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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/044.jpg"/>
            <subchap1 n="23" type="proposition">
              <p type="head">
                <s id="s.000299">PROPOSITIO XXIII.</s>
              </p>
              <subchap2 n="23" type="statement">
                <p type="main">
                  <s id="s.000300">Duo gravia descendentia super planis diversa
                    <lb/>
                  ratione declinantibus, perveniunt ad idem
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                  planum orizontale ea ratione, ut sit eadem
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                  proportio inter diuturnitates, quae inter
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                  dicta plana si ab eodem puncto ad idem
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                  planum orizontale producta sint.
                    <figure id="id.064.01.044.1.jpg" xlink:href="064/01/044/1.jpg" number="24"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="24" type="proof">
                <p type="main">
                  <s id="s.000301">Datis planis AB, AC declinantibus, ductis
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                  ab eodem puncto A ad planum orizontale BC.
                    <lb/>
                  </s>
                  <s id="s.000302">Dico quod diuturnitates gravium descendentium
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                  per AB, AC sint ut AB ad AC.</s>
                </p>
                <p type="main">
                  <s id="s.000303">Fiat ut AC ad AB ita AB ad AD, ita ut grave
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                  perveniat in D eodem tempore quo pervenit in B
                    <arrow.to.target n="marg68"/>
                  .</s>
                </p>
                <p type="margin">
                  <s id="s.000304">
                    <margin.target id="marg68"/>
                  Per 17. huius.</s>
                </p>
                <p type="main">
                  <s id="s.000305">Quoniam est ut AD ad AC, ita quadratum tem­
                    <lb/>
                  poris AD ad quadratum temporis AC
                    <arrow.to.target n="marg69"/>
                  , &
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                  tempora AD, AB sunt aequalia
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                  , & proinde
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                  eorum quadrata; ergo ut AD ad AC ita qua­
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                  dratum temporis AB, ad quadratum tempo­
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                  ris AC
                    <arrow.to.target n="marg71"/>
                  , sed ut AD ad AC, ita quadra­
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                  tum AB ad quadratum AC
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                  , ergo ut quadra­
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                  tum temporis AB ad quadratum temporis AC,
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                  ita quadratum AB ad quadratum AC, ergo
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                  ut tempus AB ad tempus AC, ita AB ad AC
                    <arrow.to.target n="marg73"/>
                  . </s>
                  <s id="s.000306">Quod fuit probandum.</s>
                </p>
                <p type="margin">
                  <s id="s.000307">
                    <margin.target id="marg69"/>
                  Per Cor. 7. huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000308">
                    <margin.target id="marg70"/>
                  Per const.</s>
                </p>
                <p type="margin">
                  <s id="s.000309">
                    <margin.target id="marg71"/>
                  Per 2. pronun.</s>
                </p>
                <p type="margin">
                  <s id="s.000310">
                    <margin.target id="marg72"/>
                  Per 10. sexti.</s>
                </p>
                <p type="margin">
                  <s id="s.000311">
                    <margin.target id="marg73"/>
                  Per 22. sexti.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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