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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/036.jpg"/>
            <subchap1 n="15" type="proposition">
              <p type="head">
                <s id="s.000210">PROPOSITIO XV.</s>
              </p>
              <subchap2 n="15" type="statement">
                <p type="main">
                  <s id="s.000211">Si duo gravia descendunt alterum quidem
                    <lb/>
                  perpendiculariter, alterum vero super pla­
                    <lb/>
                  no declinante, perveniunt ad idem pla­
                    <lb/>
                  num Orizontale tali ratione, ut sit eadem
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                  proportio inter diuturnitates eorum, quae
                    <lb/>
                  inter perpendicularem, & declinantem.
                    <figure id="id.064.01.036.1.jpg" xlink:href="064/01/036/1.jpg" number="16"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="16" type="proof">
                <p type="main">
                  <s id="s.000212">Sit linea AB perpendiculariter erecta super
                    <lb/>
                  plano Orizontali BC, & AC planum declinans.</s>
                </p>
                <p type="main">
                  <s id="s.000213">Dico quod diuturnitates gravium descendentium
                    <lb/>
                  per AB, & per AC, sunt ut AB ad AC.</s>
                </p>
                <p type="main">
                  <s id="s.000214">Fiat AD tertia proportionalis ad AC, & AB
                    <arrow.to.target n="marg37"/>
                  ,</s>
                </p>
                <p type="margin">
                  <s id="s.000215">
                    <margin.target id="marg37"/>
                  Per 11. Sexti.</s>
                </p>
                <p type="main">
                  <s id="s.000216">Quoniam est ut AD ad AC ita quadratum tem­
                    <lb/>
                  poris AD ad quadratum temporis AC
                    <arrow.to.target n="marg38"/>
                  , &
                    <lb/>
                  tempora AD, & AB sunt aequalia
                    <arrow.to.target n="marg39"/>
                  , & proin­
                    <lb/>
                  de eorum quadrata
                    <arrow.to.target n="marg40"/>
                  , ergo ut AD, ad AC
                    <lb/>
                  ita quadratum temporis AB ad quadratum
                    <lb/>
                  temporis AC, sed ut AD ad AC ita quadra­
                    <lb/>
                  tum AB ad quadratum AC
                    <arrow.to.target n="marg41"/>
                  , ergo ut quadratum temporis AB ad quadratum temporis A
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                  C, ita quadratum AB ad quadratum AC
                    <arrow.to.target n="marg42"/>
                  ,
                    <lb/>
                  sed quia latera sunt inter se ut eorum qua­
                    <lb/>
                  drata
                    <arrow.to.target n="marg43"/>
                  , est ut AB ad AC ita tempus AB ad
                    <lb/>
                  tempus AC. </s>
                  <s id="s.000217">Quod, etc.</s>
                </p>
                <p type="margin">
                  <s id="s.000218">
                    <margin.target id="marg38"/>
                  Per cor. 7. huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000219">
                    <margin.target id="marg39"/>
                  Per 14. huius.</s>
                </p>
                <p type="margin">
                  <s id="s.000220">
                    <margin.target id="marg40"/>
                  Per 2. pron.</s>
                </p>
                <p type="margin">
                  <s id="s.000221">
                    <margin.target id="marg41"/>
                  Per 19. Sexti.</s>
                </p>
                <p type="margin">
                  <s id="s.000222">
                    <margin.target id="marg42"/>
                  Per 11. Quinti.</s>
                </p>
                <p type="margin">
                  <s id="s.000223">
                    <margin.target id="marg43"/>
                  Per 22. Sexti.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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