Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XX.
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<
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>Omnis portio ſphæræ, vel ſphæroidis abſciſsa
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duobus planis parallelis centrum intercipienti
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bus, ad cylindrum, vel cylindri portionem, cuius
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baſis æqualis eſt circulo maximo, vel ſimilis, &
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æqualis ellipſi per centrum baſibus portionis pa
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rallelæ, & eadem altitudo portioni, eam habet
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proportionem, quam duo ſolida rectangula ex ter
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norum ſphæræ, vel ſphæroidis axis ſegmentorum
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eundem terminum habentium alterutrius ba
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ſium portionis centrum, binis ſphæræ, vel ſphæ
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roidis axem complentibus, & ſingulis axis por
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tionis itidem à centro ſphæræ, vel ſphæroidis fa
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ctis, vnà cum binis tertijs partibus duorum cubo
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rum ex ſegmentis axis portionis à centro ſphæræ,
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vel ſphæroidis factis; ad ſolidum rectangulum,
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quod duobus ſphæræ, vel ſphæroidis axis dimi
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diis, & axe portionis continetur. </
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<
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>Sit portio ABCD ſphæræ, vel ſphæroidis, cuius cen
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trum E, axis portionis KEH: ipſi autem portioni cir
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cumſcriptus cylindrus, vel cylindrica portio NO, vt in
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antecedenti, cuius communis ſectio cum ſphæra, vel ſphæ
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roide AFDG, ſit circulus maximus, vel ellipſis circa dia
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metrum LEM; quamobrem baſis ſolidi NO, eiuſdem
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altitudinis portioni ABCD circulus erit æqualis circu
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lo maximo, vel ellipſis æqualis, & ſimilis ellipſi circa LM
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baſibus portionis parallelæ. </
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<
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>Dico portionem ABCD </
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