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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/025.jpg"/>
            <subchap1 n="6" type="proposition">
              <p type="head">
                <s id="s.000123">PROPOSITIO VI.</s>
              </p>
              <subchap2 n="6" type="statement">
                <p type="main">
                  <s id="s.000124">Gravia naturali motu descendunt semper velo­
                    <lb/>
                  cius ea ratione, ut temporibus aequalibus de­
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                  scendant per spatia semper maiora, iuxta
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                  proportionem quam habent impares nu­
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                  meri ab unitate inter se.
                    <figure id="id.064.01.025.1.jpg" xlink:href="064/01/025/1.jpg" number="7"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="7" type="proof">
                <p type="main">
                  <s id="s.000125">Sit grave A quod descendat per lineam ABC,
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                  & tempus quo descendit ab A in B sit aequale
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                  tempori, quo descendit a B in C, & a C in D.</s>
                </p>
                <p type="main">
                  <s id="s.000126">Dico quod lineae AB, BC, CD sunt inter se ut 1.
                    <lb/>
                  3.5.& sic deinceps.</s>
                </p>
                <p type="main">
                  <s id="s.000127">Sit G linea mensurans tempus, quo A descendit
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                  in B, & H, quo de­
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                  scendit a B in C, & I, quo descendit a C in D, quae tempora sunt ex suppositione
                    <lb/>
                  aequalia, & sit K latus quadrati ipsius G, & L
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                  quadrati GH, & N quadrati totius GHI.</s>
                </p>
                <p type="main">
                  <s id="s.000128">Quoniam quadrata K, L, N sunt ut AB, AC, A
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                  D
                    <arrow.to.target n="marg20"/>
                  , quae quadrata sunt ut 1, 4, 9, sunt itidem
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                  AB, AC, AD, ut 1. 4. 9. & dividendo AB,
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                  BC, CD, ut 1. 3. 5. & sic deinceps. </s>
                  <s id="s.000129">Quod
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                  probandum fuit.</s>
                </p>
                <p type="margin">
                  <s id="s.000130">
                    <margin.target id="marg20"/>
                  Per 3. huius.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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