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

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          <pb o="46" file="527.01.046" n="46" rhead="1 L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div218" type="section" level="1" n="158">
          <head xml:id="echoid-head170" xml:space="preserve">C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1432" xml:space="preserve">Hinc facile iſtud deducitur. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">Quò anguli ductariarum linearum unde pon-
              <lb/>
            dera ſuſpenſa ſunt, recto angulo proximiores ſunt: </s>
            <s xml:id="echoid-s1434" xml:space="preserve">eò ponderum por
              <unsure/>
            étias eſſe
              <lb/>
            majores. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Et contra, quo longius indidem, id eſt ab angulo recto diffident, po-
              <lb/>
            tentias eorundem eò quoque minores eſſe.</s>
            <s xml:id="echoid-s1436" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div219" type="section" level="1" n="159">
          <head xml:id="echoid-head171" xml:space="preserve">16 THEOREMA. 25 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1437" xml:space="preserve">Duæ annuentes lineæ, unde columna dependet,
              <note symbol="*" position="left" xlink:label="note-527.01.046-01" xlink:href="note-527.01.046-01a" xml:space="preserve">Inaæquali-
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              ter diftantes,
                <lb/>
              n
                <unsure/>
              on paral
                <unsure/>
              -
                <lb/>
              le@e
                <unsure/>
              .</note>
            nitùm continuatæ, in columnæ pendula gravitatis dia-
              <lb/>
            metro ſeſe interſecant.</s>
            <s xml:id="echoid-s1438" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div221" type="section" level="1" n="160">
          <head xml:id="echoid-head172" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1439" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">AB columna, ex duabus lineis annuentibus C D, E F, depen-
              <lb/>
            deto, quæ in G & </s>
            <s xml:id="echoid-s1441" xml:space="preserve">H continuatæ, ſeſe inutuò in I ſecant.</s>
            <s xml:id="echoid-s1442" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1443" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">Punctum I in columnæ A B pendulâ gravitatis diame-
              <lb/>
            tro eſſe, demonſtrandum eſt.</s>
            <s xml:id="echoid-s1445" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div222" type="section" level="1" n="161">
          <head xml:id="echoid-head173" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1446" xml:space="preserve">Anguli FEC, IEC, HEC unus idemq́;
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            </s>
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            eſt angulus; </s>
            <s xml:id="echoid-s1448" xml:space="preserve">idem de DCE, ICE, GCE
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            judicum eſto, ut quicunq; </s>
            <s xml:id="echoid-s1449" xml:space="preserve">punctus in rectis
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            HE, GF pro extremo ſumptus fuerit, co-
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            lumna, ex eo datum ſitum ſervet. </s>
            <s xml:id="echoid-s1450" xml:space="preserve">Eſto autern
              <unsure/>
              <lb/>
            I extremus punctus, utriuſque lineæ com-
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            munis, ex illo igitur columna ſitum ſuum
              <lb/>
            retinebit. </s>
            <s xml:id="echoid-s1451" xml:space="preserve">Atqui columnâ ex I dependente,
              <lb/>
            perpendicularis per I columnæ pendula
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            gravitatis diametris fuerit, in qua eſt I.</s>
            <s xml:id="echoid-s1452" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div224" type="section" level="1" n="162">
          <head xml:id="echoid-head174" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1453" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1454" xml:space="preserve">AB columna ex duabus lineis annuentibus CD, EF depen-
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            deto, continuatis in G, H uſque, mutuò ſe in I ſecantibus.</s>
            <s xml:id="echoid-s1455" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1456" xml:space="preserve">Q*VAESITVM* Punctum I in columnæ AB pendulâ gravitatis diame-
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            tro eſſe, demonſtrandum eſt.</s>
            <s xml:id="echoid-s1457" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div225" type="section" level="1" n="163">
          <head xml:id="echoid-head175" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1458" xml:space="preserve">DG, & </s>
            <s xml:id="echoid-s1459" xml:space="preserve">FH tibicines & </s>
            <s xml:id="echoid-s1460" xml:space="preserve">fulcra ſunto, vel
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            rigidæ & </s>
            <s xml:id="echoid-s1461" xml:space="preserve">inflexibiles lineæ, per 2 poſtulat.
              <lb/>
            </s>
            <s xml:id="echoid-s1462" xml:space="preserve">quibus columna ſuffulcitur; </s>
            <s xml:id="echoid-s1463" xml:space="preserve">quarũ potentiæ
              <lb/>
            æquales ſunt potétiis CD. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">DF, ut enim iftę,
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            ita etiam illæ columnam in ſuo ſitu ſuſtinent. </s>
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              <lb/>
            Et quodcun que punctum in illis extremum
              <lb/>
            nobis fuerit, illud columnam in ſuo ſitu ſer-
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            vaverit. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Eſto autem I extremus & </s>
            <s xml:id="echoid-s1467" xml:space="preserve">utriuſque
              <lb/>
            lineæ communis punctus; </s>
            <s xml:id="echoid-s1468" xml:space="preserve">ex iſto igitur co-
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            lumna (Mathematicè intelligas) datum ſi-
              <lb/>
            rum retinet, & </s>
            <s xml:id="echoid-s1469" xml:space="preserve">pendula gravitatis diametrus
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            per I fuerit, & </s>
            <s xml:id="echoid-s1470" xml:space="preserve">in eâ punctum I.</s>
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