Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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        <div xml:id="echoid-div225" type="section" level="1" n="163">
          <pb o="47" file="527.01.047" n="47" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div227" type="section" level="1" n="164">
          <head xml:id="echoid-head176" xml:space="preserve">3 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1472" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1473" xml:space="preserve">AB columna, lineis CD, & </s>
            <s xml:id="echoid-s1474" xml:space="preserve">EF, obliquè illâ demittente, hae
              <lb/>
            extollente in dato ſitu conſervetur, iſtæ autem continuatæ in I ſe interſecent.</s>
            <s xml:id="echoid-s1475" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1476" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">Punctum I in columnæ AB pendulâ gravitatis diame-
              <lb/>
            tro eſſe, nobis demonſtrandum eſt.</s>
            <s xml:id="echoid-s1478" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div228" type="section" level="1" n="165">
          <head xml:id="echoid-head177" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1479" xml:space="preserve">Primum GC tibicen, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">inflexibilis li-
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            nea, deinde potétia ducendi deorſum, quæ
              <lb/>
            erat in D, eſto deorium, contingenti inter
              <lb/>
            C & </s>
            <s xml:id="echoid-s1481" xml:space="preserve">G puncto, quoquo loco ſumatur. </s>
            <s xml:id="echoid-s1482" xml:space="preserve">Co-
              <lb/>
            lumna itaq; </s>
            <s xml:id="echoid-s1483" xml:space="preserve">AB quovis puncto inter GC
              <lb/>
            & </s>
            <s xml:id="echoid-s1484" xml:space="preserve">EH medio, quod pro extremo ſumitur,
              <lb/>
            datum ſitum ſervabit. </s>
            <s xml:id="echoid-s1485" xml:space="preserve">I autem extremus,
              <lb/>
            & </s>
            <s xml:id="echoid-s1486" xml:space="preserve">communis utriuſque lineę terminus fue-
              <lb/>
            rit; </s>
            <s xml:id="echoid-s1487" xml:space="preserve">columna itaq; </s>
            <s xml:id="echoid-s1488" xml:space="preserve">inde ſuſpenſa datũ ſitum
              <lb/>
            retinebit, & </s>
            <s xml:id="echoid-s1489" xml:space="preserve">propterea ipſius pendula gra-
              <lb/>
            vitatis linea per I erit: </s>
            <s xml:id="echoid-s1490" xml:space="preserve">& </s>
            <s xml:id="echoid-s1491" xml:space="preserve">I in ipsâ.</s>
            <s xml:id="echoid-s1492" xml:space="preserve"/>
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        <div xml:id="echoid-div230" type="section" level="1" n="166">
          <head xml:id="echoid-head178" xml:space="preserve">4 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1493" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1494" xml:space="preserve">Columnam AB in fitu ſuo ſervent, hinc quidem CD obli-
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            què demittens, illinc EF obliquè extollens, quæ continuatæ interſecant ſe
              <lb/>
            in I. </s>
            <s xml:id="echoid-s1495" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1496" xml:space="preserve">I in columnæ pendulâ gravitatis diametro eſſe nobis
              <lb/>
            demonſtrandum eſt.</s>
            <s xml:id="echoid-s1497" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div231" type="section" level="1" n="167">
          <head xml:id="echoid-head179" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1498" xml:space="preserve">HE pro tibicine nobis eſto, & </s>
            <s xml:id="echoid-s1499" xml:space="preserve">linea inflexibili, potentia quoque ſurſum
              <lb/>
            ducendi, quæ fuerat in E, eſto ſurſum contingenti inter C & </s>
            <s xml:id="echoid-s1500" xml:space="preserve">G puncto,
              <lb/>
            quoquo loco ſumatur. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">Columna AB quo-
              <lb/>
            vis puncto inter CG, & </s>
            <s xml:id="echoid-s1502" xml:space="preserve">EH medio, quod
              <lb/>
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            pro extremo ſumitur, datum fitũ retinebit.
              <lb/>
            </s>
            <s xml:id="echoid-s1503" xml:space="preserve">I autem extremus, & </s>
            <s xml:id="echoid-s1504" xml:space="preserve">utriuſque lineæ com-
              <lb/>
            munis terminus fuerit, in quo datum ſitum
              <lb/>
            columna retinebit, atqui in eo quieſcĕte co-
              <lb/>
            lumnâ, pĕdula gravitatis diametrus eſt per I,
              <lb/>
            & </s>
            <s xml:id="echoid-s1505" xml:space="preserve">I in ipsâ diametro. </s>
            <s xml:id="echoid-s1506" xml:space="preserve">C*ONCLUSIO*. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">Dua-
              <lb/>
            bus igitur lineis annuĕtibus, unde columna
              <lb/>
            dependet, in infinitum continuatis, in co-
              <lb/>
            lumnæ pendulâ gravitatis diametro ſeſe in-
              <lb/>
            terſecant, quod nobis demóſtrandum erat.</s>
            <s xml:id="echoid-s1508" xml:space="preserve"/>
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        <div xml:id="echoid-div233" type="section" level="1" n="168">
          <head xml:id="echoid-head180" xml:space="preserve">17 THEOREMA. 26 PROPOSITIO.</head>
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            <s xml:id="echoid-s1509" xml:space="preserve">Si duarum linearum unde columna dependet, alt
              <unsure/>
            era
              <lb/>
            horizontieſt perpendicularis, erit & </s>
            <s xml:id="echoid-s1510" xml:space="preserve">reliqua: </s>
            <s xml:id="echoid-s1511" xml:space="preserve">ſin </s>
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