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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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E. L. L. IP 5 IS.
Demonstratio.
Vadrarum AB aequale esta quadracis AF, F B vnZ
cum rectangulo AEB id est b quadraco HIF bis
Cumpeos quadracum vero C D aequale cAt quadraris CF,
ED, _ CFD rectangulo id est quadraco F C bis sum-
pro, sed ijidemcquadraris aequalia lune quadraca AC
EB, CFI, ITD, igicur axium quadraca simul sumpea a-
qualia sunr quadraris AC, GB, C FB TID. Ouod eraE
demonstrandum.
P R OPOSITIO LXXX.
Vadraca linearum extrema axium coniun:
gentium aequalia Cunic quadracis lincarum
qua excrema cuiuluis coniusationis coniungut.
Demonstratio.
InE ABC ellipleos axes AC, BD e alia quaevis
diameerorum coningacio P P, OFI. iungancurque
BC, C. D, F FF, FFI. dico quadrara BC, CD simulcum-
Dcaxquari quadracis P FTT, FFI simul lumpris. quadraca
BC, CD Simul Cumpca d aequalia sune quadrats BI.
TC biS Cumpeiss quadFAEA aUFeM F FTS FTF AGUANEUE
quadraris F I, PFI bis sumpris: Sed quadeata P. L, TTI. si-
nul Cumpeac sunc aqualia quadraris BI, TC Cimul sum-
Peis; igicur quadrara BC, CD simul sumpra; aqualia c
luncquadraris PHI, HIF. simul sumpris. Quod erarde-
monstrandum.
eROPOSITIO L.XXZI
ECenE ABC ellipsim, cuius cenerum D dux diametrorum coniuei-
L.DtiOneS AB, DC, BD, DE, iunctisque punctis AB, C P dividateur
AB, C F linec bitariaM IH F et C, duCanCUTq; DF; DC qux producta
Occurranc ellipli in FI e 1.
Dico HID, ID diamerrosesse coniusacas.
Demonstratio.
FOMaHI AB, DC, B D, DF, olameeri sune coniu-
SACX, CrunEE A DC; BDE lectores xquales: ablaco
SICuE COMMUNI BD C, CrUNE ADB; CD P reliqui a
quales: rursum cum AB lineam secec in F; bitariam
diamerer DH, erlinecam AD FB, BD HI i sectoreS, qud
AF D, BF D crianoula aequalia. eodem modo ostendi-
cuF F. DI sector aqualis lectori CDI, sectoros isicur
AD FTS F DI sunexquales incer se: Addicoigicur com-
muni IDI, eric sector ADI aequalis sectori HDF,
contusaca ersoh sunE DFI, DI.
H 3
erim.
a. 10. dete
E77. huius.
FCoroI. 46.
haius
8) . Muiuts.
1 erot. 60