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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/039.jpg"/>
            <subchap1 n="18" type="proposition">
              <p type="head">
                <s id="s.000247">PROPOSITIO XVIII. PROBL. X.</s>
              </p>
              <subchap2 n="18" type="statement">
                <p type="main">
                  <s id="s.000248">Datis planis declinantibus ortis ab eodem
                    <lb/>
                  puncto, reperire in magis declinante pun­
                    <lb/>
                  ctum quo grave perveniat eo tempore, quo
                    <lb/>
                  pertransit planum minus declinans.
                    <figure id="id.064.01.039.1.jpg" xlink:href="064/01/039/1.jpg" number="19"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="19" type="proof">
                <p type="main">
                  <s id="s.000249">Datum sit planum minus declinans AC, &
                    <lb/>
                  magis AD, terminantia super plano ori­
                    <lb/>
                  zontali BD.</s>
                </p>
                <p type="main">
                  <s id="s.000250">Oportet in AD producta reperire punctum, quo
                    <lb/>
                  perveniat grave eo tempore, quo pertransivit
                    <lb/>
                  planum minus declinans AC.</s>
                </p>
                <p type="main">
                  <s id="s.000251">Fiat ut AD ad AC ita AC ad dictam AD pro­
                    <lb/>
                  ductam in E, quod est punctum quaesitum.</s>
                </p>
                <p type="main">
                  <s id="s.000252">Quoniam ut AE ad AD ita est quadratum AC
                    <lb/>
                  ad quadratum AD
                    <arrow.to.target n="marg52"/>
                  , sed AE ad AD est ut
                    <lb/>
                  quadratum tempo­
                    <lb/>
                  ris AE, ad quadratum temporis AD
                    <arrow.to.target n="marg53"/>
                  , ergo ut quadra­
                    <lb/>
                  tum AC ad quadratum AD, ita quadratum temporis AE ad qua­
                    <lb/>
                  dratum temporis AD
                    <arrow.to.target n="marg54"/>
                  , unde AC ad AD ut
                    <lb/>
                  tempus AE ad tempus AD
                    <arrow.to.target n="marg55"/>
                  , sed AC ad AD
                    <lb/>
                  est ut tempus AC ad tempus AD
                    <arrow.to.target n="marg56"/>
                  , ergo tem­
                    <lb/>
                  pora AE, AC sunt aequalia. </s>
                  <s id="s.000253">Quod, etc.</s>
                </p>
                <p type="margin">
                  <s id="s.000254">
                    <margin.target id="marg52"/>
                  Per 19. sexti.</s>
                </p>
                <p type="margin">
                  <s id="s.000255">
                    <margin.target id="marg53"/>
                  Per cor. 7. huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000256">
                    <margin.target id="marg54"/>
                  Per 11. Quinti.</s>
                </p>
                <p type="margin">
                  <s id="s.000257">
                    <margin.target id="marg55"/>
                  Per 22. sexti.</s>
                </p>
                <p type="margin">
                  <s id="s.000258">
                    <margin.target id="marg56"/>
                  Per 15. huius.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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