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

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        <div xml:id="echoid-div201" type="section" level="1" n="145">
          <pb o="42" file="527.01.042" n="42" rhead="1 L*IBER* S*TATICÆ*"/>
          <p>
            <s xml:id="echoid-s1280" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">Si igitur axis columnæ puncta habeat firmum & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">mo-
              <lb/>
            bile, &</s>
            <s xml:id="echoid-s1283" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1284" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div202" type="section" level="1" n="146">
          <head xml:id="echoid-head158" xml:space="preserve">NOTATO</head>
          <p>
            <s xml:id="echoid-s1285" xml:space="preserve">Si linearum alteralatus columnæ non ſecet, eò uſque continuandum eſſe
              <lb/>
            latus donec ſecetur, ut in proximè antecedentium figurarum noviſſimâ vi-
              <lb/>
            dere eſt.</s>
            <s xml:id="echoid-s1286" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div203" type="section" level="1" n="147">
          <head xml:id="echoid-head159" xml:space="preserve">13 THEOREMA. 21 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1287" xml:space="preserve">Si axis columnæ puncta habeat firmum, & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">mobile, ex
              <lb/>
            quo dependentia pondera, unum rectè, alterum obliquè
              <lb/>
            demittens in dato ſitu columnam conſervant: </s>
            <s xml:id="echoid-s1289" xml:space="preserve">erit quem-
              <lb/>
            admodum linea rectè demittens ad lineam obliquè de-
              <lb/>
            mitten tem: </s>
            <s xml:id="echoid-s1290" xml:space="preserve">ita pondus rectum ad pondus obliquum.</s>
            <s xml:id="echoid-s1291" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1292" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1293" xml:space="preserve">AB eſto columna, cujus axis ſit CD, in eoq́ue E punctum fir-
              <lb/>
            mum, F mobile, cui G pondus rectè demittens appenſum columnam in da-
              <lb/>
            to ſitu ſervat: </s>
            <s xml:id="echoid-s1294" xml:space="preserve">indidem quoque dependĕs pondus H obliquè demittens (coër-
              <lb/>
            cito velamoto G) in ſitu ſuo eandem ſervat: </s>
            <s xml:id="echoid-s1295" xml:space="preserve">linea rectè demittens ſecat la-
              <lb/>
            tus illius in I, obliquè autem demittens in K.</s>
            <s xml:id="echoid-s1296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1297" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">Demonſtrandum nobis eſt, quemadmodum I F rectè de-
              <lb/>
            mittens, ad FK obliquè demittentem: </s>
            <s xml:id="echoid-s1299" xml:space="preserve">ita eſſe pondus G rectè demittens, ad
              <lb/>
            pondus H demittens obliquè.</s>
            <s xml:id="echoid-s1300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1301" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1302" xml:space="preserve">Punctum L ſignator, ut EL æquetur EF, hinc pun-
              <lb/>
            cto L accommodetur pondus M rectè attollens, columnamq́ue in ſitu ſer-
              <lb/>
            vans, cujus recta attollens L N: </s>
            <s xml:id="echoid-s1303" xml:space="preserve">itidem pondus O obliquè attollens, colu-
              <lb/>
            mnamq́ue in ſitu ſervans, cujus linea obliquè attollens LP parallela ſit ad F K.</s>
            <s xml:id="echoid-s1304" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div204" type="section" level="1" n="148">
          <head xml:id="echoid-head160" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1305" xml:space="preserve">Quemadmodum N L ad L P: </s>
            <s xml:id="echoid-s1306" xml:space="preserve">ita M
              <lb/>
              <figure xlink:label="fig-527.01.042-01" xlink:href="fig-527.01.042-01a" number="73">
                <image file="527.01.042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.042-01"/>
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            ad O per 20 propoſitionem, atqui po-
              <lb/>
            tentia G in columnam æquatur poten-
              <lb/>
            tiæ M, & </s>
            <s xml:id="echoid-s1307" xml:space="preserve">potentia H potentiæ O per
              <lb/>
            13 propoſitionĕ, & </s>
            <s xml:id="echoid-s1308" xml:space="preserve">recta I F rectæ L N,
              <lb/>
            atque F K æqualis eſt LP. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">Quemad-
              <lb/>
            modum igitur IF rectè demittens ad
              <lb/>
            F K obliquè demittentem : </s>
            <s xml:id="echoid-s1310" xml:space="preserve">ita pondus
              <lb/>
            G rectè demittens, ad H demittens
              <lb/>
            obliquè. </s>
            <s xml:id="echoid-s1311" xml:space="preserve">eadem demonſtratio erit alio-
              <lb/>
            rum omnium, ut videre eſt in ſubje-
              <lb/>
            ctis exemplis.</s>
            <s xml:id="echoid-s1312" xml:space="preserve"/>
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