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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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 PL A N V 1.
R OPOSITIO XVI
Emicirculus ductus in se, superticies duas proue CMMaticas, qua-
rum communisincerlectio, higura e plica.
demonstratio.
Emicirculus ponatur A B C: aeoHlum in se ductim rel in semicireulund AFC
xoualem; superhcies proddcere exlindricas B C CK. guarum communis
incerlectio A GC Fgura es ellipECa. Facto super A C rectangulo A FC, suman-
tur in RC, puncta quevis D Cquibus ad AC normales erigancur D B: ponan-
curque DF in plario AF C agMdistanceS AF. rectx DB ductx in DF supexti-
ciem producune cxlindricam BFI, ixirur _ BC lincae quae pars sunc B FL, 3d su- ais huins.
perticiem (unc cylindricam. Similicer octendetur O F. superticiem esse cylindricam.
quod vero AC C figura sic ellixeica, six osendo: unganeur DG. rectxe DB du-
Ax in se, quadrata generane D B C K, quoruin diameeri sune D G; quia vero qua-
deaca illa, b recta sune ad planum A C F, _ AF, D F parallelX, planA ABO P X. b Fix hy po
nest in
quidistane, ec criangula quoque DF C ParalIelZ lunE: quia verO D P. C anSU. defin. huins
li sune recti, e DF, G F linex aequales, anguli F. DG, FC D semirecri luNE:
in codemigitur sunc plano; clinox DC: rursum cum DO diametri sinE qua- c Educisur
deacorum DBGF, quadraca DC dupla sunc quadrarorum DB: vnde VE BD ex ctemiti.
quadracu aa ac B, le eleteclangulum ADC ad rectangulum AV C,
BC D et quadracum ad quadeatum D Cr: elliplis d ioicUF eA A G C. VOCCTUF aV. d +. D.
cet corpus constaris supertciebus DB OP, insula: Euius propricraces; et cuba. Ctis.
curam luo loco crademus.
RO P OStLIO XVII
Emicirculo si reclacis llum eruldem alcirudimis in dircetum adicta-
cur.
Dico coram illam quanticarem in se ductam superficies producere cy
lindricas, quarum communis incerlectio fipura eA elliptica.
Demon