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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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N CV LA CYLINDRTCA.
Demonstratio.
E
Motosicionem paulo ance demonstrauimus quidem: veruim praelens demonstra-
cio commodior mihitucura est ad vlceriores proporriones indagandas. Ponaneur
itaque deocirculi A BC, D F F, quorum singuli in sciplos duai produeane lingulas
ongulas. inlcribantur circulss Parabola I. I, MIMI. Demonstracum fuit 2 vngulam 2128. Duc.
productam ex ductuplani circularis GTI in sciplum, aequalem esse Colido quod ba.
Sim habee P. II, alcicudinem Cemidiamerro xqualem. codem modo oltentum cA le
micirculum TK in se ductum exhribere corpus sub bas MI K, ex alcicudine qua x
qualis est semidiam eero. Igitur eandem habebuncrationem incer se iIlx dux visulaex
quam concinene corpora ex balibus parabolicis constancia. Aequi horum proporcio
composica est ex b proporcione alcicudinis BM ad F O, hoc eA A C ad DF, ex ex b13 huius.
racione baleos parabolicx P II ad balim parabolicam MTR. quae eadem est cum
racione circuti AB C 2d D F F, (similes enim Cuncillae parabolx, ve pacec extiguris
inseripeis euideneer,) ac proinde duplicara rationis AC ad DF. ergO Fatio COrpO
ris (uB T FIbaC, _ BM alticudino ad corpus (ub bali MK, ex alcicudine F, O. est
criplicata rationis AC ad DF; ergo rngulx illis corporibus parabolicis xequales in
criplicara suncratione carundem linearum, (cilicee diamerri AC ad diaMCEruM DF.
Quodtuic demonstrandum.
PROPOSITIO LAAI.
Vod si placuerie cam diteuCn tOa daMiDerC, qu a Vi LuIuS
aploporcionibus 4). el 47. Libri de duetu plant ia Plahum, Mccbic
etiam vericacem praecedenris cheorematishrunc in modum demon-
ACaTC.