Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO VII.
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<
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>Si conoides parabolicum, vel hyperbolicum
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ſecetur plano vtcumque ad axim inclinato, ſectio
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ellipſis erit: ſimilis autem ipſi alia quæcumque
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ſectio conoidis eidem parallela: eruntque earum
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omnes diametri, quæ eiuſdem ſunt rationis in eo
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dem plano per axem. </
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<
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>Manifeſta ſunt hæc ex ijs, quæ Federicus Commandinus
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demonſtrauit de ſectionibus horum ſolidorum, in ſuis com
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mentariis in eundem Archimedis librum de ſphæroidibus,
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& conoidibus: quemadmodum & ſphæroidis, & conoi
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dis vtriuſque ſectionem factam à plano ad axim erecto eſ
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ſe circulum. </
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PROPOSITIO VIII.
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<
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>Super datam ellipſim, circa datam rectam line
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am ab eius centro eleuatam tanquam axem, coni,
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& cylindri portionem inuenire. </
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<
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>Datoque ſphæ
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roidi, & conoidi, vel conoidis, ſphæroidiſve por
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tioni circa datum axem ſphæroidis, vel cuiuslibet
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dictarum portionum, cylindrus vel cylindri por
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tio circumſcripta eſſe poteſt: vel comprehendere
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inter eadem plana parallela, ita vt eius baſis ſit ſi
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milis baſi, vel baſibus comprehenſæ portionis, vel
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fruſti, ſi de conoidibus ſit ſermo: & diametri, quæ
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eiuſdem ſunt rationis ſectæ à centro bifariam ſint
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in eadem recta linea. </
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