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

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        <div xml:id="echoid-div237" type="section" level="1" n="170">
          <pb o="49" file="527.01.049" n="49" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div239" type="section" level="1" n="171">
          <head xml:id="echoid-head183" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1561" xml:space="preserve">F firmum nobis eſto punctum, Eautem
              <lb/>
              <figure xlink:label="fig-527.01.049-01" xlink:href="fig-527.01.049-01a" number="83">
                <image file="527.01.049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.049-01"/>
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            mobile. </s>
            <s xml:id="echoid-s1562" xml:space="preserve">Itaque (per 20 propoſit.) </s>
            <s xml:id="echoid-s1563" xml:space="preserve">Quem-
              <lb/>
            admodum LE ad EN: </s>
            <s xml:id="echoid-s1564" xml:space="preserve">ita G ad I. </s>
            <s xml:id="echoid-s1565" xml:space="preserve">E
              <lb/>
            nunc firmum nobis eſt punctum, F mobile.
              <lb/>
            </s>
            <s xml:id="echoid-s1566" xml:space="preserve">itaque (per dictam 20 propoſit.) </s>
            <s xml:id="echoid-s1567" xml:space="preserve">ut MF
              <lb/>
            ad FO: </s>
            <s xml:id="echoid-s1568" xml:space="preserve">ita H ad K.</s>
            <s xml:id="echoid-s1569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1570" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1571" xml:space="preserve">Igitur, ſi columna, & </s>
            <s xml:id="echoid-s1572" xml:space="preserve">
              <lb/>
            duo pondera obliquè extollentia ſitu æqui-
              <lb/>
            libria ſunt, erit quemadmodũ linea obliquè
              <lb/>
            extollens ad lineam rectè extollentem: </s>
            <s xml:id="echoid-s1573" xml:space="preserve">ita
              <lb/>
            quodque pondus obliquum ad ſuum pon-
              <lb/>
            dus rectum, quod nobis demonſtrandum
              <lb/>
            erat.</s>
            <s xml:id="echoid-s1574" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div241" type="section" level="1" n="172">
          <head xml:id="echoid-head184" xml:space="preserve">C*ONSECTARIUM*.</head>
          <figure number="84">
            <image file="527.01.049-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.049-02"/>
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          <p>
            <s xml:id="echoid-s1575" xml:space="preserve">Cognitâ columnâ è duabus lineis non
              <lb/>
            parallelis ſuſpensâ, ut hîc juxtà vides, quan-
              <lb/>
            tum ponderis de quaque lineâ pendeat,
              <lb/>
            quantumve potentiæ quæque linea obti-
              <lb/>
            neat, innotel
              <unsure/>
            cere poſſe manifeſtum eſt.</s>
            <s xml:id="echoid-s1576" xml:space="preserve"/>
          </p>
          <figure number="85">
            <image file="527.01.049-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.049-03"/>
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        <div xml:id="echoid-div242" type="section" level="1" n="173">
          <head xml:id="echoid-head185" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s1577" xml:space="preserve">Pleriſque omnibus in propoſitionibus hujus libri, columnam nos loco exempli uſurpa-
              <lb/>
            viſſe, tanquam figuram ad propoſiti no ſtri declar ationem accommodatißimam, in axe
              <lb/>
            prœterea fixum & </s>
            <s xml:id="echoid-s1578" xml:space="preserve">mobile punctum effinxiſſe: </s>
            <s xml:id="echoid-s1579" xml:space="preserve">hac novißimâ tandem propoſitione ge-
              <lb/>
            neralem illarum veritatem, omnium{q́ue} figurarum, qualiacunque corpora, & </s>
            <s xml:id="echoid-s1580" xml:space="preserve">quocung
              <lb/>
            loco puncta, fixum & </s>
            <s xml:id="echoid-s1581" xml:space="preserve">mobile fuerint, communem eſſe oſtendere.</s>
            <s xml:id="echoid-s1582" xml:space="preserve"/>
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          <head xml:id="echoid-head186" xml:space="preserve">19 THEOREMA. 28 PROPOSITIO.</head>
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            <s xml:id="echoid-s1583" xml:space="preserve">Quæcunque proportiones ſunt columnæ ad pondera
              <lb/>
            inde ſuſpenſa, ponderumq́; </s>
            <s xml:id="echoid-s1584" xml:space="preserve">lineas: </s>
            <s xml:id="echoid-s1585" xml:space="preserve">eaſdem cujuſvis etiam
              <lb/>
            corporis eſſe ad ſua pondera, conſimiliter inde pendentia,
              <lb/>
            ponderumq́ue lineas.</s>
            <s xml:id="echoid-s1586" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1587" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1588" xml:space="preserve">Exempli loco proportionem 20 propofitionis repetamus, iſto
              <lb/>
            pacto. </s>
            <s xml:id="echoid-s1589" xml:space="preserve">Columnæ AB, axis eſto CD, gravitatis centrum E, punctum fixum </s>
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