Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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NACO, ad cylindrum, vel portionem cylindricam NM,
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eſse vt rectangulum BER, vnà cum duabus tertiis ED
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quadrati, ad quadratum BD. </
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>Ijſdem enim quæ in præce
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denti conſtructis, & notatis, ſit præterea cylindrus, vel por
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tio cylindrica PL, circa axim ED circumſcripta cono,
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vel portioni conicæ KDL, Quoniam igitur reliquum
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cylindri, vel portionis cylindricæ NM, dempta portione
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NACO æquale eſt cono, vel portioni conicæ
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K
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DL,
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erit reliqua portio NACO æqualis reliquo eiuſdem NM,
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dempto cono, vel portione conica KDL. </
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culi, & ſimiles ellipſes inter ſe ſunt vt quadrata diametro
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rum, vel
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eiuſdem rationis: cylindri autem,
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& portiones cylindricæ
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altitudinis inter ſe vt baſes;
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erit vt quadratum EM, hoc eſt quadratum BG, ad qua
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dratum EL, hoc eſt vt quadratum BD ad quadratum
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DE, propter ſimilitudinem triangulorum, ita ſolidum NM
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ad ſolidum PL: & per conuerſionem rationis, vt quadra
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tum BD ad rectangulum BED bis, vnà cum quadrato
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BE, ita ſolidum MN, ad ſui reliquum dempto ſolido
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PL: & conuertendo, vt rectangulum BED bis, vnà cum
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quadrato BE, hoc eſt rectangulum BER, ad quadratum
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BD, ita reliquum ſolidi NM dempto ſolido PL ad ſo
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lidum NM. Rurſus, quoniam eſt vt quadratum EL ad
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quadratum EM, ſiue BG, hoc eſt vt quadratum ED ad
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quadratum BD, ita ſolidum PL ad ſolidum NM, ob
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ſimilem rationem ſupradictæ: & duæ tertiæ partes ſolidi
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PL eſt ſolidum KDL; erit ex æquali, vt duæ tertiæ qua
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drati ED ad quadratum BD, ita reliquum ſolidi PL
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dempto ſolido KDL, ad ſolidum NM: ſed vt rectangu
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lum BER ad quadratum BD, ita erat ſolidi NM reli
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quum dempto ſolido PL, ad ſolidum NM; vt igitur pri
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ma cum quinta ad ſecundam, ita erit tertia cum ſexta ad
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quartam; videlicet, vt rectangulum BED, vnà cum dua
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bus tertiis ED quadrati ad quadratum BD, ita reliquum </
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