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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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V ADR A Y VR A CIR CYLI
Svrotos 1
ipso cylindro quanticare minori quam C, quo Facto etic corpus extindeo inscripeum
eciam maius corpore quod sic ex ductu mucuo parabolarum. Procrahaneur deinde
Paralselae F B verimque in D, ex F, FI, compleancurque rectangula cam F. DI, in-
icripea parabola AD C, quam B FI, conseripes parabole FC A: ac deinde rectan-
sula F. I, ducta in rectansula P. HI producane parallelepipeda que corporinato ex
parabolis parcim inscripea cruneparcim circumseripea, bases aurem habebune re.
ctangula D F P, alcicudines vero lineas F. F. Demonstranimus in libro ductuum
~rectangula omnia D P F aquari rectangulis BF, AC. Ouare cum reccangula
DF F bases sint paraltelepipedorum adscripeorum corpori parabolico quae AWNE ex
FD I n F HI: reccangula vero BF AC, BF. AC sine bases parallelepipedorum in-
scriptorum crlindeo ee alcicudines verobique sine communes, lineola munirum P. P,
manifeltum cAt agoresarum paralle lexipedorum adscripeorum corpori parabolico
aequariageresaro parallelepipedorum cxlindro inscrixcorum, (ed aggregacum paral.
lelepipedorum inscripeorum cxlindro maius ponicur corpore naco exparabolis ergo
e aeoregacum parallelepipedorum ad scripcoru corpori ex parabolis producco ma-
inselt eodem corpore; quo drepusnac propolicionis o. in qua demonstrauimus cAC
minus, non isicurminor eA erlindrus corpore a parabolis producro.
Superest ve ostendamus eundem cxlindrum non esse minorem COrPOre GenicO
ex parabolis. Si enim cxlindrusminor sic, crie corpus parabolicummaius cylindio v.
8. quancirare C, ostenlum est in libro ductuum b A C in eoc posse aqualesparces sub-
dividi, duccisque per divisionum puncca reccis D R E ad AC normalibus coc in-
scribi parabolis subalcernis posse recrangula E. DL, FDT, RPR, F. F K, reomnia
F. D T ducca in omnia P FR inscribanc corpori ex parabolis Cuhalcernis genieo ap
Sresacum parallelepipedorum defciens ab iplo corporenaco e parabolis quanTIca-
ce minoridacd C. Faccumigicur hoc sic: erir ergoaggresacum illu L paraltelepipe
dorum maius cxlindro. Duare si produeris lineis D F compleancur reccangul+ F. LI.
F HI parabole FC A circumlcripta; e reccangula FDI, F. D I ducra in reccan-
sula F. II, P FT, Producane agzrcgacum parallelepipedorum, eric hoc aggregacu mul.
romaius cxlindeo. (e d hoc aggresacum paralle lepipedoru, que niirum GUINECX
F DL, F FI. supra ostendi in prima parce demonstrationis eguari ropreraco paralle.
lepipedorum cxlinden inscripeorum. Ergo etiam hoc cxlindro maius cAt, pars luoco-
co, quodherinon porest. Non est ervo cylindrusminor corpore a parabolis producto.
sed neque maiorem cAe oltendimus. Pidem isiur xqualis est. Ouod erac demon-
Arandum.
Corollarium.
Odem dilcurlu demontenu eena lublcetta pacabolica DLLD. AtLl
dueca in se muruo aquale colidum producere sesmenco exlindrieo cujus balis est
sexmencum circularc B L. F. B, alcicudo AC.