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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/031.jpg"/>
            <subchap1 n="11" type="proposition">
              <p type="head">
                <s id="s.000167">PROPOSITIO XI.</s>
              </p>
              <subchap2 n="11" type="statement">
                <p type="main">
                  <s id="s.000168">Si Duo gravia descendant alterum super li­
                    <lb/>
                  nea perpendiculari, alterum vero super
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                  inclinata; proportio velocitatum est reci­
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                  proca proportioni linearum.
                    <figure id="id.064.01.031.1.jpg" xlink:href="064/01/031/1.jpg" number="12"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="12" type="proof">
                <p type="main">
                  <s id="s.000169">Sit ABC planum normaliter erectum super
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                  lineam orizontalem BC, cuius latus AB sit
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                  perpendiculare, & AC, inclinatum.</s>
                </p>
                <p type="main">
                  <s id="s.000170">Dico quod proportio velocitatum solidorum gra­
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                  vium motorum secundum lineam AB perpen­
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                  dicularem, & AC inclinatum, est ut propor­
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                  tio longitudinis inclinatae AC ad longitudinem
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                  perpendicularis AB; videlicet ita est longitudo
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                  AB ad longitudinem AC, ut velocitas super
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                  AC ad velocitatem in AB.</s>
                </p>
                <p type="main">
                  <s id="s.000171">Quoniam est ut AC ad AB, ita momentum in
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                  AB, ad momentum in AC
                    <arrow.to.target n="marg28"/>
                  ; & ut momentum
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                  in AB ad momentum in AC, ita velocitas in
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                  AB ad velocitatem in AC
                    <arrow.to.target n="marg29"/>
                  ; ergo est etiam
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                  ut AC ad AB, ita velocitas in AB ad veloci­
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                  tatem in AC. </s>
                  <s id="s.000172">Quod fuit probandum.</s>
                </p>
                <p type="margin">
                  <s id="s.000173">
                    <margin.target id="marg28"/>
                  Per 4. supp.</s>
                </p>
                <p type="margin">
                  <s id="s.000174">
                    <margin.target id="marg29"/>
                  Per 2. pet.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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