Valerio, Luca, De centro gravitatis solidorum, 1604

Table of figures

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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. </s>
              <s>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. </s>
              <s>Et quoniam cir
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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 </s>
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