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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1019, page id 1815201908:1076
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V N GVLA CYLINDR IC A.
1O19
ita etiam parces superticierum sphaerx diuilx pex circulos rectos ad axem
eandem racionem corinent quae incer segmenca axis facta elt.
VrcM diamerer circuli ad semiperimetrum ciuldem, ita quoque cst
Ephaerae luperficies ad cylindrum alcicudinis que xquatur perimetro cir-
culimaximi: Pari pactovr diamecerunsula est ad perimerrum semicir-
cularem, ita est ongularis superkicies ad semicylindricam ejuldem altieu-
dinis.
Ouam racionem obcinet superticies rnius (phaerx ad alcerius superti-
ciem, eandem leruane inter se proportionem vngulares luperticies, modo
proporcionales linebales ongulares cum maximis circulis sphxrarum.
Ouemadmodum superticies sphaerx quadrupla est maximi circuli, ita
d superticies curua vrigulx cuius alcicudo par est perimerro circuli qui
balis est rngula, quadrupla est eiuldem circuli.
Sicur superhcies cxlindri sphaeram ambientis selquialeera cAt (up erH-
ciei spharae, ita et prilmatis rngulam concinencis, ca lupertcies qua cur-
nam rnsulxe superticiem cingic, ciuldem est se lquialcera.
VII
Ouemadmodum sphaerx superkcies aqualis est circulo cuius radius
par elt (phaera diamerro: ica eriam rngula cuius alcicudo par est diame-
ero balis, xquacur quadraro cuius larus eAt diameter.
Alias Gymbolizaciones non prosequor, Cufficir enim hac inlinuasse Le-
ctori, ne longiorsim quam oporcet. demonstrariones veroharum pro-
prictatum pleraq: a nobis in propolirionibus peaecedencibus eradiex
Tunc: exerera vel exnoctris, vel ex Archimede d Pappo non ditficulrer
ExVICHTOT.
n