUS L.OM. MMaGi
LMI in PT, DE AB est dinila in C, agatur per Nnormalis OP, secans elliplim in
Oe R: ducantudetemidiame L.L. ALit L. KCaaMMIUM BC AC
ad quadracum D C, ve rectangulum L NMT ad quadracum ON, de permucando
 e at i   ste tete  t e a te s e te te ee    et  t ste tet  t e s t i   e e te et e e es et   e t  t  et st  te e 1 1  u e e      p  l u 1t 1