Valerio, Luca, De centro gravitatis solidorvm libri tres

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/146.jpg" pagenum="59"/>
              tij ad quartum, & ſic ſemper deinceps vſque ad vltimum
                <lb/>
              XF (duplicatæ enim ſunt talium cylindrorum rationes
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              earum, quas inter ſe habent diametri æqualibus exceſsibus
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              differentes circulorum, qui ſunt ſectiones coni, & baſes cy­
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              lindrorum, ex quibus conſtat figura cono EDF circum­
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              ſcripta, ſumpta progreſſione proportionum eodem ordine
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              gradatim à minima diametro vſque ad maximam EF) ita
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              erit cylindrorum deficientium, ex quibus conſtat figura
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              circumſcripta reliquo cylindri AF, dempto ABC hemi­
                <lb/>
              ſphærio, minimi, cuius axis DL ad ſecundum minor pro­
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              portio, quàm ſecundi ad tertium, & ſic deinceps, vſque ad
                <lb/>
                <expan abbr="maximũ">maximum</expan>
              XF, communiter ad conum EDF, & prædictum
                <lb/>
              reſiduum pertinentem, ſicut & eorum baſes circuli deficien
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              tes, quæ ſunt dicti reſidui ſectiones. </s>
              <s>Cum igitur tam maxi­
                <lb/>
              mi cylindri XF communis, quàm binorum quorumque reli
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              quorum cylindrorum circa conum EDF, & prædictum reſi
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              duum inter eadem plana parallela conſiſtentium, quorum
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              axis communis in BD, commune centrum grauitatis in axe
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              BD exiſtat, erit ex antecedenti punctum K, quod pono
                <lb/>
              centrum grauitatis coni EDF, idem reſidui ex cylindro
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              AF, dempto ABC, hemiſphærio centrum grauitatis.
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              </s>
              <s>Quoniam igitur quarum partium eſt octo axis BD talium
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              eſt BG quinque, & BK duarum (ponimus enim nunc K
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              coni EDF centrum grauitatis) qualium eſt BD octo, ta­
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              lium erit GK trium: ſed KH eſt æqualis BK; qualium
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              igitur partium eſt GK trium, talium erit KH duarum, ta­
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              liſque vna GH; dupla igitur KH ipſius GH: ſed ABC
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              hemiſphærium duplum eſt prædicti reſidui, cum ſit cylin­
                <lb/>
              dri AF, ſubſeſquialterum; vt igitur eſt
                <expan abbr="hemiſphæriũ">hemiſphærium</expan>
              ABC,
                <lb/>
              ad prædictum reſiduum, ita ex contraria parte erit
                <expan abbr="lõgitudo">longitudo</expan>
                <lb/>
              KH, adlongitudinem GH: ſed H eſt centrum grauitatis
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              totius cylindri AF & K, prædicti reſidui dempto ABC
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              hemiſphærio; ergo ABC hemiſphærij centrum grauitatis
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              erit G. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
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