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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/030.jpg"/>
            <subchap1 n="10" type="proposition">
              <p type="head">
                <s id="s.000159">PROPOSITIO X.</s>
              </p>
              <subchap2 n="10" type="statement">
                <p type="main">
                  <s id="s.000160">Gravia descendunt super planis inclinatis per
                    <lb/>
                  spatia semper maiora, iuxta rationem, quam
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                  habent impares numeri successive inter se.
                    <figure id="id.064.01.030.1.jpg" xlink:href="064/01/030/1.jpg" number="11"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="11" type="proof">
                <p type="main">
                  <s id="s.000161">Sit grave A, quod descendat super plano ABC
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                  inclinato, & tempus quo descendit ab A in
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                  B sit aequale tempori, quo descendit a B in C,
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                  & a C in D.</s>
                </p>
                <p type="main">
                  <s id="s.000162">Dico quod lineae AB, BC, CD sunt inter se ut
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                  1. 3. 5. &. sic deinceps.</s>
                </p>
                <p type="main">
                  <s id="s.000163">Sit E numerus mensurans tempus, quo A descen­
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                  dit in B, & F quo descendit a B in C, & G
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                  quo descendit a C in D, quae tempora sunt ex
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                  suppositione aequalia, & sit H quadratum ip­
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                  sius E, & I quadratum EF, & K quadra­
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                  tum totius EFG.</s>
                </p>
                <p type="main">
                  <s id="s.000164">Quoniam quadrata HIK sunt ut AB, AC, AD
                    <arrow.to.target n="marg27"/>
                  ,
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                  quae quadrata sunt ut 1. 4. 9. sunt pariter
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                  AB, AC, AD, ut 1. 4. 9. & dividendo AB,
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                  BC, CD, sunt ut 1. 3. 5. & sic deinceps.
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                  </s>
                  <s id="s.000165">Quod probandum erat.</s>
                </p>
                <p type="margin">
                  <s id="s.000166">
                    <margin.target id="marg27"/>
                  Per 7. huius.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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