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

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          <pb o="12" file="527.01.012" n="12" rhead="1 L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div48" type="section" level="1" n="44">
          <head xml:id="echoid-head51" xml:space="preserve">PARS ALTERA
            <lb/>
          DE PROPOSITIONIBVS.</head>
          <head xml:id="echoid-head52" xml:space="preserve">1 THE OREMA. I PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s242" xml:space="preserve">Duarum gravitatũ ſitu æquilibriũ ponderoſior illam ra-
              <lb/>
            tionĕ habet ad leviorĕ, quę lõgioris radii eſt, ad breviorem.</s>
            <s xml:id="echoid-s243" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div49" type="section" level="1" n="45">
          <head xml:id="echoid-head53" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s244" xml:space="preserve">DA*TVM*. </s>
            <s xml:id="echoid-s245" xml:space="preserve">ABCD 6 ℔ columna eſto in ſex partes æquales à
              <lb/>
            planisad baſin AD parallelis partita, ut ſunt EF, GH, IK, LM,
              <lb/>
            NO, axem PQ in R, S, T, V, X ſecantibus: </s>
            <s xml:id="echoid-s246" xml:space="preserve">LMDA gravi-
              <lb/>
            tas eſto ponderoſior, ejusq́ue centrum S, LMCB verò levior
              <lb/>
            & </s>
            <s xml:id="echoid-s247" xml:space="preserve">centrum X, partium iſtarum ſecundũ 7 de-
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              <figure xlink:label="fig-527.01.012-01" xlink:href="fig-527.01.012-01a" number="11">
                <image file="527.01.012-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.012-01"/>
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            finitionem jugum erit SX, T autem columnæ
              <lb/>
            totius centrum, TI anſa, ex qua LMDA
              <lb/>
            & </s>
            <s xml:id="echoid-s248" xml:space="preserve">LMCB ſitu æquilibria dependent, & </s>
            <s xml:id="echoid-s249" xml:space="preserve">
              <lb/>
            TX radius longior, TS autem brevior ex 8
              <lb/>
            definit. </s>
            <s xml:id="echoid-s250" xml:space="preserve">ſententiâ.</s>
            <s xml:id="echoid-s251" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s252" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s253" xml:space="preserve">Demonſtrandum nobis
              <lb/>
            eſt ſic longiorem radium TX eſſe ad brevio-
              <lb/>
            rem TS: </s>
            <s xml:id="echoid-s254" xml:space="preserve">q@emadmodum ponderoſior gra-
              <lb/>
            vitas LMDA eſt ad leviorem LMCB.</s>
            <s xml:id="echoid-s255" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div51" type="section" level="1" n="46">
          <head xml:id="echoid-head54" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s256" xml:space="preserve">LMDA 4 libras pendet, LMCB vero 2, ratio autem longioris radii
              <lb/>
            TX ad breviorem TS eſtut 2 ad 1 ex dato: </s>
            <s xml:id="echoid-s257" xml:space="preserve">Atqui ut 4. </s>
            <s xml:id="echoid-s258" xml:space="preserve">ad 2: </s>
            <s xml:id="echoid-s259" xml:space="preserve">ita 2 ad 1, ut
              <lb/>
            igitur ponderoſius LMDA ad levius LMCB: </s>
            <s xml:id="echoid-s260" xml:space="preserve">ita TX longior radius ad
              <lb/>
            TS breviorem.</s>
            <s xml:id="echoid-s261" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s262" xml:space="preserve">VErumenimvero ne caſu potius quam ſolidâ ſcientiâ ita habere ſe iſta vi-
              <lb/>
            deantur, Mathematicam demonſtrationem ſubjungemus.</s>
            <s xml:id="echoid-s263" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div52" type="section" level="1" n="47">
          <head xml:id="echoid-head55" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s264" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s265" xml:space="preserve">ABCD iterum eſto columna, ſecta plano EF parallelo ad
              <lb/>
            AD, ſecanteaxem GH in puncto contingenti, ut I, ſegmentiq́ue EFDA
              <lb/>
            centrum gravitatis K medium in GI, ſegmentiq́ue EFCB centrum L me-
              <lb/>
            diumin IH, totiusautem ABCD, M medium in GH, MN verò ſegmen-
              <lb/>
            torum EFDA & </s>
            <s xml:id="echoid-s266" xml:space="preserve">EFCB anſa, unde ſitu æquilibria dependent.</s>
            <s xml:id="echoid-s267" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s268" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s269" xml:space="preserve">Demonſtrandum eſt,
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              <figure xlink:label="fig-527.01.012-02" xlink:href="fig-527.01.012-02a" number="12">
                <image file="527.01.012-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.012-02"/>
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            quemadmodum corpus five gravitas (quæ
              <lb/>
            hic propter illorum proportionem, unum
              <lb/>
            idemq́ue ſunt ut enim corpus EFDA ad
              <lb/>
            corpus EFCB: </s>
            <s xml:id="echoid-s270" xml:space="preserve">ita illius gravitas, ad gra-
              <lb/>
            vitatem hujus, columna enim ex poſitu ubiq;
              <lb/>
            </s>
            <s xml:id="echoid-s271" xml:space="preserve">æquabilis gravitatis eſt) EFDA ad EFCB: </s>
            <s xml:id="echoid-s272" xml:space="preserve">
              <lb/>
            ita longiorem radium ML eſſe ad brevio-
              <lb/>
            rem MK.</s>
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