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

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          <pb o="32" file="527.01.032" n="32" rhead="1 L*IBER* S*TATICÆ*"/>
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        <div xml:id="echoid-div162" type="section" level="1" n="126">
          <head xml:id="echoid-head135" xml:space="preserve">9 THEOREMA. 17 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s938" xml:space="preserve">Columnâ ſuper duobus in axe punctis quieſcente:
              <lb/>
            </s>
            <s xml:id="echoid-s939" xml:space="preserve">quemadmodum axis ſegmentum inter gravitatis cen-
              <lb/>
            trum punctumq́ue ſiniſtrum, ad ejuſdem ſegmentum in-
              <lb/>
            ter gravitatis centrum punctumq́ue dextrum: </s>
            <s xml:id="echoid-s940" xml:space="preserve">ita co-
              <lb/>
            lumnæ pondus ſuper puncto dextro quieſcens, ad reli-
              <lb/>
            quum ponderis ſuper ſiniſtro quieſcentis.</s>
            <s xml:id="echoid-s941" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s942" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s943" xml:space="preserve">ABCD columna 6 ℔ pendeat, ſecta quemadmodum in 1 pro-
              <lb/>
            poſitione, duobus punctis R, V, ſuper OE, Æ quieſcens.</s>
            <s xml:id="echoid-s944" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s945" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s946" xml:space="preserve">Demonſtrandũ nobis eſt, quemadmodum axis ſegmen-
              <lb/>
            tum T R ad ejuſdem T V: </s>
            <s xml:id="echoid-s947" xml:space="preserve">ita eſſe pondus puncto V quieſcens in Æ, ad re-
              <lb/>
            liquum ponderis puncto R, ſuper OE quieſcentis.</s>
            <s xml:id="echoid-s948" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div163" type="section" level="1" n="127">
          <head xml:id="echoid-head136" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s949" xml:space="preserve">T R duplum eſtad T V extheſi, & </s>
            <s xml:id="echoid-s950" xml:space="preserve">ſuper
              <lb/>
              <figure xlink:label="fig-527.01.032-01" xlink:href="fig-527.01.032-01a" number="50">
                <image file="527.01.032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.032-01"/>
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            Æ 4 ℔ ſuper OE verò 2 ℔ quieſcunt, ex
              <lb/>
            1 conſect. </s>
            <s xml:id="echoid-s951" xml:space="preserve">14 propoſitionis, atqui 4 ℔ ad
              <lb/>
            2 ℔ etiam dupla eſtratio; </s>
            <s xml:id="echoid-s952" xml:space="preserve">quemadmodum
              <lb/>
            T R ad T V: </s>
            <s xml:id="echoid-s953" xml:space="preserve">ita & </s>
            <s xml:id="echoid-s954" xml:space="preserve">pondus quod ſuper pun-
              <lb/>
            cto Æ eſt, ad reliquum ponderis quieſcen-
              <lb/>
            tis ſuper OE.</s>
            <s xml:id="echoid-s955" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s956" xml:space="preserve">Verumenimvero generalis conſectarii
              <lb/>
            neceſſitas demonſtretur; </s>
            <s xml:id="echoid-s957" xml:space="preserve">V R in Z cõtinua-
              <lb/>
            tor, ut R Z æquetur R V, ſumptoq́ue R
              <lb/>
            pro puncto fixo, ex Z pondus
              <lb/>
              <figure xlink:label="fig-527.01.032-02" xlink:href="fig-527.01.032-02a" number="51">
                <image file="527.01.032-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.032-02"/>
              </figure>
            114 ℔ ſuſpendi neceſſe eſt, ut
              <lb/>
            columna ſuo in ſitu cõſervetur,
              <lb/>
            ex 3 propoſit. </s>
            <s xml:id="echoid-s958" xml:space="preserve">quod verò ex V,
              <lb/>
            columnam eodĕ in ſitu, quo Æ,
              <lb/>
            ſervat, parem cum 11 potentiam
              <lb/>
            habere ex 13 propoſitione ne-
              <lb/>
            ceſſe eſt. </s>
            <s xml:id="echoid-s959" xml:space="preserve">In Æ igitur pondus par
              <lb/>
            ipſi 11 quieſcit. </s>
            <s xml:id="echoid-s960" xml:space="preserve">Cõſimiliter R V
              <lb/>
            in Φ continuator, ut V Φ æque-
              <lb/>
            tur V R, ſumptoq́ue V pro pun-
              <lb/>
            cto firmo, de Φ ſuſpendi Δ 2 ℔
              <lb/>
            neceſſe eſt, ut columna eodem in ſitu ſuſtineatur, per 3 exemplum. </s>
            <s xml:id="echoid-s961" xml:space="preserve">quod
              <lb/>
            verò ex R columnam ſive vectem eodem in ſitu ſuſtinet, quo OE, r
              <unsure/>
            antun-
              <lb/>
            dem potentiæ habet, quantum Δ, per 13 propoſit. </s>
            <s xml:id="echoid-s962" xml:space="preserve">pondus igitur in OE quieſ-
              <lb/>
            cens æquatur ponderi Δ. </s>
            <s xml:id="echoid-s963" xml:space="preserve">Quandoquidem autem 11, ex R communi fulci-
              <lb/>
            menti puncto, contra columnam ſitu æquilibre eſt, ratio radii T R eſt ad ra-
              <lb/>
            dium R Z, quæ eſt 11 ad columnam, per 1 propoſitionem. </s>
            <s xml:id="echoid-s964" xml:space="preserve">Cõſimiliter V pro
              <lb/>
            firmo puncto uſurpato, ratio radii T V ad radium V Φ eadem eſt cum ra-
              <lb/>
            z
              <unsure/>
            ione Δ, ad columnam, atque R Z æquatur V Φ Duæ igitur proportiones
              <lb/>
            nobishic ſunt quaternûm terminorum, quorum ſecundi quartique </s>
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