Valerio, Luca, De centro gravitatis solidorvm libri tres

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/106.jpg" pagenum="19"/>
              nium prædictorum cylindri AE cylindrorum ſupremus
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              FE, cuius axis BH, & communis ſectio plani per pun­
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              ctum H tranſeuntis baſi hemiſphærij cum plano per axim
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              BD, ſit recta FGKHMNL. </s>
              <s>Quoniam igitur rectan­
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              gulum DHB bis vna cum duobus quadratis DH, BH,
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              æquale eſt BD quadrato: & rectangulum DHB bis
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              vna cum quadrato BH, eſt rectangulum ex BD DH tan­
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              quam vna, & BH; rectangulum ex BD, DH tanquam
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              vna & BH, vna cum quadrato DH æquale erit quadra­
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              to BD, hoc eſt quadrato FH: quorum quadratum KH
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              æquale eſt rectangulo ex BD, DH, tanquam vna, & BH;
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              reliquum igitur quadrati FH dempto quadrato KH æ­
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              quale erit reliquo quadrato DH, hoc eſt quadrato GH:
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              & quadruplum quadruplo reliquum quadrati FL dempto
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              quadrato MK toti GN quadrato, hoc eſt reliquum circu
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              li, FL dempto circulo MK, æquale circulo GN. </s>
              <s>Qua­
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              re & GP, cylindrus reliquo cylindri FE dempto QK,
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              cylindro æqualis erit, propter æqualitatem altitudinum.
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              </s>
              <s>Similiter oſtenderemus ſingula reliqua cylindrorum eiuſ­
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              dem altitudinis, in quos totus cylindrus AE ſectus fuit,
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              demptis cylindris hemiſphærio circumſcriptis æqualia eſ­
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              ſe ſingulis cylindris cono EDR inſcriptis, quæ inter ea­
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              dem plana interijciuntur. </s>
              <s>Tota igitur figura ex prædictis
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              cylindrorum reſiduis reliquo cylindri AE, dempto he­
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              miſphærio inſcripta æqualis erit figuræ cono EDR in­
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              ſcriptæ: deficit autem vtraque harum figurarum hæc à co­
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              no ADR, illa à reſiduo cylindri AE dempto hemiſphæ­
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              rio minori exceſsu magnitudine vtcumque propoſita; re­
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              liquum igitur cylindri AE dempto hemiſphærio æquale
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              eſt cono EDR, ſed conus EDR; hoc eſt conus ABC cylin
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              dri AE eſt pars tertia; reliquum igitur cylindri AE dem­
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              pto hemiſphærio, cylindri AE eſt pars tertia, hoc eſt cylin­
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              drus AE triplus dicti reſidui:
                <expan abbr="quamobrẽ">quamobrem</expan>
              AE cylindrus ſeſ­
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              quialter hemiſphærij ABC: &
                <expan abbr="cõuertendo">conuertendo</expan>
              , hemiſphærium </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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