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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 345, page id 1815201908:0402
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PROPOSTTIO CNOI
ELLTPSTS.
348
Scrriangulum maximum, continger recta BF. _ circulum _ ellipsim: igieur a (C- 2159. hu-
micirculus AB C aequarur semiellips AP. C. Ouod erat demonstrandum.
auclemiellipl.
Lliplis est ad cirtu et Cmpm veeriangulum Maximum inseri.
spcum semiellip l ae asulum maximum inleripeum lemicirculo
Demonstralio.
Vm enim se velemiellipls ad semicirculum aue lemiellipum, ica coca ellipES 2d
eorum circulum aur ellipsim; erieb verriangulum maximum AF C SemieslIp (IBIgO. hu
inseriprum ad criansulum maximum D P. P semicirculo auc lemiellipsi interipeum, no.
ica ellipsis ad circulum ad ellipsim. Ouod erat demonstrandum.
PROPOSITIO CXCII
 circulo vel CliplI DF F elliplim aqualem exhibere. Ft dacxe
elliphreteuut aqualem.
Constructio e demonstracio.
Emicirculo VeL SCMTCMPU D F F inscribacur crianculum maximum D P, F, cui
Aat aequale aliud quodcumque criangulum A B C, dinisaque A C bitariam in C)
dueaeur B G, _ procrahatur B CF in FI, DE B C, GFT SnE aequales, _ S AC, BFI
selead rectosinterlecene, describatur ellipss A B CFI cuius aXeS SInE A CBFI, A
aurem non ad rectos sele interlecent, daris A C BHI coniugatis diamerris axes in-
venianEuEC circa quoS deseribacur ellipsS AB C TI. Dico cMlipHM ABC FT circu. C60 huins.
10vel ellips D F F aeguari: est enim criangulum AB C maximum eorum quae se-
mielliph inscribi pollune aquia A C BF ponuneux diamerri coniusacX. quare cum  A2. huius.
criansulum maximum semiellips inscripeum aequale sic criangulo maximo cir-
30. hu-
culo vel elliphi inscripro, exic e elliplis AB C circulo vel ellips D E. F. aqualis. Cx- ins:
BO quodpecebatur.
Ex his secundx partis constructio et demonstrario est manifesta.
Corollarium.
paceaasdari eiples cleculo vel ellipu ABC aequales, qud cltalis
ABC dancur insinica rriansula aequalia.