Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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vel portionis cylindricæ reſiduum dempto fruſto,
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ad totum cylindrum, vel cylindri portionem; vt
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rectangulum contentum diametro minoris baſis
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fruſti, & differentia diametri maioris, vnà cum
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duabus tertiis quadrati differentiæ, ad quadra
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tum diametri maioris baſis. </
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>Sit coni, vel eius portionis fruſtum ABCD, cuius baſes
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oppoſitæ, circuli vel ſimiles ellipſes, quarum diametri mi
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noris baſis AB cuius centrum E: maioris autem CD,
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& ſuper baſim circulum, vel ellipſim CD ſtet cylindrus,
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vel portio cylindrica CG comprehendens fruſtum AB
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CD, eiuſdemque altitudinis cum ipſo, & conus, vel co
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ni portio ECD. quo autem AC diameter ſuperat dia
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metrum AB, quæ differentia di
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citur, ſit DF. </
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<
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>Dico fruſtum AD
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ad cylindrum, vel portionem cy
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lindricam CG, eſſe vt rectangu
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lum DCF vnà cum tertia parte
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quadrati DF, ad quadratum CD.
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<
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>Ad conum autem vel coni portio
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nem ECD, vt rectangulum DCF,
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vna cum tertia parte quadrati DF,
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ad tertiam partem quadrati CD.
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<
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>Cylindri autem, vel cylindri por
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tionis CG reſiduum dempto fru
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ſto AD, ad cylindrum, vel portionem cylindricam CG,
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vt rectangulum CFD vna cum duabus tertiis quadrati
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FD, ad quadratum CD. </
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<
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>Cono enim, vel portioni coni
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cæ, cuius fruſtum AD, & cylindro, vel portioni cylindri
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cæ, cuius baſis eſt circulus, vel ellipſis CD, altitudo au
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tem eadem completo cono, vel portioni conicæ iam dictæ,
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illi pyramis, huic priſma inſcripta intelligantur, quorum </
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