Baliani, Giovanni Battista, De motv natvrali gravivm solidorvm et liqvidorvm

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    <archimedes>
      <text>
        <body>
          <chap type="bk">
            <pb xlink:href="064/01/091.jpg"/>
            <subchap1 n="5" type="proposition">
              <p type="head">
                <s id="s.000670">PROPOSITIO V</s>
              </p>
              <subchap2 n="5" type="statement">
                <p type="main">
                  <s id="s.000671">Data diuturnitate in plano perpendiculari
                    <lb/>
                  motus gravis, quod perseveret moveri super
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                  plano declinante; & data super eo diutur­
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                  nitate, reperire longitudinem.
                    <figure id="id.064.01.091.1.jpg" xlink:href="064/01/091/1.jpg" number="52"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="5" type="proof">
                <p type="main">
                  <s id="s.000672">Ducatur grave perpendiculariter per AB diu­
                    <lb/>
                  turnitate C, & demum super plano incli­
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                  nato BD, & data sit diuturnus E.</s>
                </p>
                <p type="main">
                  <s id="s.000673">Perquirenda sit longitudo super BD quam grave
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                  conficiat diuturnitate E.</s>
                </p>
                <p type="main">
                  <s id="s.000674">Fiat ut C ad E ita AB ad BF
                    <arrow.to.target n="marg167"/>
                  , unde si AB
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                  concipiatur tanquam diuturnitas motus super
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                  AB, erit BF diuturnitas motus super BD.
                    <lb/>
                  </s>
                  <s id="s.000675">Producatur FB donec concurrat cum A G ori­
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                  zontaliter ducta in G. </s>
                  <s id="s.000676">Et fiat CD tertia pro­
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                  portionalis ad GB, GF
                    <arrow.to.target n="marg168"/>
                  .</s>
                </p>
                <p type="margin">
                  <s id="s.000677">
                    <margin.target id="marg167"/>
                  Per 12. sexti.</s>
                </p>
                <p type="margin">
                  <s id="s.000678">
                    <margin.target id="marg168"/>
                  Per 11. sexti.</s>
                </p>
                <p type="main">
                  <s id="s.000679">Dico BD esse longitudinem quaesitam.</s>
                </p>
                <p type="main">
                  <s id="s.000680">Quoniam AB est diuturnitas ipsius AB per sup­
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                  pos; GB erit diuturnitas ipsius GB
                    <arrow.to.target n="marg169"/>
                  , at GF
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                  est diuturnitas ipsius GD
                    <arrow.to.target n="marg170"/>
                  , igitur residuum BF
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                  est diuturnitas BD. </s>
                  <s id="s.000681">Quod etc.</s>
                </p>
                <p type="margin">
                  <s id="s.000682">
                    <margin.target id="marg169"/>
                  Per 15. primi huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000683">
                    <margin.target id="marg170"/>
                  Per 3. pr. huius.</s>
                </p>
              </subchap2>
              <subchap2 type="corollary">
                <p type="head">
                  <s id="s.000684">Corollarium.</s>
                </p>
                <p type="main">
                  <s id="s.000685">Grave prodibit per AB, BD aequis tempo­
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                  ribus si diuturnitas E fiat aequalis diu­
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                  turnitati C.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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