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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="064/01/022.jpg"/>
            <subchap1 n="3" type="proposition">
              <p type="head">
                <s id="s.000090">PROPOSITIO TERTIA</s>
              </p>
              <subchap2 n="3" type="statement">
                <p type="main">
                  <s id="s.000091">Lineae descensus gravium, dum naturali motu
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                  perpendiculariter feruntur, sunt in dupli­
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                  cata ratione diuturnitatum.
                    <figure id="id.064.01.022.1.jpg" xlink:href="064/01/022/1.jpg" number="4"/>
                  </s>
                </p>
              </subchap2>
              <subchap2 n="4" type="proof">
                <p type="main">
                  <s id="s.000092">Sint LN, KM linea descensus gravium L, K,
                    <lb/>
                  & sint PO ipsorum diuturnitates.</s>
                </p>
                <p type="main">
                  <s id="s.000093">Dico LN, KM esse in duplicata ratione ipsarum P, O.</s>
                </p>
                <p type="main">
                  <s id="s.000094">Sint pendula AH, AI, dependentia a puncto A, &
                    <lb/>
                  eleventur ad libellam ipsius A usque ad E, B,
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                  quae in elevatione producant arcus HB, IE, &
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                  sint talis longitudinis, ut ducta ACF, secet ar­
                    <lb/>
                  cus BC, & EF, tam parvae curvitatis ut pro
                    <lb/>
                  rectis habeantur, puta portionis minimae, &
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                  proinde aequales quo ad sensum rectis KM, LN,
                    <arrow.to.target n="marg8"/>
                    <lb/>
                  & fiat V tertia proportionalis ad O, P,
                    <arrow.to.target n="marg9"/>
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s id="s.000095">
                    <margin.target id="marg8"/>
                  Per 3 pet.</s>
                </p>
                <p type="margin">
                  <s id="s.000096">
                    <margin.target id="marg9"/>
                  Per 11 sexti.</s>
                </p>
                <p type="main">
                  <s id="s.000097">Quoniam O, P sunt diuturnitates KM, LN ex
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                  constr., sunt itidem diuturnitates BC, EF,
                    <arrow.to.target n="marg10"/>
                  &
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                  quia diuturnitates vibrorum AH, AI sunt
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                  etiam ut O ad P
                    <arrow.to.target n="marg11"/>
                  AH AI sunt ut O, ad V
                    <arrow.to.target n="marg12"/>
                    <lb/>
                  & pariter BC, & EF sunt ut O ad V
                    <arrow.to.target n="marg13"/>
                  Ergo
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                  KM, LN eis aequales per constr. sunt etiam ut
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                  O ad V, & proinde in duplicata ratione O, P,
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                  temporum seu diuturnitatum earumdem. </s>
                  <s id="s.000098">Quod, etc.</s>
                </p>
                <p type="margin">
                  <s id="s.000099">
                    <margin.target id="marg10"/>
                  Per 5 pet.</s>
                </p>
                <p type="margin">
                  <s id="s.000100">
                    <margin.target id="marg11"/>
                  Per p. pet.</s>
                </p>
                <p type="margin">
                  <s id="s.000101">
                    <margin.target id="marg12"/>
                  Per 3 supp.</s>
                </p>
                <p type="margin">
                  <s id="s.000102">
                    <margin.target id="marg13"/>
                  Per p. pet.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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