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

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        <div xml:id="echoid-div94" type="section" level="1" n="78">
          <pb o="19" file="527.01.019" n="19" rhead="*DE STATICÆ ELEMENTIS.*"/>
        </div>
        <div xml:id="echoid-div95" type="section" level="1" n="79">
          <head xml:id="echoid-head88" xml:space="preserve">NOTATO.</head>
          <p>
            <s xml:id="echoid-s514" xml:space="preserve">Quemadmodum Arithmeticæ & </s>
            <s xml:id="echoid-s515" xml:space="preserve">Geometricæ propoſitiones diverſas pra-
              <lb/>
            gmatias habent, ita etiam *STATICAE*, de columna enim ſegmentum deſe-
              <lb/>
            cari poſſet, cujus ratio ad totam eſſepoſſet,
              <lb/>
              <figure xlink:label="fig-527.01.019-01" xlink:href="fig-527.01.019-01a" number="26">
                <image file="527.01.019-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.019-01"/>
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            quæ eſt 2 ad 3. </s>
            <s xml:id="echoid-s516" xml:space="preserve">Aut etiam columnâ integrâ
              <lb/>
            manente quævis alia materia contra illam
              <lb/>
            ponderari poſſet, indeq́ue {1/3} auferri, verum
              <lb/>
            Staticè illud ipſum efficere volumus, hoc
              <lb/>
            pacto.</s>
            <s xml:id="echoid-s517" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="80">
          <head xml:id="echoid-head89" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s518" xml:space="preserve">A centro G, F verſus 5 puncta (5 ſcilicet
              <lb/>
            pro toto datorum terminorum 2 & </s>
            <s xml:id="echoid-s519" xml:space="preserve">3) ut
              <lb/>
            H, I, K, L, M æqualiter ſpacio inter ſe diſſi-
              <lb/>
            ta, ſignanda erunt, & </s>
            <s xml:id="echoid-s520" xml:space="preserve">in ſecundo puncto I (à ſecundo puncto inquam, quia
              <lb/>
            2 datorum numerorum alter eſt) columna è pendulâ gravitatis diametro I N
              <lb/>
            ſuſpendenda, necnon ex quinto puncto M aliquod pondus demittendum,
              <lb/>
            ut O tantæ gravitatis, ut omnia in ſitus æquilibritate pendeant. </s>
            <s xml:id="echoid-s521" xml:space="preserve">Dico pondus
              <lb/>
            O eâ eſſe in rationead columnæ pondus, in qua eſt 2 ad 3, aut O æquare {2/3} co-
              <lb/>
            lumnæ.</s>
            <s xml:id="echoid-s522" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div98" type="section" level="1" n="81">
          <head xml:id="echoid-head90" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s523" xml:space="preserve">G gravitatis centrum eſt columnæ A B C D, M P vero pendula gravi-
              <lb/>
            tatis diametros ipſius O, propterea ut radius I G ad radium I M: </s>
            <s xml:id="echoid-s524" xml:space="preserve">ita O ad co-
              <lb/>
            lumnam per primam propoſitionem. </s>
            <s xml:id="echoid-s525" xml:space="preserve">Atqui I G rationem habet ad I M,
              <lb/>
            quam 2 ad 3, ergo & </s>
            <s xml:id="echoid-s526" xml:space="preserve">O ad columnam habet eandem rationem 2 ad 3, quod
              <lb/>
            nobis fuit demonſtrandum.</s>
            <s xml:id="echoid-s527" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div99" type="section" level="1" n="82">
          <head xml:id="echoid-head91" xml:space="preserve">NOTATO.</head>
          <p>
            <s xml:id="echoid-s528" xml:space="preserve">Etiam incommenſurabilium terminorum exempla in medium
              <note symbol="*" position="right" xlink:label="note-527.01.019-01" xlink:href="note-527.01.019-01a" xml:space="preserve"> aſymmetre-
                <lb/>
              rum.</note>
            poſſemus, niſi ex antecedentibus manifeſta eſſent, etiam ex iis, quæ de incom-
              <lb/>
            menſurabilibus magnitudinibus alibi præcepimus.</s>
            <s xml:id="echoid-s529" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div101" type="section" level="1" n="83">
          <head xml:id="echoid-head92" xml:space="preserve">2 THEOREMA. 6 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s530" xml:space="preserve">Pendulâ columnâ per gravitatis centrum à plano ad
              <lb/>
            baſin parallelo ſectâ, firmitudinis autem puncto ſupra
              <lb/>
            gravitatis centrum fixo: </s>
            <s xml:id="echoid-s531" xml:space="preserve">Axis horizonti eſt parallelus.</s>
            <s xml:id="echoid-s532" xml:space="preserve"/>
          </p>
          <figure number="27">
            <image file="527.01.019-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.019-02"/>
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          <p>
            <s xml:id="echoid-s533" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s534" xml:space="preserve">* A B C D columna eſto
              <lb/>
            per gravitatis centrum à plano F G ad
              <lb/>
            baſin A D parallelo ſecta, H autem
              <lb/>
            firmitudinis punctum in pendulâ gra-
              <lb/>
            vitatis diametro I G fixum, ſupra gra-
              <lb/>
            vitatis centrum E. </s>
            <s xml:id="echoid-s535" xml:space="preserve">& </s>
            <s xml:id="echoid-s536" xml:space="preserve">K L axis, M N
              <lb/>
            denique horizon.</s>
            <s xml:id="echoid-s537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s538" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s539" xml:space="preserve">* K L axem ad ho-
              <lb/>
            rizontem M N parallelum eſſe demon-
              <lb/>
            ſtrari oportet.</s>
            <s xml:id="echoid-s540" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div102" type="section" level="1" n="84">
          <head xml:id="echoid-head93" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s541" xml:space="preserve">Axis K L, ſi fieri quidem poteſt ab horizonte M N inæqualiter </s>
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