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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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CAt
LLIDSIS
ROPOSETIO XLIV
Llipsima ABC Secet diameter BD, ad quam ordinatim pOSICa BIE
AE. C: jutictis AB, CB inscribatur LGho AFB triangulum
axIuAFB, e ex FPonacur F C; Parallela A C, iungancurque B G,  C.
Dico BCC criangulum esse maximunt corum qua seomento BO C
etor poctum, de  ata, aico f. li elle paralle-
tam ad AC.
Demonstratio
DVoniam = PFI G I linex lunc aquales, criangula FBH, GBL eandem haben
Lcia alcicudinem, ae qualia erunc. Similicer criansula F A FI, CTC incer paralle-
laS F G, AC consticura crune xqualia ac proinde a quabuncurcora riangula B F A,
BOC: S isicur BC C non sic maximum, ponatur aliud BP C, maius criangulo
BOC, e ex L ducacur L. M aequidistans AC, cririsiturre priuscriansulum BL. C.
aequale criangulo AMB, adeoque ec AM B criangulum, maius criansulo BCC
id ek AF B, quod est concra supposicum, cu B F A maximum ponacursgitur B GC
criangulum maximum est eoru quxe segmento B C. C inscribi posunc. quod erac pri-
mum. sinc deinde exiangula BF A, BC C. maximque demonstrabimus iunctam LiC
parallelam eAe AC. E enim non est parallela, sc alia lupra vel intra iplam F C P2-
callela ad AC, nimirum recta F L: iungancurque BL, CI. ergoper primam par-
cem huius criangulum BL C eriemaximum, quod heri non porest cum LCC ex
hypochesi siemaximum. Non igicur F L, aur alia vIla praecer FC est parallela ad AC.
Ouoderat secundo loco demonttrandum.
226. hulus.
Corouarui permum.
Ine lequieur si erianoula BF A, B C C maxima Cnc eorum gua segmentis inseri-
Apipostune, esse aequalia. Nam per secuman palcemuuas ee en parallela ad
AC. Vndeb FHI, CI aequateslun, de proinde eriansula liBL, BLCr, _ F AR, 1bid.
BC acebs de tota BL A, BC C. equalia lune.
Corol